Dropout Rate Meta-analysis of Substance Abuse Studies
Sara Lappan, PhD1
Code: Andrew W Brown, PhD2
Peter Hendricks, PhD3
02 June 2019
1 Information
This is the full data analysis code for the Dropout Meta-analysis.
Note: Confirming individual pieces of this code is challenging if running interactively. If the dropout.Rmd file is opened and knit in its entirety there have been no problems. When the code is run chunk by chunk, on the other hand, the call to knit_child throws an error because it is apparently not designed to be run interactively. The environment successfully stores the information needed for the child document to run, so this error can be circumvented by expanding the for loops for each variable and running the child code manually if need be.
2 Data import and cleaning
Data were imported from Excel, extraneous columns were removed, and incidental empty rows and columns removed.
2.1 Cleaning and checking study-level variables
After data were imported and the data frame formatted, several important checks were conducted.
First, each study should have a unique ID within a paper. If non-unique arms were detected, they were flagged for evaluation.
Next, the proportion of participants dropping out is checked. The data were extracted as a proportion, so any value less than 0 or greater than 1 is impossible.
Because meta-analysis functions are dependent on n being an integer, the number who dropped out was calculated, but also checked for whether there were more estimated to have dropped out than were in the study arm total, which is impossible.
Papers returned by a warning indicated that some studies showed that less than 1 person dropped out (note that a fraction of a person could be estimated to have dropped out at this point because the number of dropouts was rounded to integers later). Papers with such low dropouts were checked and confirmed.
2.2 Data inclusion/exclusion rules
Nine data inclusion/exclusion cases were identified.
| Case | Dropout | Moderator | Decision/Notes |
|---|---|---|---|
| 1 | Averaged over included and excluded arms | All cases | Exclude Study Dropout ‘tainted’ by excluded groups |
| 2 | Reported separately per arm | None | Include as arm nested in study in hierarchical analysis |
| 3 | Pooled only over included arms | None | Include as single value for study (remove replicate arms) |
| 4 | Reported separately per arm | Reported separately per arm | Include as arm nested in study in hierarchical analysis |
| 5 | Pooled only over included arms | Reported separately per arm; non-poolable (categorical) moderator | Exclude Study Cannot pool across separate categories (e.g., average over male/female) Including it in both categories separately would bias toward the null and violate the independence assumption |
| 6 | Pooled only over included arms | Reported separately per arm; Poolable (continuous) moderator | Include after pooling moderator Assumes the average ‘effect’ of two moderator values would converge on the pooled dropout(e.g., a single pooled dropout rate for multiple moderator values) Unclear if this induces regression dilution/attenuation bias |
| 7 | Reported separately per arm | Pooled across arms | Include as arm nested in study in hierarchical analysis Analogous to school being treated with an intervention and measuring the outcome on multiple classrooms. Not all studies have this structure, and in some cases very few are pooled Unclear if this inflates variance (e.g., multiple dropout rates for a single pooled moderator value) |
| 8 | Pooled only over included arms | Pooled only over included arms | Include single value for study |
| 9 | Any | Multiple values for the same comorbid diagnosis or substance class | Exclude Arm Example: a study reports proportion of participants using two different opioids or with two mental comorbid diagnoses separately. There is no way to pool the values because the proportions may refer to the same or different individuals. |
The following processing accounts for these various cases. The plo.rma.mv function also accounts for some of these pooling rules dependent on whether the moderator is continuous or categorical through the pool.cleaning function.
2.3 Processing averaged dropout rates
Some studies reported dropout rates averaged across multiple study arms. In some analyses, this can still be used. However, if a study involved study arms that were excluded from our analysis and pooled the dropout rate, then the study has to be excluded. There is no way to get the dropout rate only for arms we are interested in. This is most easily detected if an average dropout rate is reported but only one study arm is included. (See Case 1 above).
All studies with average dropout rates and multiple study arms were manually checked to be sure that all study arms in the original paper were eligible for inclusion for this analysis. Only Stevens & Hollis (1989) was removed for this reason.
2.4 Cleaning and formatting study-arm-level substance and comorbid diagnosis data
Data from the substances and comorbid diagnoses worksheets were merged with the study-level data by first confirming that the Author (year) lists matched perfectly.
Each study arm in the merged set should have at least one substance, given that all studies were about substance abuse. On the other hand, not all studies will have reported comorbid diagnoses, so those arms were removed from the merged comorbid diagnosis data set. Typically, if one study arm reported a comorbid diagnosis the others should, too; if they did not, they were flagged for follow-up.
Occasionally, studies will report more than one substance in the same category within a study arm, such as multiple opiates. Unfortunately, the values are not able to be included easily into models because of dependence of observations (i.e., the same subjects would be counted twice for the same substance; see Case 9 above). The overlap can also be because of a data entry error, so they were flagged and confirmed.
Similarly, multiple of the same category of comorbid diagnoses may be listed, so they were also confirmed.
2.5 Final counts of studies included
The PRISMA diagram has information regarding inclusion/exclusion from the point of search. Below is inclusion/exclusion summaries starting from the final data file.
- Studies in imported file: 153
- Study arms in imported file: 341
- Studies in processed data set: 151
- Study arms in processed data set: 338
- Dropout rates in processed data set: 299
- Total subjects in processed data set: 26243
NOTE:
- The difference between study arms and dropout rates is because some studies include only pooled dropout rates over multiple study arms.
- The number of included studies and dropout rates varies from analysis to analysis dependent on whether the moderator was reported in a given study. The number of included studies and dropout rates are reported for each analysis.
3 Estimating overall dropout rates
Several estimates were made of the overall dropout rate, from the simplistic to the appropriately complex. These multiple models were fit to demonstrate the variability from one method to the next, but also to demonstrate that the dropout rates among methods are not unreasonably different from each other.
3.1 Manual fixed-effects meta-analysis of proportions
The overall dropout rate was manually calculated as a fixed-effects, individual-value meta-analysis, not taking into consideration that study arms are related within study for studies that reported dropout rates for each arm independently. This was accomplished by simply looking at the proportion of dropouts summed across all studies divided by the total number of participants across all studies. This method makes three unreasonable assumptions: there is no random effect of study; that study arms are not clustered within study; and (taken together) that each individual across studies essentially is a completely random and independent sample from the population.
| Dropout | Lower 95% CI | Upper 95% CI |
|---|---|---|
| 33.68 | 33.1 | 34.25 |
3.2 Manual, inverse variance, fixed-effects, logit meta-analysis
The overall dropout rate was then calculated by first estimating the logit proportion and variance, followed by manual calculation of the mean effect size (proportion dropout) and its variance. This approach makes the untested assumption that there is no heterogeneity among studies, and that study arms are independent (i.e., ignores any ICC among study arms within studies).
| Dropout | Lower 95% CI | Upper 95% CI |
|---|---|---|
| 35.96 | 35.32 | 36.6 |
3.3 Overall dropout by fixed-effects meta-analysis using rma.mv
Next, the overall dropout rate was calculated using the rma.mv function of the metafor package. The same assumptions are made as in the above manual calculation.
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components: none
Test for Heterogeneity:
Q(df = 298) = 3268.2932, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.5771 0.0142 -40.5492 <.0001 -0.6050 -0.5492 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 | Dropout | Lower 95% CI | Upper 95% CI |
|---|---|---|
| 35.96 | 35.32 | 36.6 |
3.4 Overall random-effects
Building onto the fixed-effects models, a random-effects model was fit using rma.mv that continues to assume each dropout rate is independent. This also applies to studies in which the dropout rate was pooled.
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2 0.9296 0.9641 299 no arm
Test for Heterogeneity:
Q(df = 298) = 3268.2932, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.7730 0.0605 -12.7715 <.0001 -0.8917 -0.6544 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI |
|---|---|---|---|---|
| 31.58 | 29.08 | 34.2 | 6.5 | 75.41 |
3.5 Overall dropout by multi-level, random-effects meta-analysis
Finally, the overall dropout rate was estimated using a multilevel random-effects meta-analysis using a logit transformed proportion. This was accomplished through the custom plo.rma.mv wrapper function for the rma.mv function of metafor (see functions.r file). This model also included the hierarchical nature of the data, with study arms being nested with studies. Note that in cases where dropout rates were pooled, the study was reported as a single entry and thus no within-study correlation could be calculated.
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7853 0.8862 151 no ID
sigma^2.2 0.1287 0.3587 299 no ID/arm
Test for Heterogeneity:
Q(df = 298) = 3268.2932, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.8273 0.0797 -10.3767 <.0001 -0.9836 -0.6711 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8592
I^2.1 80.5
I^2.2 13.2| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|
| Overall | 30.42 | 27.22 | 33.83 | 6.25 | 74.14 |
Figure: Overall, random-effects, hierarchical, logit meta-analysis. Each horizontal line represents the point estimate and 95% CI of each study, back-transformed from logit scale. Symbols demark the point estimate, and are not proportional to study or study-arm weight. The dashed line represents the mean proportion dropout across studies. The polygon represents the average proportion dropout and its 95% CI, with a 95% prediction interval.
3.6 Conclusion about overall dropout rate
The manual and random-effects analyses are not identical, as would be expected. Although there are differences among them, they are not large differences, giving some degree of face validity. The model with the highest theoretical support is the hierarchical random-effects model, and is considered the primary analysis for the overall dropout rate.
Importantly, there remains significant residual heterogeneity, as is expected given the wide variety of studies included. To investigate sources of this heterogeneity, a series of moderator meta-regressions (for continuous predictors) or sub-group meta-analyses (for categorical preditors) are described below.
The interpretation of the dropout rates and 95% CI are limited in the random-effects models, as indicated by the 95% Prediction Interval (PI). The sizeable heterogeneity indicates that although the average across all studies is expected to be around 30%, the expectation for any given study is much less predictable, with a 95% range of study dropout rates from about 6% to 74%.
4 Testing study-level moderators
To evaluate whether characteristics of the studies could help explain the heterogeneity scene in the overall models, moderator sub-group meta-analyses and meta-regressions were calculated. This section describes study-level moderators, which are moderator variables that were constant at the study level, meaning they did not vary from study-arm to study-arm.
4.1 Categorical study-level moderators
Sub-group meta-analyses were conducted for moderator variables that were categorical. These models used the same inverse-variance, hierarchical approach as the overall model, but included categorical, study-level variables for sub-group analyses. For each moderator analysis, profile plots may be created to evaluate the two variance components (within and between study), and the intraclass correlation (ICC) is also reported. In cases where the ICC is 0 or 1, the profile plots for one of the variance components is maxed out at 0.
4.1.1 Degree
Multivariate Meta-Analysis Model (k = 158; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7983 0.8935 82 no ID
sigma^2.2 0.0836 0.2891 158 no ID/arm
Test for Residual Heterogeneity:
QE(df = 153) = 1678.8840, p-val < .0001
Test of Moderators (coefficient(s) 2:5):
QM(df = 4) = 5.4466, p-val = 0.2445
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.6739 0.1545 -4.3612 <.0001 -0.9768 -0.3711
factor(get(varname))3 -0.6078 0.4341 -1.4002 0.1614 -1.4586 0.2430
factor(get(varname))4 -0.3862 0.2227 -1.7346 0.0828 -0.8227 0.0502
factor(get(varname))5 -0.1658 0.3011 -0.5507 0.5818 -0.7559 0.4243
factor(get(varname))6 -1.1610 0.8430 -1.3773 0.1684 -2.8132 0.4912
intrcpt ***
factor(get(varname))3
factor(get(varname))4 .
factor(get(varname))5
factor(get(varname))6
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9053
I^2.1 84.4
I^2.2 8.8| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Mixed | 33.76 | 27.35 | 40.83 | 7.32 | 76.70 | 71 | 36 |
| Bachelors | 21.73 | 11.14 | 38.07 | 3.60 | 67.33 | 8 | 6 |
| Masters | 25.73 | 19.64 | 32.93 | 5.05 | 69.28 | 55 | 27 |
| Doctorate | 30.16 | 20.43 | 42.08 | 6.00 | 74.51 | 22 | 14 |
| Certificate | 13.77 | 3.05 | 44.75 | 1.35 | 65.02 | 2 | 2 |
Figure: Subgroup meta-analysis for ‘Degree’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.2 Substance Being Treated
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7030 0.8385 151 no ID
sigma^2.2 0.1319 0.3631 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 290) = 2915.3922, p-val < .0001
Test of Moderators (coefficient(s) 2:9):
QM(df = 8) = 21.9463, p-val = 0.0050
Model Results:
estimate se zval pval ci.lb
intrcpt -1.0428 0.2032 -5.1326 <.0001 -1.4411
factor(get(varname))2 -0.0292 0.2342 -0.1246 0.9009 -0.4882
factor(get(varname))3 0.9894 0.2988 3.3114 0.0009 0.4038
factor(get(varname))4 0.6060 0.3584 1.6909 0.0909 -0.0964
factor(get(varname))5 1.1832 0.9203 1.2857 0.1986 -0.6206
factor(get(varname))7 0.4198 0.4560 0.9205 0.3573 -0.4740
factor(get(varname))9 0.2214 0.2667 0.8300 0.4066 -0.3014
factor(get(varname))11 -0.0481 0.7159 -0.0672 0.9464 -1.4511
factor(get(varname))12 0.9144 0.9134 1.0010 0.3168 -0.8760
ci.ub
intrcpt -0.6446 ***
factor(get(varname))2 0.4299
factor(get(varname))3 1.5750 ***
factor(get(varname))4 1.3085 .
factor(get(varname))5 2.9870
factor(get(varname))7 1.3135
factor(get(varname))9 0.7442
factor(get(varname))11 1.3550
factor(get(varname))12 2.7047
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8421
I^2.1 78.4
I^2.2 14.7| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Alcohol | 26.06 | 19.14 | 34.42 | 5.33 | 68.82 | 47 | 21 |
| Tobacco | 25.50 | 21.41 | 30.08 | 5.33 | 67.55 | 117 | 65 |
| Cocaine | 48.66 | 38.16 | 59.29 | 13.07 | 85.67 | 42 | 18 |
| Opioid | 39.25 | 26.59 | 53.54 | 8.96 | 80.93 | 24 | 10 |
| Methamphetamine | 53.50 | 16.54 | 86.98 | 8.55 | 93.41 | 2 | 1 |
| Cannabis | 34.91 | 19.42 | 54.42 | 7.01 | 79.22 | 11 | 5 |
| Polysubstance | 30.55 | 23.86 | 38.16 | 6.64 | 73.13 | 50 | 29 |
| Heroin | 25.14 | 8.04 | 56.33 | 3.45 | 75.93 | 4 | 2 |
| Major stimulant | 46.79 | 13.31 | 83.44 | 6.73 | 91.47 | 2 | 1 |
Figure: Subgroup meta-analysis for ‘Substance Being Treated’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.3 Pregnant Participants?
