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Read data.

D <- readSheet("Mortality")

Tidy up the data (do not show the code).

study treatment responders sampleSize
ARISTOTLE Apixaban_5_mg 603 9120
ARISTOTLE Warfarin 669 9081
ARISTOTLE-J Apixaban_5_mg 0 74
ARISTOTLE-J Warfarin 0 74
ENGAGE AF-TIMI Edoxaban_30_mg 737 7034
ENGAGE AF-TIMI Edoxaban_60_mg 773 7035
ENGAGE AF-TIMI Warfarin 839 7036
J-ROCKET Rivaroxaban_15_mg 7 637
J-ROCKET Warfarin 5 637
RE-LY Dabigatran_110_mg 446 6015
RE-LY Dabigatran_150_mg 438 6076
RE-LY Warfarin 487 6022
ROCKET-AF Rivaroxaban_20_mg 208 7061
ROCKET-AF Warfarin 250 7062
Yamashita, 2012 Edoxaban_30_mg 0 131
Yamashita, 2012 Edoxaban_60_mg 1 131
Yamashita, 2012 Warfarin 1 129

Run the model using fixed-effects.

M <- mtc.model(network, type="consistency", linearModel=effect)
plot(M)

results <- mtc.run(M, n.adapt=nAdapt, n.iter=nIter, thin=thin)

Summary

Direct and indirect odds ratios and 95% confidence bounds are stored in mtcMortalityOddsRatios.csv.

or <- combineResults()
write.csv(or, file="mtcMortalityOddsRatios.csv", row.names=FALSE)
print(xtable(or), type="html", include.rownames=FALSE)
treatment Apixaban 5 mg Dabigatran 110 mg Dabigatran 150 mg Edoxaban 30 mg Edoxaban 60 mg Rivaroxaban 15 mg Rivaroxaban 20 mg Warfarin
Apixaban 5 mg vs 0.98 (0.82, 1.17) 1.01 (0.85, 1.20) 1.03 (0.88, 1.21) 0.98 (0.83, 1.14) 0.62 (0.18, 2.01) 1.08 (0.87, 1.34) 0.89 (0.79, 1.00)
Dabigatran 110 mg vs 1.02 (0.86, 1.22) 1.03 (0.90, 1.18) 1.05 (0.89, 1.25) 1.00 (0.84, 1.18) 0.63 (0.18, 2.08) 1.10 (0.87, 1.39) 0.91 (0.80, 1.04)
Dabigatran 150 mg vs 0.99 (0.83, 1.18) 0.97 (0.85, 1.11) 1.02 (0.86, 1.21) 0.97 (0.82, 1.15) 0.62 (0.17, 2.01) 1.07 (0.85, 1.35) 0.88 (0.77, 1.01)
Edoxaban 30 mg vs 0.97 (0.83, 1.14) 0.95 (0.80, 1.12) 0.98 (0.83, 1.16) 0.95 (0.85, 1.06) 0.60 (0.17, 1.97) 1.05 (0.84, 1.30) 0.86 (0.78, 0.96)
Edoxaban 60 mg vs 1.02 (0.88, 1.20) 1.00 (0.84, 1.19) 1.03 (0.87, 1.22) 1