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7720 0.8786 151 no ID
sigma^2.2 0.1283 0.3582 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 297) = 3255.2996, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 3.9073, p-val = 0.0481
Model Results:
estimate se zval pval ci.lb
intrcpt -0.8164 0.0793 -10.2911 <.0001 -0.9719
factor(get(varname))1 -2.3617 1.1948 -1.9767 0.0481 -4.7034
ci.ub
intrcpt -0.6609 ***
factor(get(varname))1 -0.0200 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8575
I^2.1 80.3
I^2.2 13.3| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| No or not indicated | 30.65 | 27.45 | 34.05 | 6.40 | 74.07 | 298 | 150 |
| Yes | 4.00 | 0.40 | 30.12 | 0.21 | 45.22 | 1 | 1 |
Figure: Subgroup meta-analysis for ‘Pregnant Participants?’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.4 Manualized Treatment?
Multivariate Meta-Analysis Model (k = 296; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7823 0.8845 148 no ID
sigma^2.2 0.1274 0.3569 296 no ID/arm
Test for Residual Heterogeneity:
QE(df = 294) = 3183.7959, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.9614, p-val = 0.3268
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.7605 0.1068 -7.1195 <.0001 -0.9699 -0.5512
factor(get(varname))1 -0.1323 0.1349 -0.9805 0.3268 -0.3966 0.1321
intrcpt ***
factor(get(varname))1
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8600
I^2.1 80.5
I^2.2 13.1| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| No or not indicated | 31.85 | 27.49 | 36.56 | 6.65 | 75.41 | 130 | 74 |
| Yes | 29.05 | 25.07 | 33.38 | 5.88 | 72.86 | 166 | 81 |
Figure: Subgroup meta-analysis for ‘Manualized Treatment?’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.5 Setting of Trial
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7793 0.8828 151 no ID
sigma^2.2 0.1297 0.3602 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 293) = 3162.7535, p-val < .0001
Test of Moderators (coefficient(s) 2:6):
QM(df = 5) = 6.4229, p-val = 0.2672
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.5409 0.5562 -0.9725 0.3308 -1.6309 0.5492
factor(get(varname))2 -0.6790 0.6133 -1.1071 0.2682 -1.8811 0.5231
factor(get(varname))3 -0.2000 0.5637 -0.3548 0.7227 -1.3048 0.9048
factor(get(varname))4 -0.5162 0.6207 -0.8317 0.4056 -1.7327 0.7003
factor(get(varname))5 -0.9476 0.7227 -1.3111 0.1898 -2.3641 0.4690
factor(get(varname))6 -0.0596 0.7178 -0.0830 0.9339 -1.4664 1.3472
intrcpt
factor(get(varname))2
factor(get(varname))3
factor(get(varname))4
factor(get(varname))5
factor(get(varname))6
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8573
I^2.1 80.2
I^2.2 13.3| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Institution | 36.80 | 16.37 | 63.40 | 6.27 | 83.52 | 4 | 3 |
| Outpatient (hospital/medical school) | 22.80 | 15.10 | 32.89 | 4.09 | 67.18 | 28 | 15 |
| Outpatient (public) | 32.28 | 28.48 | 36.33 | 6.80 | 75.70 | 227 | 113 |
| University affiliated clinic | 25.79 | 16.84 | 37.35 | 4.73 | 70.85 | 26 | 12 |
| Inpatient | 18.42 | 8.37 | 35.81 | 2.75 | 64.28 | 8 | 5 |
| Mixed | 35.42 | 18.40 | 57.17 | 6.48 | 81.29 | 6 | 4 |
Figure: Subgroup meta-analysis for ‘Setting of Trial’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.6 Pharmacotherapy Category
Multivariate Meta-Analysis Model (k = 291; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.8060 0.8978 143 no ID
sigma^2.2 0.1278 0.3574 291 no ID/arm
Test for Residual Heterogeneity:
QE(df = 287) = 3041.1501, p-val < .0001
Test of Moderators (coefficient(s) 2:4):
QM(df = 3) = 3.0625, p-val = 0.3821
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.8630 0.1117 -7.7272 <.0001 -1.0819 -0.6441
factor(get(varname))1 0.2375 0.1950 1.2180 0.2232 -0.1447 0.6197
factor(get(varname))2 0.1840 0.2030 0.9063 0.3648 -0.2139 0.5820
factor(get(varname))3 -0.0493 0.1749 -0.2818 0.7781 -0.3920 0.2935
intrcpt ***
factor(get(varname))1
factor(get(varname))2
factor(get(varname))3
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8632
I^2.1 80.7
I^2.2 12.8| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| No | 29.67 | 25.31 | 34.43 | 5.90 | 73.95 | 136 | 79 |
| Placebo | 34.85 | 28.06 | 42.33 | 7.27 | 78.49 | 33 | 26 |
| Not agonist | 33.65 | 26.63 | 41.47 | 6.90 | 77.63 | 41 | 24 |
| Agonist | 28.65 | 23.44 | 34.51 | 5.60 | 73.13 | 81 | 43 |
Figure: Subgroup meta-analysis for ‘Pharmacotherapy Category’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.7 Treatment Approach
Multivariate Meta-Analysis Model (k = 290; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7947 0.8915 142 no ID
sigma^2.2 0.1305 0.3613 290 no ID/arm
Test for Residual Heterogeneity:
QE(df = 284) = 2969.2258, p-val < .0001
Test of Moderators (coefficient(s) 2:6):
QM(df = 5) = 5.5873, p-val = 0.3485
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.9202 0.1033 -8.9049 <.0001 -1.1227 -0.7176
factor(get(varname))2 -0.0390 0.2053 -0.1901 0.8492 -0.4415 0.3634
factor(get(varname))3 0.2028 0.1115 1.8188 0.0689 -0.0157 0.4212
factor(get(varname))4 0.0210 0.8425 0.0249 0.9802 -1.6303 1.6722
factor(get(varname))5 0.4404 0.3529 1.2480 0.2120 -0.2512 1.1321
factor(get(varname))6 0.0220 0.1793 0.1224 0.9026 -0.3295 0.3734
intrcpt ***
factor(get(varname))2
factor(get(varname))3 .
factor(get(varname))4
factor(get(varname))5
factor(get(varname))6
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8589
I^2.1 80.3
I^2.2 13.2| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Cognitive and/or behavioral | 28.49 | 24.55 | 32.79 | 5.65 | 72.63 | 121 | 72 |
| Motivational | 27.70 | 20.83 | 35.82 | 5.31 | 72.38 | 17 | 16 |
| Non-specific | 32.80 | 28.55 | 37.35 | 6.83 | 76.47 | 114 | 74 |
| Psychodynamic | 28.92 | 7.28 | 67.84 | 3.22 | 83.25 | 1 | 1 |
| 12-step | 38.23 | 23.68 | 55.26 | 7.67 | 82.17 | 4 | 3 |
| Integrative | 28.94 | 22.53 | 36.33 | 5.66 | 73.44 | 33 | 21 |
Figure: Subgroup meta-analysis for ‘Treatment Approach’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.8 Limited Treatment Time?
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7935 0.8908 151 no ID
sigma^2.2 0.1253 0.3540 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 297) = 3209.6266, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.2725, p-val = 0.2593
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.4625 0.3333 -1.3876 0.1653 -1.1159 0.1908
factor(get(varname))1 -0.3776 0.3347 -1.1280 0.2593 -1.0337 0.2785
intrcpt
factor(get(varname))1
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8636
I^2.1 81.0
I^2.2 12.8| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| No or not indicated | 38.64 | 24.68 | 54.76 | 7.93 | 82.15 | 10 | 6 |
| Yes | 30.15 | 26.93 | 33.58 | 6.15 | 73.99 | 289 | 147 |
Figure: Subgroup meta-analysis for ‘Limited Treatment Time?’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.9 Training for Fidelity?
Multivariate Meta-Analysis Model (k = 298; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7917 0.8898 150 no ID
sigma^2.2 0.1285 0.3585 298 no ID/arm
Test for Residual Heterogeneity:
QE(df = 296) = 3232.4573, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.1424, p-val = 0.7059
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.8495 0.1092 -7.7822 <.0001 -1.0634 -0.6355
factor(get(varname))1 0.0578 0.1532 0.3774 0.7059 -0.2424 0.3580
intrcpt ***
factor(get(varname))1
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8603
I^2.1 80.6
I^2.2 13.1| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| No or not indicated | 29.95 | 25.67 | 34.63 | 6.06 | 73.94 | 155 | 78 |
| Yes | 31.18 | 26.65 | 36.11 | 6.39 | 75.05 | 143 | 75 |
Figure: Subgroup meta-analysis for ‘Training for Fidelity?’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.10 Treatment Format
Multivariate Meta-Analysis Model (k = 297; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7540 0.8683 149 no ID
sigma^2.2 0.1264 0.3556 297 no ID/arm
Test for Residual Heterogeneity:
QE(df = 292) = 3164.1785, p-val < .0001
Test of Moderators (coefficient(s) 2:5):
QM(df = 4) = 10.9702, p-val = 0.0269
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.6998 0.1371 -5.1030 <.0001 -0.9686 -0.4310
factor(get(varname))2 -0.2875 0.1573 -1.8279 0.0676 -0.5958 0.0208
factor(get(varname))3 0.2514 0.2142 1.1737 0.2405 -0.1684 0.6713
factor(get(varname))4 -1.2926 1.0434 -1.2389 0.2154 -3.3375 0.7524
factor(get(varname))5 -0.1815 0.8872 -0.2046 0.8379 -1.9205 1.5574
intrcpt ***
factor(get(varname))2 .
factor(get(varname))3
factor(get(varname))4
factor(get(varname))5
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8564
I^2.1 80.1
I^2.2 13.4| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Group | 33.18 | 27.52 | 39.39 | 7.19 | 76.11 | 74 | 41 |
| Individual | 27.14 | 23.50 | 31.12 | 5.54 | 70.30 | 171 | 87 |
| Mixed | 38.97 | 31.36 | 47.17 | 8.97 | 80.55 | 50 | 28 |
| Not specified | 12.00 | 1.76 | 50.87 | 0.88 | 67.80 | 1 | 1 |
| Couple therapy | 29.29 | 6.91 | 69.80 | 3.23 | 83.70 | 1 | 1 |
Figure: Subgroup meta-analysis for ‘Treatment Format’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.11 Efficacy Study?
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7874 0.8874 151 no ID
sigma^2.2 0.1288 0.3589 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 297) = 3250.0512, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.6515, p-val = 0.4196
Model Results:
estimate se zval pval ci.lb
intrcpt -0.8503 0.0847 -10.0377 <.0001 -1.0163
factor(get(varname))2 0.2042 0.2530 0.8071 0.4196 -0.2916
ci.ub
intrcpt -0.6843 ***
factor(get(varname))2 0.7000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8594
I^2.1 80.5
I^2.2 13.2| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Efficacy | 29.94 | 26.57 | 33.53 | 6.10 | 73.75 | 277 | 134 |
| Effectiveness | 34.39 | 24.73 | 45.54 | 7.05 | 78.37 | 22 | 17 |
Figure: Subgroup meta-analysis for ‘Efficacy Study?’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.12 Codification of Dependence
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7147 0.8454 151 no ID
sigma^2.2 0.1309 0.3618 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 297) = 3110.3733, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 11.6791, p-val = 0.0006
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.5344 0.1144 -4.6697 <.0001 -0.7586 -0.3101
factor(get(varname))2 -0.5272 0.1543 -3.4175 0.0006 -0.8296 -0.2248
intrcpt ***
factor(get(varname))2 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8452
I^2.1 78.8
I^2.2 14.4| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| DSM | 36.95 | 31.89 | 42.31 | 8.70 | 78.28 | 139 | 68 |
| Other | 25.70 | 22.02 | 29.76 | 5.34 | 67.96 | 160 | 83 |
Figure: Subgroup meta-analysis for ‘Codification of Dependence’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.13 Treatment Seeking?
Multivariate Meta-Analysis Model (k = 298; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7668 0.8757 150 no ID
sigma^2.2 0.1308 0.3617 298 no ID/arm
Test for Residual Heterogeneity:
QE(df = 295) = 3205.7958, p-val < .0001
Test of Moderators (coefficient(s) 2:3):
QM(df = 2) = 4.6733, p-val = 0.0967
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.8387 0.2267 -3.6998 0.0002 -1.2831 -0.3944
factor(get(varname))1 0.0411 0.2244 0.1830 0.8548 -0.3988 0.4809
factor(get(varname))2 -1.2158 0.6199 -1.9614 0.0498 -2.4308 -0.0009
intrcpt ***
factor(get(varname))1
factor(get(varname))2 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8542
I^2.1 80.0
I^2.2 13.6| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| No or not indicated | 30.18 | 21.70 | 40.27 | 6.02 | 74.47 | 20 | 8 |
| Yes | 31.05 | 27.76 | 34.55 | 6.53 | 74.38 | 272 | 140 |
| Mixed | 11.36 | 3.97 | 28.42 | 1.44 | 52.99 | 6 | 3 |
Figure: Subgroup meta-analysis for ‘Treatment Seeking?’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.1.14 Country Classification
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7893 0.8884 151 no ID
sigma^2.2 0.1292 0.3594 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 297) = 3263.5004, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.5191, p-val = 0.4712
Model Results:
estimate se zval pval ci.lb
intrcpt -0.8398 0.0817 -10.2763 <.0001 -1.0000
factor(get(varname))2 0.2810 0.3901 0.7205 0.4712 -0.4835
ci.ub
intrcpt -0.6796 ***
factor(get(varname))2 1.0455
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8593
I^2.1 80.6
I^2.2 13.2| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Developed | 30.16 | 26.89 | 33.63 | 6.15 | 73.99 | 289 | 144 |
| Developing | 36.38 | 21.31 | 54.70 | 7.04 | 81.20 | 10 | 7 |
Figure: Subgroup meta-analysis for ‘Country Classification’. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Intervals are not included.
4.2 Continuous study-level moderators
Continuous study-level moderators were evaluated using meta-regressions, again based on the inverse-variance, hierarchical, random-effects approach described above. Profile plots were also fit as described in the ‘Categorical’ section, and meta-regression plots were created.
4.2.1 Age (mean years)
Multivariate Meta-Analysis Model (k = 294; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7510 0.8666 146 no ID
sigma^2.2 0.1315 0.3626 294 no ID/arm
Test for Residual Heterogeneity:
QE(df = 292) = 3187.8891, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 2.8457, p-val = 0.0916
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.1228 0.4321 -0.2841 0.7763 -0.9697 0.7242
get(varname) -0.0185 0.0110 -1.6869 0.0916 -0.0400 0.0030 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8510
I^2.1 79.5
I^2.2 13.9| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 20.5972 | 37.66 | 28.42 | 47.89 | 8.37 | 79.97 |
| 1st Qu. | 34.4000 | 31.87 | 28.07 | 35.93 | 6.85 | 74.85 |
| Median | 39.0000 | 30.06 | 26.88 | 33.43 | 6.34 | 73.17 |
| Mean | 38.5664 | 30.22 | 27.04 | 33.61 | 6.39 | 73.32 |
| 3rd Qu. | 43.0000 | 28.52 | 24.98 | 32.35 | 5.90 | 71.74 |
| Max. | 57.5000 | 23.38 | 16.52 | 31.99 | 4.40 | 66.92 |
Figure: Meta-regression for ‘Age (mean years)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.2 Sex (proportion male)
Multivariate Meta-Analysis Model (k = 289; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7991 0.8939 145 no ID
sigma^2.2 0.1349 0.3674 289 no ID/arm
Test for Residual Heterogeneity:
QE(df = 287) = 3115.8747, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.1944, p-val = 0.6593
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.9104 0.2066 -4.4071 <.0001 -1.3153 -0.5055 ***
get(varname) 0.1418 0.3215 0.4409 0.6593 -0.4884 0.7719
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8555
I^2.1 80.2
I^2.2 13.5| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 28.69 | 21.16 | 37.62 | 5.48 | 73.63 |
| 1st Qu. | 0.4800 | 30.10 | 26.56 | 33.91 | 6.04 | 74.27 |
| Median | 0.6000 | 30.46 | 27.17 | 33.97 | 6.14 | 74.57 |
| Mean | 0.5926 | 30.44 | 27.15 | 33.94 | 6.14 | 74.55 |
| 3rd Qu. | 0.7400 | 30.88 | 27.05 | 35.00 | 6.24 | 74.99 |
| Max. | 1.0000 | 31.68 | 25.48 | 38.60 | 6.37 | 75.95 |
Figure: Meta-regression for ‘Sex (proportion male)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.3 Education (mean years)
Multivariate Meta-Analysis Model (k = 70; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.6571 0.8106 34 no ID
sigma^2.2 0.1054 0.3247 70 no ID/arm
Test for Residual Heterogeneity:
QE(df = 68) = 758.0816, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 2.0166, p-val = 0.1556
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.9800 1.1484 0.8533 0.3935 -1.2709 3.2309
get(varname) -0.1291 0.0909 -1.4201 0.1556 -0.3072 0.0491
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8618
I^2.1 79.0
I^2.2 12.7| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 8.9100 | 45.76 | 29.31 | 63.19 | 11.68 | 84.33 |
| 1st Qu. | 11.5000 | 37.66 | 29.82 | 46.20 | 9.52 | 77.61 |
| Median | 12.3500 | 35.12 | 28.57 | 42.28 | 8.69 | 75.48 |
| Mean | 12.5524 | 34.52 | 28.07 | 41.60 | 8.49 | 74.98 |
| 3rd Qu. | 13.8000 | 30.98 | 23.54 | 39.56 | 7.22 | 72.14 |
| Max. | 16.0000 | 25.26 | 14.51 | 40.22 | 5.07 | 68.13 |
Figure: Meta-regression for ‘Education (mean years)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.4 White (proportion)
Multivariate Meta-Analysis Model (k = 225; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.8026 0.8959 112 no ID
sigma^2.2 0.1100 0.3316 225 no ID/arm
Test for Residual Heterogeneity:
QE(df = 223) = 2350.2549, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 3.5181, p-val = 0.0607
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.4847 0.1932 -2.5086 0.0121 -0.8634 -0.1060 *
get(varname) -0.5464 0.2913 -1.8757 0.0607 -1.1174 0.0246 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8795
I^2.1 82.4
I^2.2 11.3| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 38.11 | 29.66 | 47.35 | 8.36 | 80.62 |
| 1st Qu. | 0.3800 | 33.35 | 28.75 | 38.29 | 7.06 | 76.72 |
| Median | 0.6400 | 30.27 | 26.52 | 34.30 | 6.20 | 74.02 |
| Mean | 0.5924 | 30.82 | 27.09 | 34.83 | 6.36 | 74.51 |
| 3rd Qu. | 0.8600 | 27.80 | 23.22 | 32.88 | 5.51 | 71.77 |
| Max. | 1.0000 | 26.29 | 20.90 | 32.49 | 5.08 | 70.37 |
Figure: Meta-regression for ‘White (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.5 Hispanic/Latino (proportion)
Multivariate Meta-Analysis Model (k = 130; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.8793 0.9377 69 no ID
sigma^2.2 0.1468 0.3832 130 no ID/arm
Test for Residual Heterogeneity:
QE(df = 128) = 1654.8930, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 3.5824, p-val = 0.0584
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.6818 0.1414 -4.8203 <.0001 -0.9590 -0.4046 ***
get(varname) -1.0953 0.5787 -1.8927 0.0584 -2.2295 0.0389 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8569
I^2.1 81.2
I^2.2 13.6| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 33.59 | 27.71 | 40.02 | 6.38 | 78.97 |
| 1st Qu. | 0.0000 | 33.59 | 27.71 | 40.02 | 6.38 | 78.97 |
| Median | 0.0445 | 32.51 | 27.14 | 38.37 | 6.11 | 78.10 |
| Mean | 0.1118 | 30.91 | 25.97 | 36.33 | 5.71 | 76.78 |
| 3rd Qu. | 0.1538 | 29.94 | 25.03 | 35.35 | 5.46 | 75.96 |
| Max. | 1.0000 | 14.47 | 5.69 | 32.15 | 1.77 | 61.29 |
Figure: Meta-regression for ‘Hispanic/Latino (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.6 African American (proportion)
Multivariate Meta-Analysis Model (k = 142; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.6886 0.8298 74 no ID
sigma^2.2 0.1507 0.3882 142 no ID/arm
Test for Residual Heterogeneity:
QE(df = 140) = 1454.5424, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 12.5011, p-val = 0.0004
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.2199 0.1593 -7.6556 <.0001 -1.5322 -0.9076 ***
get(varname) 1.3149 0.3719 3.5357 0.0004 0.5860 2.0438 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8204
I^2.1 76.5
I^2.2 16.7| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 22.80 | 17.77 | 28.75 | 4.55 | 64.63 |
| 1st Qu. | 0.0700 | 24.46 | 19.70 | 29.93 | 5.00 | 66.57 |
| Median | 0.2776 | 29.84 | 25.56 | 34.51 | 6.52 | 72.18 |
| Mean | 0.3222 | 31.08 | 26.72 | 35.81 | 6.89 | 73.34 |
| 3rd Qu. | 0.5222 | 36.98 | 31.12 | 43.24 | 8.72 | 78.27 |
| Max. | 1.0000 | 52.37 | 38.98 | 65.44 | 14.42 | 87.77 |
Figure: Meta-regression for ‘African American (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.7 Other Race/Ethnicity (proportion)
Multivariate Meta-Analysis Model (k = 142; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7856 0.8863 74 no ID
sigma^2.2 0.1464 0.3826 142 no ID/arm
Test for Residual Heterogeneity:
QE(df = 140) = 1603.6324, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 7.0827, p-val = 0.0078
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.6745 0.1278 -5.2792 <.0001 -0.9249 -0.4241 ***
get(varname) -1.3494 0.5070 -2.6613 0.0078 -2.3432 -0.3556 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8429
I^2.1 79.3
I^2.2 14.8| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 33.75 | 28.40 | 39.55 | 7.02 | 77.45 |
| 1st Qu. | 0.0000 | 33.75 | 28.40 | 39.55 | 7.02 | 77.45 |
| Median | 0.0400 | 32.55 | 27.61 | 37.91 | 6.69 | 76.46 |
| Mean | 0.1226 | 30.15 | 25.66 | 35.07 | 6.04 | 74.37 |
| 3rd Qu. | 0.0848 | 31.24 | 26.61 | 36.27 | 6.33 | 75.34 |
| Max. | 1.0000 | 11.67 | 5.06 | 24.70 | 1.59 | 51.88 |
Figure: Meta-regression for ‘Other Race/Ethnicity (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.8 Adjusted Mean Annual Income ($)
Multivariate Meta-Analysis Model (k = 34; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.5481 0.7403 16 no ID
sigma^2.2 0.3726 0.6104 34 no ID/arm
Test for Residual Heterogeneity:
QE(df = 32) = 180.4242, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 4.2994, p-val = 0.0381
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.1779 0.3247 -0.5480 0.5837 -0.8142 0.4584
get(varname) -0.0000 0.0000 -2.0735 0.0381 -0.0000 -0.0000 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.5953
I^2.1 52.6
I^2.2 35.8| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 6727.000 | 42.41 | 29.65 | 56.27 | 9.38 | 83.96 |
| 1st Qu. | 9725.625 | 41.02 | 29.08 | 54.12 | 8.98 | 83.07 |
| Median | 15684.000 | 38.30 | 27.71 | 50.14 | 8.18 | 81.23 |
| Mean | 25638.691 | 33.93 | 24.59 | 44.71 | 6.91 | 78.04 |
| 3rd Qu. | 26670.250 | 33.49 | 24.21 | 44.25 | 6.78 | 77.71 |
| Max. | 121000.000 | 7.70 | 1.37 | 33.36 | 0.62 | 52.85 |
Figure: Meta-regression for ‘Adjusted Mean Annual Income ($)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.9 Not Married (proportion)
Multivariate Meta-Analysis Model (k = 155; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7403 0.8604 80 no ID
sigma^2.2 0.1280 0.3577 155 no ID/arm
Test for Residual Heterogeneity:
QE(df = 153) = 1565.3776, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.5757, p-val = 0.4480
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.9743 0.3442 -2.8309 0.0046 -1.6488 -0.2997 **
get(varname) 0.3732 0.4919 0.7587 0.4480 -0.5909 1.3374
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8526
I^2.1 79.9
I^2.2 13.8| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 27.40 | 16.13 | 42.56 | 5.11 | 72.56 |
| 1st Qu. | 0.5550 | 31.71 | 26.87 | 36.98 | 6.86 | 74.54 |
| Median | 0.6850 | 32.77 | 28.34 | 37.53 | 7.20 | 75.39 |
| Mean | 0.6758 | 32.69 | 28.28 | 37.44 | 7.17 | 75.33 |
| 3rd Qu. | 0.8225 | 33.91 | 28.40 | 39.90 | 7.50 | 76.44 |
| Max. | 1.0000 | 35.41 | 27.19 | 44.59 | 7.82 | 77.99 |
Figure: Meta-regression for ‘Not Married (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.10 Unemployed (proportion)
Multivariate Meta-Analysis Model (k = 141; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.8965 0.9468 71 no ID
sigma^2.2 0.1617 0.4022 141 no ID/arm
Test for Residual Heterogeneity:
QE(df = 139) = 1589.5370, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.3419, p-val = 0.5588
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.7961 0.2837 -2.8058 0.0050 -1.3522 -0.2400 **
get(varname) 0.2873 0.4914 0.5847 0.5588 -0.6758 1.2504
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8472
I^2.1 80.2
I^2.2 14.5| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 31.09 | 20.55 | 44.03 | 5.28 | 78.51 |
| 1st Qu. | 0.4100 | 33.66 | 28.05 | 39.79 | 6.23 | 79.50 |
| Median | 0.5300 | 34.44 | 29.20 | 40.08 | 6.45 | 80.01 |
| Mean | 0.5476 | 34.55 | 29.28 | 40.24 | 6.48 | 80.09 |
| 3rd Qu. | 0.7388 | 35.81 | 28.81 | 43.46 | 6.75 | 81.12 |
| Max. | 0.9630 | 37.30 | 26.70 | 49.27 | 6.95 | 82.57 |
Figure: Meta-regression for ‘Unemployed (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.11 Not Unemployed (proportion)
Multivariate Meta-Analysis Model (k = 128; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7073 0.8410 61 no ID
sigma^2.2 0.1785 0.4224 128 no ID/arm
Test for Residual Heterogeneity:
QE(df = 126) = 1242.2804, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.1010, p-val = 0.2940
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.4076 0.2689 -1.5160 0.1295 -0.9347 0.1194
get(varname) -0.5058 0.4820 -1.0493 0.2940 -1.4506 0.4390
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.7985
I^2.1 74.8
I^2.2 18.9| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0370 | 39.50 | 28.45 | 51.74 | 8.81 | 81.51 |
| 1st Qu. | 0.2770 | 36.64 | 29.67 | 44.22 | 8.17 | 78.98 |
| Median | 0.5000 | 34.06 | 28.98 | 39.54 | 7.45 | 76.84 |
| Mean | 0.4700 | 34.40 | 29.26 | 39.94 | 7.55 | 77.11 |
| 3rd Qu. | 0.6555 | 32.32 | 26.55 | 38.68 | 6.88 | 75.52 |
| Max. | 1.0000 | 28.63 | 19.12 | 40.51 | 5.56 | 73.22 |
Figure: Meta-regression for ‘Not Unemployed (proportion)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.12 Experience (years)
Multivariate Meta-Analysis Model (k = 36; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 1.0802 1.0393 21 no ID
sigma^2.2 0.0513 0.2265 36 no ID/arm
Test for Residual Heterogeneity:
QE(df = 34) = 329.8837, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 2.6664, p-val = 0.1025
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.2013 0.4271 -2.8129 0.0049 -2.0383 -0.3643 **
get(varname) 0.0833 0.0510 1.6329 0.1025 -0.0167 0.1833
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9547
I^2.1 90.3
I^2.2 4.3| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 23.12 | 11.52 | 40.99 | 3.08 | 73.99 |
| 1st Qu. | 3.3000 | 28.37 | 17.91 | 41.82 | 4.33 | 77.59 |
| Median | 6.9500 | 34.93 | 24.98 | 46.38 | 5.95 | 82.00 |
| Mean | 6.7611 | 34.57 | 24.69 | 45.99 | 5.86 | 81.77 |
| 3rd Qu. | 9.9250 | 40.75 | 28.08 | 54.78 | 7.35 | 85.64 |
| Max. | 14.0000 | 49.13 | 29.06 | 69.47 | 9.20 | 90.20 |
Figure: Meta-regression for ‘Experience (years)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.13 Publication Year
Multivariate Meta-Analysis Model (k = 299; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7919 0.8899 151 no ID
sigma^2.2 0.1288 0.3589 299 no ID/arm
Test for Residual Heterogeneity:
QE(df = 297) = 3266.5313, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.0134, p-val = 0.9080
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -3.3093 21.4704 -0.1541 0.8775 -45.3905 38.7718
get(varname) 0.0012 0.0107 0.1156 0.9080 -0.0198 0.0222
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8601
I^2.1 80.6
I^2.2 13.1| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 1980.000 | 29.79 | 19.97 | 41.91 | 5.67 | 74.96 |
| 1st Qu. | 2000.500 | 30.32 | 26.76 | 34.13 | 6.18 | 74.20 |
| Median | 2006.000 | 30.46 | 27.15 | 33.99 | 6.22 | 74.31 |
| Mean | 2004.217 | 30.42 | 27.20 | 33.83 | 6.21 | 74.26 |
| 3rd Qu. | 2009.000 | 30.54 | 26.73 | 34.64 | 6.23 | 74.43 |
| Max. | 2016.000 | 30.73 | 24.85 | 37.31 | 6.20 | 74.85 |
Figure: Meta-regression for ‘Publication Year’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.14 Sessions (n)
Multivariate Meta-Analysis Model (k = 276; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7026 0.8382 138 no ID
sigma^2.2 0.1194 0.3456 276 no ID/arm
Test for Residual Heterogeneity:
QE(df = 274) = 2824.7969, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 9.9709, p-val = 0.0016
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.0991 0.1139 -9.6532 <.0001 -1.3222 -0.8759 ***
get(varname) 0.0188 0.0060 3.1577 0.0016 0.0071 0.0305 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8547
I^2.1 79.5
I^2.2 13.5| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 1.0000 | 25.35 | 21.50 | 29.62 | 5.36 | 67.03 |
| 1st Qu. | 7.0000 | 27.54 | 24.21 | 31.15 | 5.99 | 69.39 |
| Median | 12.0000 | 29.46 | 26.31 | 32.82 | 6.56 | 71.32 |
| Mean | 15.4881 | 30.85 | 27.60 | 34.29 | 6.97 | 72.64 |
| 3rd Qu. | 14.0000 | 30.25 | 27.07 | 33.63 | 6.79 | 72.08 |
| Max. | 75.0000 | 57.78 | 39.65 | 74.03 | 16.68 | 90.35 |
Figure: Meta-regression for ‘Sessions (n)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.15 Session Length (min)
Multivariate Meta-Analysis Model (k = 145; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7335 0.8564 79 no ID
sigma^2.2 0.0428 0.2068 145 no ID/arm
Test for Residual Heterogeneity:
QE(df = 143) = 1583.3283, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 6.2834, p-val = 0.0122
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.2494 0.1635 -7.6423 <.0001 -1.5698 -0.9290 ***
get(varname) 0.0050 0.0020 2.5067 0.0122 0.0011 0.0090 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9449
I^2.1 87.7
I^2.2 5.1| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 7.5000 | 22.94 | 18.10 | 28.63 | 4.91 | 63.20 |
| 1st Qu. | 45.0000 | 26.46 | 22.49 | 30.86 | 5.94 | 67.22 |
| Median | 60.0000 | 27.96 | 24.04 | 32.25 | 6.38 | 68.83 |
| Mean | 61.6578 | 28.13 | 24.20 | 32.43 | 6.43 | 69.01 |
| 3rd Qu. | 90.0000 | 31.11 | 26.39 | 36.25 | 7.33 | 72.05 |
| Max. | 240.0000 | 49.06 | 31.71 | 66.63 | 12.87 | 86.26 |
Figure: Meta-regression for ‘Session Length (min)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
4.2.16 Duration (weeks)
Multivariate Meta-Analysis Model (k = 275; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7245 0.8511 138 no ID
sigma^2.2 0.1249 0.3535 275 no ID/arm
Test for Residual Heterogeneity:
QE(df = 273) = 2863.5481, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.1901, p-val = 0.6628
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.8212 0.1067 -7.6956 <.0001 -1.0304 -0.6121 ***
get(varname) 0.0020 0.0045 0.4360 0.6628 -0.0068 0.0107
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8529
I^2.1 79.6
I^2.2 13.7| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 1.0000 | 30.59 | 26.45 | 35.07 | 6.68 | 73.08 |
| 1st Qu. | 8.0000 | 30.88 | 27.35 | 34.66 | 6.79 | 73.28 |
| Median | 12.0000 | 31.05 | 27.71 | 34.60 | 6.84 | 73.41 |
| Mean | 16.1436 | 31.22 | 27.94 | 34.71 | 6.90 | 73.57 |
| 3rd Qu. | 14.0000 | 31.13 | 27.84 | 34.63 | 6.87 | 73.49 |
| Max. | 156.0000 | 37.37 | 14.68 | 67.43 | 6.24 | 84.25 |
Figure: Meta-regression for ‘Duration (weeks)’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
5 Study-arm level moderators: Substances
Data were also extracted on study-arm level moderators. This included characterizing the participants’ target substance use, off-target substance use, and comorbid diagnoses. In this section, we desscribe the substances.
Simultaneous moderation of substances is not possible with these data because of independence issues, namely that the same study arm could have reported more than one substance and would therefore be counted twice. We chose to test each substance separately, excluding arms with more than one substance in the same class (e.g., multiple different opiates). Continuous and categorical moderators were fit as described above.
Arm 1 of ID 58 removed for multiple subtances within the class of Substance 4Arm 1 of ID 92 removed for multiple subtances within the class of Substance 10Arm 2 of ID 92 removed for multiple subtances within the class of Substance 105.1 Alcohol
5.1.1 Drinks per Day
Multivariate Meta-Analysis Model (k = 22; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.3068 0.5539 9 no ID
sigma^2.2 0.0000 0.0000 22 no ID/arm
Test for Residual Heterogeneity:
QE(df = 20) = 99.8243, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 3.5743, p-val = 0.0587
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.1768 0.4938 0.3581 0.7203 -0.7909 1.1445
get(varname) -0.0808 0.0428 -1.8906 0.0587 -0.1646 0.0030 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 1.0000
I^2.1 77.6
I^2.2 0.0| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 1.9500 | 50.48 | 30.96 | 69.85 | 20.72 | 79.90 |
| 1st Qu. | 8.8000 | 36.95 | 27.83 | 47.10 | 15.47 | 65.23 |
| Median | 10.4000 | 33.99 | 25.81 | 43.24 | 13.97 | 62.02 |
| Mean | 10.6568 | 33.52 | 25.42 | 42.73 | 13.72 | 61.53 |
| 3rd Qu. | 13.2500 | 29.02 | 20.65 | 39.12 | 11.20 | 57.00 |
| Max. | 20.1000 | 19.03 | 8.80 | 36.41 | 5.46 | 48.90 |
Figure: Meta-regression for ‘Alcohol Drinks per Day’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.1.2 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 40; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.9039 0.9507 19 no ID
sigma^2.2 0.0863 0.2937 40 no ID/arm
Test for Residual Heterogeneity:
QE(df = 38) = 385.8780, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.4399, p-val = 0.5072
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.3926 0.4796 -0.8186 0.4130 -1.3326 0.5474
get(varname) -0.0059 0.0088 -0.6632 0.5072 -0.0232 0.0115
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9129
I^2.1 86.4
I^2.2 8.2| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 6.7000 | 39.37 | 21.89 | 60.07 | 7.21 | 84.45 |
| 1st Qu. | 25.9000 | 36.72 | 24.35 | 51.11 | 7.03 | 81.65 |
| Median | 57.2258 | 32.56 | 22.90 | 43.97 | 6.08 | 78.27 |
| Mean | 49.6107 | 33.55 | 24.23 | 44.36 | 6.38 | 78.91 |
| 3rd Qu. | 70.8250 | 30.83 | 19.51 | 45.05 | 5.46 | 77.48 |
| Max. | 86.1000 | 28.96 | 15.35 | 47.81 | 4.70 | 77.10 |
Figure: meta-regression for Alcohol Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.1.3 Length of Use (years)
Multivariate Meta-Analysis Model (k = 27; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.4687 0.6846 13 no ID
sigma^2.2 0.1134 0.3367 27 no ID/arm
Test for Residual Heterogeneity:
QE(df = 25) = 224.8565, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.0009, p-val = 0.9762
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.3480 0.5709 -0.6096 0.5421 -1.4670 0.7710
get(varname) -0.0011 0.0353 -0.0298 0.9762 -0.0703 0.0682
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8052
I^2.1 74.4
I^2.2 18.0| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 3.9000 | 41.29 | 22.68 | 62.76 | 11.06 | 79.90 |
| 1st Qu. | 12.4400 | 41.07 | 30.70 | 52.30 | 12.75 | 76.88 |
| Median | 15.0000 | 41.00 | 31.41 | 51.33 | 12.83 | 76.65 |
| Mean | 15.3346 | 40.99 | 31.39 | 51.34 | 12.82 | 76.65 |
| 3rd Qu. | 20.3000 | 40.87 | 28.38 | 54.65 | 12.30 | 77.31 |
| Max. | 25.9000 | 40.73 | 22.47 | 61.96 | 10.89 | 79.43 |
Figure: meta-regression for Alcohol Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.1.4 Use Pattern Degree
[1] "Model not fit - only one moderator value."5.2 Tobacco
5.2.1 Cigarettes per Day
Multivariate Meta-Analysis Model (k = 106; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.5920 0.7694 54 no ID
sigma^2.2 0.0674 0.2596 106 no ID/arm
Test for Residual Heterogeneity:
QE(df = 104) = 1013.0115, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 3.8763, p-val = 0.0490
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.1870 0.4806 -0.3890 0.6972 -1.1289 0.7550
get(varname) -0.0420 0.0213 -1.9688 0.0490 -0.0837 -0.0002 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8978
I^2.1 82.4
I^2.2 9.4| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 10.5000 | 34.81 | 23.96 | 47.49 | 9.08 | 74.06 |
| 1st Qu. | 18.8000 | 27.37 | 22.49 | 32.86 | 6.99 | 65.41 |
| Median | 21.6000 | 25.10 | 21.06 | 29.62 | 6.29 | 62.58 |
| Mean | 22.1428 | 24.67 | 20.69 | 29.14 | 6.16 | 62.05 |
| 3rd Qu. | 26.4750 | 21.45 | 16.86 | 26.89 | 5.13 | 57.96 |
| Max. | 31.4000 | 18.17 | 12.32 | 25.99 | 4.07 | 53.78 |
5.2.2 Frequency of Use (% days)
[1] "Model not fit - only one study fits the criteria."5.2.3 Length of Use (years)
Multivariate Meta-Analysis Model (k = 85; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.4918 0.7013 45 no ID
sigma^2.2 0.0615 0.2480 85 no ID/arm
Test for Residual Heterogeneity:
QE(df = 83) = 830.0813, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.6796, p-val = 0.4097
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.4013 0.3625 -3.8654 0.0001 -2.1119 -0.6908 ***
get(varname) 0.0122 0.0148 0.8244 0.4097 -0.0168 0.0411
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8888
I^2.1 81.3
I^2.2 10.2| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 4.9000 | 20.72 | 12.79 | 31.79 | 5.17 | 55.64 |
| 1st Qu. | 20.1000 | 23.93 | 19.73 | 28.70 | 6.69 | 57.98 |
| Median | 23.6800 | 24.73 | 20.71 | 29.24 | 6.98 | 58.97 |
| Mean | 23.0532 | 24.59 | 20.59 | 29.08 | 6.94 | 58.78 |
| 3rd Qu. | 26.5000 | 25.37 | 20.97 | 30.34 | 7.19 | 59.87 |
| Max. | 42.4000 | 29.21 | 18.47 | 42.91 | 7.86 | 66.62 |
Figure: meta-regression for Tobacco Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.2.4 Use Pattern Degree
Multivariate Meta-Analysis Model (k = 108; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.6114 0.7819 55 no ID
sigma^2.2 0.0679 0.2607 108 no ID/arm
Test for Residual Heterogeneity:
QE(df = 106) = 1037.2642, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.0206, p-val = 0.8858
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.9923 0.8269 -1.2001 0.2301 -2.6129 0.6283
factor(get(varname))3 -0.1200 0.8352 -0.1437 0.8858 -1.7569 1.5169
intrcpt
factor(get(varname))3
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9000
I^2.1 82.8
I^2.2 9.2| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Moderate | 27.05 | 6.83 | 65.21 | 3.62 | 78.52 | 2 | 1 |
| Heavy | 24.75 | 20.70 | 29.28 | 6.04 | 62.70 | 106 | 54 |
Figure: subgroup meta-analysis for Tobacco Degree of Use Pattern. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Interval are not included.
5.3 Cocaine
5.3.1 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 46; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7516 0.8670 22 no ID
sigma^2.2 0.0472 0.2172 46 no ID/arm
Test for Residual Heterogeneity:
QE(df = 44) = 458.5177, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 3.1371, p-val = 0.0765
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.0186 0.4347 -2.3433 0.0191 -1.8705 -0.1666 *
get(varname) 0.0176 0.0100 1.7712 0.0765 -0.0019 0.0371 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9409
I^2.1 87.0
I^2.2 5.5| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 3.2000 | 27.64 | 14.69 | 45.87 | 5.28 | 72.36 |
| 1st Qu. | 30.9000 | 38.37 | 29.13 | 48.54 | 9.33 | 79.03 |
| Median | 44.3603 | 44.12 | 34.64 | 54.05 | 11.58 | 82.64 |
| Mean | 41.7649 | 42.99 | 33.84 | 52.66 | 11.14 | 81.94 |
| 3rd Qu. | 55.0000 | 48.78 | 36.71 | 61.00 | 13.36 | 85.47 |
| Max. | 84.0000 | 61.37 | 37.83 | 80.57 | 17.73 | 92.13 |
Figure: meta-regression for Cocaine Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.3.2 Length of Use (years)
Multivariate Meta-Analysis Model (k = 47; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.5403 0.7351 20 no ID
sigma^2.2 0.1305 0.3613 47 no ID/arm
Test for Residual Heterogeneity:
QE(df = 45) = 390.6141, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.2235, p-val = 0.2687
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.2175 0.4214 0.5162 0.6057 -0.6083 1.0434
get(varname) -0.0456 0.0412 -1.1061 0.2687 -0.1263 0.0352
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.8054
I^2.1 72.6
I^2.2 17.5| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 3.6000 | 51.34 | 37.17 | 65.29 | 16.07 | 85.32 |
| 1st Qu. | 6.1450 | 48.44 | 37.77 | 59.26 | 15.11 | 83.22 |
| Median | 9.3800 | 44.78 | 36.12 | 53.76 | 13.53 | 80.78 |
| Mean | 9.4739 | 44.67 | 36.01 | 53.67 | 13.48 | 80.71 |
| 3rd Qu. | 11.7000 | 42.18 | 32.56 | 52.43 | 12.21 | 79.28 |
| Max. | 19.7000 | 33.63 | 16.80 | 55.99 | 7.38 | 76.33 |
Figure: meta-regression for Cocaine Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.3.3 Use Pattern Degree
Multivariate Meta-Analysis Model (k = 9; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 4 no ID
sigma^2.2 0.2645 0.5143 9 no ID/arm
Test for Residual Heterogeneity:
QE(df = 6) = 14.9585, p-val = 0.0206
Test of Moderators (coefficient(s) 2:3):
QM(df = 2) = 8.1184, p-val = 0.0173
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -1.2432 0.5920 -2.1001 0.0357 -2.4034 -0.0829
factor(get(varname))2 1.3142 0.6780 1.9385 0.0526 -0.0146 2.6430
factor(get(varname))3 1.9360 0.6835 2.8323 0.0046 0.5963 3.2757
intrcpt *
factor(get(varname))2 .
factor(get(varname))3 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.0000
I^2.1 0.0
I^2.2 59.7| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Light | 22.39 | 8.29 | 47.93 | 5.84 | 57.29 | 1 | 1 |
| Moderate | 51.77 | 35.97 | 67.23 | 24.47 | 78.06 | 4 | 3 |
| Heavy | 66.66 | 50.57 | 79.62 | 37.34 | 87.02 | 4 | 3 |
Figure: subgroup meta-analysis for Cocaine Degree of Use Pattern. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Interval are not included.
5.4 Opioid
5.4.1 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 16; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 6 no ID
sigma^2.2 0.2157 0.4644 16 no ID/arm
Test for Residual Heterogeneity:
QE(df = 14) = 90.2903, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.0051, p-val = 0.3161
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.3383 0.2400 -1.4100 0.1586 -0.8086 0.1320
get(varname) 0.0039 0.0039 1.0025 0.3161 -0.0038 0.0117
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.0000
I^2.1 0.0
I^2.2 86.8| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 3.8000 | 41.99 | 31.67 | 53.05 | 20.80 | 66.60 |
| 1st Qu. | 30.7841 | 44.60 | 37.45 | 51.97 | 23.61 | 67.70 |
| Median | 65.7000 | 48.02 | 41.38 | 54.73 | 26.34 | 70.47 |
| Mean | 52.8153 | 46.75 | 40.68 | 52.93 | 25.48 | 69.28 |
| 3rd Qu. | 80.4250 | 49.47 | 41.29 | 57.68 | 27.10 | 72.06 |
| Max. | 88.7000 | 50.29 | 40.98 | 59.57 | 27.42 | 73.03 |
Figure: meta-regression for Opioid Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.4.2 Length of Use (years)
Multivariate Meta-Analysis Model (k = 25; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.5568 0.7462 10 no ID
sigma^2.2 0.2339 0.4836 25 no ID/arm
Test for Residual Heterogeneity:
QE(df = 23) = 171.6504, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.5031, p-val = 0.4782
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.0971 0.4786 -0.2029 0.8392 -1.0352 0.8409
get(varname) -0.0420 0.0592 -0.7093 0.4782 -0.1581 0.0741
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.7042
I^2.1 66.3
I^2.2 27.8| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.9400 | 46.59 | 27.14 | 67.13 | 11.15 | 85.85 |
| 1st Qu. | 2.2000 | 45.28 | 28.24 | 63.49 | 11.07 | 84.62 |
| Median | 9.2000 | 38.14 | 25.03 | 53.24 | 8.86 | 79.64 |
| Mean | 8.1149 | 39.22 | 26.87 | 53.12 | 9.37 | 80.12 |
| 3rd Qu. | 12.8000 | 34.64 | 17.81 | 56.46 | 6.95 | 78.99 |
| Max. | 14.4000 | 33.14 | 14.79 | 58.59 | 6.09 | 79.12 |
Figure: meta-regression for Opioid Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.4.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.5 Methamphetamine
5.5.1 Frequency of Use (% days)
[1] "Model not fit - only one study fits the criteria."5.5.2 Length of Use (years)
[1] "Model not fit - only one study fits the criteria."5.5.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.6 Depressants
5.6.1 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 5; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.1157 0.3401 3 no ID
sigma^2.2 0.0000 0.0000 5 no ID/arm
Test for Residual Heterogeneity:
QE(df = 3) = 5.9106, p-val = 0.1160
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.0054, p-val = 0.9417
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.2067 0.3007 -0.6872 0.4920 -0.7961 0.3828
get(varname) -0.0022 0.0301 -0.0732 0.9417 -0.0613 0.0569
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 1.0000
I^2.1 52.2
I^2.2 0.0| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.700 | 44.81 | 31.61 | 58.80 | 25.33 | 66.03 |
| 1st Qu. | 1.000 | 44.80 | 31.82 | 58.53 | 25.44 | 65.87 |
| Median | 1.325 | 44.78 | 32.04 | 58.25 | 25.56 | 65.70 |
| Mean | 4.485 | 44.61 | 33.57 | 56.20 | 26.31 | 64.49 |
| 3rd Qu. | 1.700 | 44.76 | 32.28 | 57.94 | 25.69 | 65.51 |
| Max. | 17.700 | 43.89 | 25.90 | 63.64 | 21.56 | 68.99 |
Figure: meta-regression for Depressants Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.6.2 Length of Use (years)
[1] "Model not fit - only one study fits the criteria."5.6.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.7 Cannabis
5.7.1 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 16; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 8 no ID
sigma^2.2 0.2265 0.4760 16 no ID/arm
Test for Residual Heterogeneity:
QE(df = 14) = 54.0228, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.5885, p-val = 0.4430
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.6631 0.2231 -2.9725 0.0030 -1.1003 -0.2259 **
get(varname) 0.0033 0.0043 0.7671 0.4430 -0.0052 0.0119
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.0000
I^2.1 0.0
I^2.2 76.9| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.700 | 34.06 | 25.10 | 44.32 | 15.59 | 59.09 |
| 1st Qu. | 3.600 | 34.27 | 25.63 | 44.10 | 15.82 | 59.14 |
| Median | 39.500 | 37.02 | 30.75 | 43.76 | 18.16 | 60.89 |
| Mean | 36.417 | 36.78 | 30.51 | 43.54 | 18.00 | 60.65 |
| 3rd Qu. | 49.000 | 37.76 | 31.18 | 44.83 | 18.58 | 61.72 |
| Max. | 98.600 | 41.72 | 28.67 | 56.04 | 19.29 | 68.19 |
Figure: meta-regression for Cannabis Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.7.2 Length of Use (years)
Multivariate Meta-Analysis Model (k = 14; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.4329 0.6579 8 no ID
sigma^2.2 0.1423 0.3773 14 no ID/arm
Test for Residual Heterogeneity:
QE(df = 12) = 99.3975, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.5645, p-val = 0.4524
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.9316 0.7309 -1.2746 0.2025 -2.3641 0.5009
get(varname) 0.0615 0.0819 0.7514 0.4524 -0.0990 0.2221
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.7526
I^2.1 69.9
I^2.2 23.0| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 4.0000 | 33.51 | 17.45 | 54.56 | 8.26 | 73.81 |
| 1st Qu. | 5.2946 | 35.30 | 21.08 | 52.72 | 9.49 | 73.95 |
| Median | 7.9600 | 39.13 | 27.44 | 52.22 | 11.71 | 75.70 |
| Mean | 8.0470 | 39.26 | 27.58 | 52.32 | 11.77 | 75.79 |
| 3rd Qu. | 10.1675 | 42.41 | 28.64 | 57.48 | 12.88 | 78.58 |
| Max. | 13.9000 | 48.10 | 24.62 | 72.45 | 13.10 | 85.06 |
Figure: meta-regression for Cannabis Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.7.3 Use Pattern Degree
Multivariate Meta-Analysis Model (k = 17; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0325 0.1804 8 no ID
sigma^2.2 0.2023 0.4498 17 no ID/arm
Test for Residual Heterogeneity:
QE(df = 14) = 49.2532, p-val < .0001
Test of Moderators (coefficient(s) 2:3):
QM(df = 2) = 1.1916, p-val = 0.5511
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.7184 0.3000 -2.3946 0.0166 -1.3063 -0.1304
factor(get(varname))2 0.0037 0.4032 0.0091 0.9927 -0.7867 0.7940
factor(get(varname))3 0.3431 0.3840 0.8936 0.3715 -0.4095 1.0958
intrcpt *
factor(get(varname))2
factor(get(varname))3
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.1385
I^2.1 9.9
I^2.2 61.4| Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | Arms | Studies | |
|---|---|---|---|---|---|---|---|
| Light | 32.78 | 21.31 | 46.74 | 13.76 | 59.84 | 5 | 2 |
| Moderate | 32.86 | 22.39 | 45.35 | 14.17 | 59.20 | 6 | 3 |
| Heavy | 40.73 | 30.05 | 52.36 | 19.23 | 66.47 | 6 | 3 |
Figure: subgroup meta-analysis for Cannabis Degree of Use Pattern. The dashed line represents the mean dropout rate across all dropout rates included in this particular analysis. Because the inclusion of studies and study arms is dependent on the reporting of the moderator, the overall dropout rate in this analysis may be different than in other analyses. Red polygons represent the mean and 95% CI for the average dropout. Note that 95% Prediction Interval are not included.
5.8 Polysubstance
5.8.1 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 10; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.8306 0.9114 5 no ID
sigma^2.2 0.0000 0.0000 10 no ID/arm
Test for Residual Heterogeneity:
QE(df = 8) = 52.8494, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.1215, p-val = 0.7274
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.4997 1.2889 -0.3877 0.6982 -3.0259 2.0264
get(varname) -0.0130 0.0373 -0.3485 0.7274 -0.0861 0.0601
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 1.0000
I^2.1 94.4
I^2.2 0.0| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 17.50 | 32.58 | 10.83 | 65.78 | 4.81 | 82.21 |
| 1st Qu. | 25.60 | 30.31 | 14.14 | 53.47 | 5.39 | 76.87 |
| Median | 37.30 | 27.20 | 13.31 | 47.62 | 4.83 | 73.32 |
| Mean | 32.83 | 28.36 | 14.82 | 47.40 | 5.25 | 73.89 |
| 3rd Qu. | 39.00 | 26.76 | 12.45 | 48.43 | 4.62 | 73.37 |
| Max. | 48.00 | 24.53 | 7.49 | 56.62 | 3.27 | 75.76 |
Figure: meta-regression for Polysubstance Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.8.2 Length of Use (years)
Multivariate Meta-Analysis Model (k = 7; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.1976 0.4445 4 no ID
sigma^2.2 0.0000 0.0000 7 no ID/arm
Test for Residual Heterogeneity:
QE(df = 5) = 15.8236, p-val = 0.0074
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.3244, p-val = 0.2498
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -2.4757 1.4069 -1.7597 0.0785 -5.2332 0.2817 .
get(varname) 0.1538 0.1336 1.1508 0.2498 -0.1081 0.4157
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 1.0000
I^2.1 81.9
I^2.2 0.0| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 7.5000 | 21.04 | 9.78 | 39.59 | 7.08 | 48.25 |
| 1st Qu. | 8.2000 | 22.88 | 12.25 | 38.69 | 8.57 | 48.44 |
| Median | 8.4000 | 23.43 | 13.01 | 38.51 | 9.02 | 48.59 |
| Mean | 9.5571 | 26.77 | 17.53 | 38.61 | 11.58 | 50.50 |
| 3rd Qu. | 11.1000 | 31.67 | 21.31 | 44.24 | 14.28 | 56.34 |
| Max. | 12.4000 | 36.15 | 21.38 | 54.10 | 15.35 | 63.87 |
Figure: meta-regression for Polysubstance Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.8.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.9 Hallucinogen
5.9.1 Frequency of Use (% days)
[1] "Model not fit - No studies fit the criteria."5.9.2 Length of Use (years)
[1] "Model not fit - No studies fit the criteria."5.9.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.10 Heroin
5.10.1 Frequency of Use (% days)
Multivariate Meta-Analysis Model (k = 12; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0000 0.0000 6 no ID
sigma^2.2 0.2043 0.4520 12 no ID/arm
Test for Residual Heterogeneity:
QE(df = 10) = 41.8674, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 14.4742, p-val = 0.0001
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 1.0604 0.3867 2.7423 0.0061 0.3025 1.8183 **
get(varname) -0.0181 0.0048 -3.8045 0.0001 -0.0275 -0.0088 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.0000
I^2.1 0.0
I^2.2 69.5| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 11.3000 | 70.17 | 54.78 | 82.04 | 43.75 | 87.68 |
| 1st Qu. | 84.9000 | 38.21 | 30.62 | 46.44 | 19.33 | 61.48 |
| Median | 94.3625 | 34.25 | 26.36 | 43.12 | 16.60 | 57.68 |
| Mean | 79.0104 | 40.77 | 33.23 | 48.77 | 21.13 | 63.87 |
| 3rd Qu. | 96.7000 | 33.30 | 25.32 | 42.37 | 15.96 | 56.76 |
| Max. | 100.0000 | 31.98 | 23.87 | 41.35 | 15.08 | 55.47 |
Figure: meta-regression for Heroin Frequency of Use (% days). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.10.2 Length of Use (years)
Multivariate Meta-Analysis Model (k = 17; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.6058 0.7783 8 no ID
sigma^2.2 0.5292 0.7275 17 no ID/arm
Test for Residual Heterogeneity:
QE(df = 15) = 138.7223, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.3847, p-val = 0.2393
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.6815 1.0750 0.6340 0.5261 -1.4254 2.7884
get(varname) -0.1124 0.0955 -1.1767 0.2393 -0.2995 0.0748
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.5337
I^2.1 48.1
I^2.2 42.1| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 4.8000 | 53.55 | 24.07 | 80.74 | 9.01 | 93.07 |
| 1st Qu. | 8.2000 | 44.03 | 25.66 | 64.20 | 7.69 | 88.13 |
| Median | 9.5000 | 40.47 | 24.91 | 58.22 | 6.95 | 86.08 |
| Mean | 10.2082 | 38.57 | 23.95 | 55.59 | 6.51 | 84.99 |
| 3rd Qu. | 13.1400 | 31.11 | 16.47 | 50.85 | 4.56 | 81.03 |
| Max. | 17.4000 | 21.87 | 6.23 | 54.09 | 2.17 | 77.93 |
Figure: meta-regression for Heroin Length of Use (years). The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval. Points are proportional to the inverse variance of the individual dropout rates.
5.10.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.11 Major stimulant
5.11.1 Frequency of Use (% days)
[1] "Model not fit - No studies fit the criteria."5.11.2 Length of Use (years)
[1] "Model not fit - No studies fit the criteria."5.11.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."5.12 GHB
5.12.1 Frequency of Use (% days)
[1] "Model not fit - only one study fits the criteria."5.12.2 Length of Use (years)
[1] "Model not fit - No studies fit the criteria."5.12.3 Use Pattern Degree
[1] "Model not fit - No studies fit the criteria."6 Study-arm level moderators: Comorbid Diagnoses
Similar to the substances, simultaneous moderation of comorbid diagnoses is also not possible with these data because of independence issues, namely that the same study arm could have more than one comorbid diagnosis and would be counted twice. Therefore, we chose to test each comorbid diagnosis separately, excluding arms with more than one comorbid diagnosis in the same class (e.g., multiple mental illnesses). Comorbid diagnoses were fit as categorical data, as described above.
6.1 Mood Disorder
Multivariate Meta-Analysis Model (k = 49; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.6086 0.7801 23 no ID
sigma^2.2 0.1596 0.3995 49 no ID/arm
Test for Residual Heterogeneity:
QE(df = 47) = 495.2212, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.3835, p-val = 0.2395
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.4623 0.2158 -2.1421 0.0322 -0.8854 -0.0393 *
get(varname) -0.0050 0.0042 -1.1762 0.2395 -0.0132 0.0033
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.7923
I^2.1 73.0
I^2.2 19.1| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 0.0000 | 38.64 | 29.21 | 49.02 | 9.70 | 78.70 |
| 1st Qu. | 14.3000 | 36.98 | 28.77 | 46.01 | 9.19 | 77.29 |
| Median | 21.0000 | 36.21 | 28.34 | 44.89 | 8.93 | 76.65 |
| Mean | 25.2728 | 35.72 | 27.98 | 44.28 | 8.77 | 76.26 |
| 3rd Qu. | 29.0000 | 35.29 | 27.61 | 43.82 | 8.62 | 75.92 |
| Max. | 100.0000 | 27.72 | 16.02 | 43.55 | 5.66 | 71.02 |
Figure: Meta-regression for ‘Mood Disorder’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
6.2 Anxiety Disorder
Multivariate Meta-Analysis Model (k = 24; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.4342 0.6590 12 no ID
sigma^2.2 0.1923 0.4385 24 no ID/arm
Test for Residual Heterogeneity:
QE(df = 22) = 152.3344, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.6038, p-val = 0.2054
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.0363 0.3433 0.1058 0.9157 -0.6365 0.7091
get(varname) -0.0216 0.0170 -1.2664 0.2054 -0.0550 0.0118
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.6931
I^2.1 62.0
I^2.2 27.4| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 3.0000 | 49.29 | 34.78 | 63.93 | 15.55 | 83.69 |
| 1st Qu. | 5.7500 | 47.81 | 34.75 | 61.17 | 15.04 | 82.57 |
| Median | 13.7000 | 43.56 | 33.14 | 54.57 | 13.33 | 79.48 |
| Mean | 15.7212 | 42.49 | 32.24 | 53.42 | 12.84 | 78.75 |
| 3rd Qu. | 23.2500 | 38.58 | 27.30 | 51.22 | 10.91 | 76.30 |
| Max. | 39.4000 | 30.71 | 15.04 | 52.61 | 6.81 | 72.89 |
Figure: Meta-regression for ‘Anxiety Disorder’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
6.3 Comorbid Substance Use Dependence/Addiction
Multivariate Meta-Analysis Model (k = 20; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.7526 0.8675 9 no ID
sigma^2.2 0.0824 0.2870 20 no ID/arm
Test for Residual Heterogeneity:
QE(df = 18) = 131.5347, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.0669, p-val = 0.3016
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.7248 0.5360 -1.3521 0.1763 -1.7754 0.3258
get(varname) 0.0119 0.0115 1.0329 0.3016 -0.0107 0.0344
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.9013
I^2.1 83.0
I^2.2 9.1| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 5.700 | 34.14 | 16.72 | 57.23 | 6.39 | 79.73 |
| 1st Qu. | 23.250 | 38.96 | 24.24 | 56.02 | 8.56 | 81.32 |
| Median | 41.150 | 44.12 | 30.08 | 59.16 | 10.65 | 83.95 |
| Mean | 37.515 | 43.06 | 29.26 | 58.03 | 10.25 | 83.34 |
| 3rd Qu. | 52.000 | 47.31 | 31.30 | 63.90 | 11.68 | 85.91 |
| Max. | 73.000 | 53.53 | 30.00 | 75.59 | 12.96 | 89.91 |
Figure: Meta-regression for ‘Comorbid Substance Use Dependence/Addiction’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
6.4 Personality Disorder
Multivariate Meta-Analysis Model (k = 32; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.6748 0.8215 16 no ID
sigma^2.2 0.2039 0.4515 32 no ID/arm
Test for Residual Heterogeneity:
QE(df = 30) = 261.7339, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.4172, p-val = 0.5183
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.5608 0.3484 -1.6095 0.1075 -1.2437 0.1221
get(varname) -0.0047 0.0073 -0.6459 0.5183 -0.0190 0.0096
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.7680
I^2.1 70.5
I^2.2 21.3| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 3.0000 | 36.01 | 22.67 | 51.93 | 7.42 | 79.81 |
| 1st Qu. | 10.5250 | 35.20 | 23.30 | 49.27 | 7.33 | 78.86 |
| Median | 24.1000 | 33.75 | 23.80 | 45.38 | 7.07 | 77.32 |
| Mean | 34.8027 | 32.63 | 23.36 | 43.49 | 6.79 | 76.31 |
| 3rd Qu. | 42.2500 | 31.86 | 22.54 | 42.91 | 6.55 | 75.72 |
| Max. | 100.0000 | 26.26 | 11.20 | 50.15 | 4.14 | 74.61 |
Figure: Meta-regression for ‘Personality Disorder’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
6.5 Psychotic Disorder
Multivariate Meta-Analysis Model (k = 10; method: REML)
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.3540 0.5950 6 no ID
sigma^2.2 0.2700 0.5196 10 no ID/arm
Test for Residual Heterogeneity:
QE(df = 8) = 64.4409, p-val < .0001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 1.6341, p-val = 0.2011
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.4679 0.8268 0.5659 0.5715 -1.1526 2.0883
get(varname) -0.0184 0.0144 -1.2783 0.2011 -0.0467 0.0098
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ICC: 0.5673
I^2.1 50.9
I^2.2 38.8| Moderator | Dropout | Lower 95% CI | Upper 95% CI | Lower 95% PI | Upper 95% PI | |
|---|---|---|---|---|---|---|
| Min. | 29.700 | 48.00 | 27.11 | 69.62 | 13.29 | 84.75 |
| 1st Qu. | 41.375 | 42.67 | 26.78 | 60.24 | 11.93 | 80.35 |
| Median | 46.950 | 40.18 | 25.87 | 56.39 | 11.12 | 78.30 |
| Mean | 60.480 | 34.35 | 21.11 | 50.58 | 8.83 | 73.88 |
| 3rd Qu. | 89.175 | 23.56 | 8.42 | 50.83 | 4.14 | 68.74 |
| Max. | 100.000 | 20.16 | 5.44 | 52.57 | 2.88 | 68.24 |
Figure: Meta-regression for ‘Psychotic Disorder’. The solid line represents the predicted dropout rate at the given predictor value; dashed lines represent the 95% CI; dotted lines represent the 95% Prediction Interval (PI). Points are proportional to the inverse variance of the individual dropout rates.
6.6 Other Psychological Diagnoses
[1] "Model not fit - only one study fits the criteria."7 Summary tables for publication
The following tables summarize the above output, divided into groups as analyzed above.
7.1 Study-level moderator meta-regression results
| Moderatora | Studies (dropout rates)b | Logit regressionc | Dropout at Q1d | Dropout at Median | Dropout at Q3 | Residual Heterogeneity % (p) | Test for Moderation (p) |
|---|---|---|---|---|---|---|---|
| Age (mean years) | 146 (294) | -0.1228-0.0185X | 34: 31.9 (28.1,35.9) | 39: 30.1(26.9,33.4) | 43: 28.5(25.0,32.4) | 93.4 (<0.0001) | 0.0916 |
| Sex (proportion male) | 145 (289) | -0.9104+0.1418X | 0.48: 30.1 (26.6,33.9) | 0.60: 30.5(27.2,34.0) | 0.74: 30.9(27.1,35.0) | 93.8 (<0.0001) | 0.6593 |
| Education (mean years) | 34 (70) | 0.9800-0.1291X | 12: 37.7 (29.8,46.2) | 12: 35.1(28.6,42.3) | 14: 31.0(23.5,39.6) | 91.6 (<0.0001) | 0.1556 |
| White (proportion) | 112 (225) | -0.4847-0.5464X | 0.38: 33.4 (28.8,38.3) | 0.64: 30.3(26.5,34.3) | 0.86: 27.8(23.2,32.9) | 93.7 (<0.0001) | 0.0607 |
| Hispanic/Latino (proportion) | 69 (130) | -0.6818-1.0953X | 0.00: 33.6 (27.7,40.0) | 0.04: 32.5(27.1,38.4) | 0.15: 29.9(25.0,35.4) | 94.8 (<0.0001) | 0.0584 |
| African American (proportion) | 74 (142) | -1.2199+1.3149X | 0.07: 24.5 (19.7,29.9) | 0.28: 29.8(25.6,34.5) | 0.52: 37.0(31.1,43.2) | 93.2 (<0.0001) | 0.0004 |
| Other Race/Ethnicity (proportion) | 74 (142) | -0.6745-1.3494X | 0.00: 33.8 (28.4,39.5) | 0.04: 32.5(27.6,37.9) | 0.08: 31.2(26.6,36.3) | 94.1 (<0.0001) | 0.0078 |
| Adjusted Mean Annual Income ($) | 16 (34) | -0.1779+-0.0000X | 9726: 41.0 (29.1,54.1) | 15684: 38.3(27.7,50.1) | 26670: 33.5(24.2,44.2) | 88.4 (<0.0001) | 0.0381 |
| Not Married (proportion) | 80 (155) | -0.9743+0.3732X | 0.56: 31.7 (26.9,37.0) | 0.68: 32.8(28.3,37.5) | 0.82: 33.9(28.4,39.9) | 93.7 (<0.0001) | 0.4480 |
| Unemployed (proportion) | 71 (141) | -0.7961+0.2873X | 0.41: 33.7 (28.1,39.8) | 0.53: 34.4(29.2,40.1) | 0.74: 35.8(28.8,43.5) | 94.6 (<0.0001) | 0.5588 |
| Not Unemployed (proportion) | 61 (128) | -0.4076-0.5058X | 0.28: 36.6 (29.7,44.2) | 0.50: 34.1(29.0,39.5) | 0.66: 32.3(26.6,38.7) | 93.7 (<0.0001) | 0.2940 |
| Experience (years) | 21 (36) | -1.2013+0.0833X | 3: 28.4 (17.9,41.8) | 7: 34.9(25.0,46.4) | 10: 40.8(28.1,54.8) | 94.6 (<0.0001) | 0.1025 |
| Publication Year | 151 (299) | -3.3093+0.0012X | 2000: 30.3 (26.8,34.1) | 2006: 30.5(27.1,34.0) | 2009: 30.5(26.7,34.6) | 93.7 (<0.0001) | 0.9080 |
| Sessions (n) | 138 (276) | -1.0991+0.0188X | 7: 27.5 (24.2,31.1) | 12: 29.5(26.3,32.8) | 14: 30.2(27.1,33.6) | 93.0 (<0.0001) | 0.0016 |
| Session Length (min) | 79 (145) | -1.2494+0.0050X | 45: 26.5 (22.5,30.9) | 60: 28.0(24.0,32.2) | 90: 31.1(26.4,36.2) | 92.8 (<0.0001) | 0.0122 |
| Duration (weeks) | 138 (275) | -0.8212+0.0020X | 8: 30.9 (27.4,34.7) | 12: 31.1(27.7,34.6) | 14: 31.1(27.8,34.6) | 93.3 (<0.0001) | 0.6628 |
| a Separate meta-regressions were calculated for each continuous moderator. | |||||||
| b The number of studies and dropout rates included varies by moderator because of differences in reporting across studies. When dropout rates were averaged across study-arms, either because of pooled moderators or dropout rates, the study has only a single dropout rate, regardless of how many study-arms were included. | |||||||
c Because the regression was calculated on the logit scale, the parameter estimates are reported on the logit scale. To use the regression to get proportion dropout, enter the value of the moderator of interest into the regression equation, and back-transform to a proportion using a function like the transf.ilogit function in the metafor package in R. The regression represents dropout rates as a function of the study-level or study-arm-level average moderator value, not individual-participant-level data.
|
|||||||
| d Q1, Median, and Q3 refer to the first quartile, median, and third quartile (respectively) of the study-level or study-arm-level values of the moderator; note these do not necessarily represent individual-participant-level data. Because the regression is on the logit scale, these columns provide interpretable, back-transformed dropout rates in percent at Q1, Median, and Q3 moderator values. Data are presented as the bolded moderator value, followed by the estimated dropout percentage and 95% CI. |
7.2 Study-level sub-group meta-analysis results
| Moderator | Moderator Value | Studies (dropout rates) | Dropout (95% CI) | Residual Heterogeneity % (p) | Test for Moderation (p) |
|---|---|---|---|---|---|
| Degree | 82(158) | 93.2 (<0.0001) | 0.2445 | ||
| Mixed | 36 (71) | 33.8 (27.4,40.8) | |||
| Bachelors | 6 (8) | 21.7 (11.1,38.1) | |||
| Masters | 27 (55) | 25.7 (19.6,32.9) | |||
| Doctorate | 14 (22) | 30.2 (20.4,42.1) | |||
| Certificate | 2 (2) | 13.8 (3.0,44.8) | |||
| Substance Being Treated | 151(299) | 93.1 (<0.0001) | 0.0050 | ||
| Alcohol | 21 (47) | 26.1 (19.1,34.4) | |||
| Tobacco | 65 (117) | 25.5 (21.4,30.1) | |||
| Cocaine | 18 (42) | 48.7 (38.2,59.3) | |||
| Opioid | 10 (24) | 39.2 (26.6,53.5) | |||
| Methamphetamine | 1 (2) | 53.5 (16.5,87.0) | |||
| Cannabis | 5 (11) | 34.9 (19.4,54.4) | |||
| Polysubstance | 29 (50) | 30.6 (23.9,38.2) | |||
| Heroin | 2 (4) | 25.1 (8.0,56.3) | |||
| Major stimulant | 1 (2) | 46.8 (13.3,83.4) | |||
| Pregnant Participants? | 151(299) | 93.7 (<0.0001) | 0.0481 | ||
| No or not indicated | 150 (298) | 30.6 (27.4,34.0) | |||
| Yes | 1 (1) | 4.0 (0.4,30.1) | |||
| Manualized Treatment? | 148(296) | 93.7 (<0.0001) | 0.3268 | ||
| No or not indicated | 74 (130) | 31.9 (27.5,36.6) | |||
| Yes | 81 (166) | 29.1 (25.1,33.4) | |||
| Setting of Trial | 151(299) | 93.5 (<0.0001) | 0.2672 | ||
| Institution | 3 (4) | 36.8 (16.4,63.4) | |||
| Outpatient (hospital/medical school) | 15 (28) | 22.8 (15.1,32.9) | |||
| Outpatient (public) | 113 (227) | 32.3 (28.5,36.3) | |||
| University affiliated clinic | 12 (26) | 25.8 (16.8,37.4) | |||
| Inpatient | 5 (8) | 18.4 (8.4,35.8) | |||
| Mixed | 4 (6) | 35.4 (18.4,57.2) | |||
| Pharmacotherapy Category | 143(291) | 93.4 (<0.0001) | 0.3821 | ||
| No | 79 (136) | 29.7 (25.3,34.4) | |||
| Placebo | 26 (33) | 34.9 (28.1,42.3) | |||
| Not agonist | 24 (41) | 33.6 (26.6,41.5) | |||
| Agonist | 43 (81) | 28.6 (23.4,34.5) | |||
| Treatment Approach | 142(290) | 93.4 (<0.0001) | 0.3485 | ||
| Cognitive and/or behavioral | 72 (121) | 28.5 (24.6,32.8) | |||
| Motivational | 16 (17) | 27.7 (20.8,35.8) | |||
| Non-specific | 74 (114) | 32.8 (28.6,37.4) | |||
| Psychodynamic | 1 (1) | 28.9 (7.3,67.8) | |||
| 12-step | 3 (4) | 38.2 (23.7,55.3) | |||
| Integrative | 21 (33) | 28.9 (22.5,36.3) | |||
| Limited Treatment Time? | 151(299) | 93.8 (<0.0001) | 0.2593 | ||
| No or not indicated | 6 (10) | 38.6 (24.7,54.8) | |||
| Yes | 147 (289) | 30.1 (26.9,33.6) | |||
| Training for Fidelity? | 150(298) | 93.7 (<0.0001) | 0.7059 | ||
| No or not indicated | 78 (155) | 29.9 (25.7,34.6) | |||
| Yes | 75 (143) | 31.2 (26.6,36.1) | |||
| Treatment Format | 149(297) | 93.5 (<0.0001) | 0.0269 | ||
| Group | 41 (74) | 33.2 (27.5,39.4) | |||
| Individual | 87 (171) | 27.1 (23.5,31.1) | |||
| Mixed | 28 (50) | 39.0 (31.4,47.2) | |||
| Not specified | 1 (1) | 12.0 (1.8,50.9) | |||
| Couple therapy | 1 (1) | 29.3 (6.9,69.8) | |||
| Efficacy Study? | 151(299) | 93.7 (<0.0001) | 0.4196 | ||
| Efficacy | 134 (277) | 29.9 (26.6,33.5) | |||
| Effectiveness | 17 (22) | 34.4 (24.7,45.5) | |||
| Codification of Dependence | 151(299) | 93.2 (<0.0001) | 0.0006 | ||
| DSM | 68 (139) | 37.0 (31.9,42.3) | |||
| Other | 83 (160) | 25.7 (22.0,29.8) | |||
| Treatment Seeking? | 150(298) | 93.6 (<0.0001) | 0.0967 | ||
| No or not indicated | 8 (20) | 30.2 (21.7,40.3) | |||
| Yes | 140 (272) | 31.1 (27.8,34.5) | |||
| Mixed | 3 (6) | 11.4 (4.0,28.4) | |||
| Country Classification | 151(299) | 93.8 (<0.0001) | 0.4712 | ||
| Developed | 144 (289) | 30.2 (26.9,33.6) | |||
| Developing | 7 (10) | 36.4 (21.3,54.7) | |||
| a Sub-group meta-analyses were calculated for categorical moderator variables. | |||||
| b The number of studies and dropout rates included varies by moderator because of differences in reporting across studies. When dropout rates were averaged across study-arms, either because of pooled moderators or dropout rates, the study has only a single dropout rate, regardless of how many study-arms were included. |
7.3 Substance use meta-regression results
| Moderatora | Studies (dropout rates)b | Logit regressionc | Dropout at Q1d | Dropout at Median | Dropout at Q3 | Residual Heterogeneity % (p) | Test for Moderation (p) |
|---|---|---|---|---|---|---|---|
| Alcohol | |||||||
| Drinks per Day | 9 (22) | 0.1768-0.0808X | 9: 37.0 (27.8,47.1) | 10: 34.0(25.8,43.2) | 13: 29.0(20.6,39.1) | 77.6 (<0.0001) | 0.0587 |
| Frequency of Use (% days) | 19 (40) | -0.3926-0.0059X | 26: 36.7 (24.4,51.1) | 57: 32.6(22.9,44.0) | 71: 30.8(19.5,45.0) | 94.6 (<0.0001) | 0.5072 |
| Length of Use (years) | 13 (27) | -0.3480-0.0011X | 12: 41.1 (30.7,52.3) | 15: 41.0(31.4,51.3) | 20: 40.9(28.4,54.6) | 92.4 (<0.0001) | 0.9762 |
| Tobacco | |||||||
| Cigarettes per Day | 54 (106) | -0.1870-0.0420X | 19: 27.4 (22.5,32.9) | 22: 25.1(21.1,29.6) | 26: 21.4(16.9,26.9) | 91.7 (<0.0001) | 0.0490 |
| Frequency of Use (% days) | Model not fit - only one study fits the criteria. | ||||||
| Length of Use (years) | 45 (85) | -1.4013+0.0122X | 20: 23.9 (19.7,28.7) | 24: 24.7(20.7,29.2) | 26: 25.4(21.0,30.3) | 91.5 (<0.0001) | 0.4097 |
| Cocaine | |||||||
| Frequency of Use (% days) | 22 (46) | -1.0186+0.0176X | 31: 38.4 (29.1,48.5) | 44: 44.1(34.6,54.0) | 55: 48.8(36.7,61.0) | 92.5 (<0.0001) | 0.0765 |
| Length of Use (years) | 20 (47) | 0.2175-0.0456X | 6: 48.4 (37.8,59.3) | 9: 44.8(36.1,53.8) | 12: 42.2(32.6,52.4) | 90.1 (<0.0001) | 0.2687 |
| Opioid | |||||||
| Frequency of Use (% days) | 6 (16) | -0.3383+0.0039X | 31: 44.6 (37.5,52.0) | 66: 48.0(41.4,54.7) | 80: 49.5(41.3,57.7) | 86.8 (<0.0001) | 0.3161 |
| Length of Use (years) | 10 (25) | -0.0971-0.0420X | 2: 45.3 (28.2,63.5) | 9: 38.1(25.0,53.2) | 13: 34.6(17.8,56.5) | 94.1 (<0.0001) | 0.4782 |
| Methamphetamine | |||||||
| Frequency of Use (% days) | Model not fit - only one study fits the criteria. | ||||||
| Length of Use (years) | Model not fit - only one study fits the criteria. | ||||||
| Depressants | |||||||
| Frequency of Use (% days) | 3 (5) | -0.2067-0.0022X | 1: 44.8 (31.8,58.5) | 1: 44.8(32.0,58.2) | 2: 44.8(32.3,57.9) | 52.2 (0.1160) | 0.9417 |
| Length of Use (years) | Model not fit - only one study fits the criteria. | ||||||
| Cannabis | |||||||
| Frequency of Use (% days) | 8 (16) | -0.6631+0.0033X | 4: 34.3 (25.6,44.1) | 40: 37.0(30.8,43.8) | 49: 37.8(31.2,44.8) | 76.9 (<0.0001) | 0.4430 |
| Length of Use (years) | 8 (14) | -0.9316+0.0615X | 5: 35.3 (21.1,52.7) | 8: 39.1(27.4,52.2) | 10: 42.4(28.6,57.5) | 92.9 (<0.0001) | 0.4524 |
| Polysubstance | |||||||
| Frequency of Use (% days) | 5 (10) | -0.4997-0.0130X | 26: 30.3 (14.1,53.5) | 37: 27.2(13.3,47.6) | 39: 26.8(12.4,48.4) | 94.4 (<0.0001) | 0.7274 |
| Length of Use (years) | 4 (7) | -2.4757+0.1538X | 8: 22.9 (12.2,38.7) | 8: 23.4(13.0,38.5) | 11: 31.7(21.3,44.2) | 81.9 (0.0074) | 0.2498 |
| Hallucinogen | |||||||
| Frequency of Use (% days) | Model not fit - No studies fit the criteria. | ||||||
| Length of Use (years) | Model not fit - No studies fit the criteria. | ||||||
| Heroin | |||||||
| Frequency of Use (% days) | 6 (12) | 1.0604-0.0181X | 85: 38.2 (30.6,46.4) | 94: 34.2(26.4,43.1) | 97: 33.3(25.3,42.4) | 69.5 (<0.0001) | 0.0001 |
| Length of Use (years) | 8 (17) | 0.6815-0.1124X | 8: 44.0 (25.7,64.2) | 10: 40.5(24.9,58.2) | 13: 31.1(16.5,50.9) | 90.2 (<0.0001) | 0.2393 |
| Major stimulant | |||||||
| Frequency of Use (% days) | Model not fit - No studies fit the criteria. | ||||||
| Length of Use (years) | Model not fit - No studies fit the criteria. | ||||||
| GHB | |||||||
| Frequency of Use (% days) | Model not fit - only one study fits the criteria. | ||||||
| Length of Use (years) | Model not fit - No studies fit the criteria. | ||||||
| a Separate meta-regressions were calculated for each substance, as well as the use pattern (e.g., Frequency of Days Used) within substance. | |||||||
| b The number of studies and dropout rates included varies by substance and substance use pattern because of differences in reporting across studies. When dropout rates were averaged across study-arms, either because of pooled moderators or dropout rates, the study has only a single dropout rate, regardless of how many study-arms were included. | |||||||
c Because the regression was calculated on the logit scale, the parameter estimates are reported on the logit scale. To use the regression to get proportion dropout, enter the value of the moderator of interest into the regression equation, and back-transform to a proportion using a function like the transf.ilogit function in the metafor package in R. The regression represents dropout rates as a function of the study-level or study-arm-level average moderator value, not individual-participant-level data.
|
|||||||
| d Q1, Median, and Q3 refer to the first quartile, median, and third quartile (respectively) of the study-level or study-arm-level values of the moderator; note these do not necessarily represent individual-participant-level data. Because the regression is on the logit scale, these columns provide interpretable, back-transformed dropout rates in percent at Q1, Median, and Q3 moderator values. Data are presented as the bolded moderator value, followed by the estimated dropout percentage and 95% CI. |
7.4 Degree of Use sub-group meta-analysis results
| Moderatora | Moderator Value | Studies (dropout rates)b | Dropout (95% CI) | Residual Heterogeneity % (p) | Test for Moderation (p) |
|---|---|---|---|---|---|
| Alcohol | Model not fit - only one moderator value. | ||||
| Tobacco | 55(108) | 92.0 (<0.0001) | 0.8858 | ||
| Moderate | 1 (2) | 27.1 (6.8,65.2) | |||
| Heavy | 54 (106) | 24.8 (20.7,29.3) | |||
| Cocaine | 4(9) | 59.7 (0.0206) | 0.0173 | ||
| Light | 1 (1) | 22.4 (8.3,47.9) | |||
| Moderate | 3 (4) | 51.8 (36.0,67.2) | |||
| Heavy | 3 (4) | 66.7 (50.6,79.6) | |||
| Opioid | Model not fit - No studies fit the criteria. | ||||
| Methamphetamine | Model not fit - No studies fit the criteria. | ||||
| Depressants | Model not fit - No studies fit the criteria. | ||||
| Cannabis | 8(17) | 71.3 (<0.0001) | 0.5511 | ||
| Light | 2 (5) | 32.8 (21.3,46.7) | |||
| Moderate | 3 (6) | 32.9 (22.4,45.4) | |||
| Heavy | 3 (6) | 40.7 (30.1,52.4) | |||
| Polysubstance | Model not fit - No studies fit the criteria. | ||||
| Hallucinogen | Model not fit - No studies fit the criteria. | ||||
| Heroin | Model not fit - No studies fit the criteria. | ||||
| Major stimulant | Model not fit - No studies fit the criteria. | ||||
| GHB | Model not fit - No studies fit the criteria. | ||||
| a Sub-group meta-analyses were calculated for degree of use pattern categories within each substance type. | |||||
| b The number of studies and study-arms included varies by substance because of the variety of substances investigated across studies. When dropout rates were averaged across study-arms, either because of pooled moderators or dropout rates, the study has only a single dropout rate, regardless of how many study-arms were included. |
7.5 Comorbid diagnosis sub-group meta-regression results
| Moderatora | Studies (dropout rates)b | Logit regressionc | Dropout at Q1d | Dropout at Median | Dropout at Q3 | Residual Heterogeneity % (p) | Test for Moderation (p) |
|---|---|---|---|---|---|---|---|
| Mood Disorder | 23 (49) | -0.4623-0.0050X | 14: 37.0 (28.8,46.0) | 21: 36.2(28.3,44.9) | 29: 35.3(27.6,43.8) | 92.1 (<0.0001) | 0.2395 |
| Anxiety Disorder | 12 (24) | 0.0363-0.0216X | 6: 47.8 (34.8,61.2) | 14: 43.6(33.1,54.6) | 23: 38.6(27.3,51.2) | 89.4 (<0.0001) | 0.2054 |
| Comorbid Substance Use Dependence/Addiction | 9 (20) | -0.7248+0.0119X | 23: 39.0 (24.2,56.0) | 41: 44.1(30.1,59.2) | 52: 47.3(31.3,63.9) | 92.1 (<0.0001) | 0.3016 |
| Personality Disorder | 16 (32) | -0.5608-0.0047X | 11: 35.2 (23.3,49.3) | 24: 33.8(23.8,45.4) | 42: 31.9(22.5,42.9) | 91.8 (<0.0001) | 0.5183 |
| Psychotic Disorder | 6 (10) | 0.4679-0.0184X | 41: 42.7 (26.8,60.2) | 47: 40.2(25.9,56.4) | 89: 23.6(8.4,50.8) | 89.7 (<0.0001) | 0.2011 |
| Other Psychological Diagnoses | Model not fit - only one study fits the criteria. | ||||||
| a Separate meta-regressions were calculated for each comorbid diagnosis. | |||||||
| b The number of studies and dropout rates included varies by diagnosis because of differences in reporting across studies. When dropout rates were averaged across study-arms, either because of pooled moderators or dropout rates, the study has only a single dropout rate, regardless of how many study-arms were included. | |||||||
c Because the regression was calculated on the logit scale, the parameter estimates are reported on the logit scale. To use the regression to get proportion dropout, enter the value of the moderator of interest into the regression equation, and back-transform to a proportion using a function like the transf.ilogit function in the metafor package in R. The regression represents dropout rates as a function of the study-level or study-arm-level average moderator value, not individual-participant-level data.
|
|||||||
| d Q1, Median, and Q3 refer to the first quartile, median, and third quartile (respectively) of the study-level or study-arm-level values of the moderator; note these do not necessarily represent individual-participant-level data. Because the regression is on the logit scale, these columns provide interpretable, back-transformed dropout rates in percent at Q1, Median, and Q3 moderator values. Data are presented as the bolded moderator value, followed by the estimated dropout percentage and 95% CI. |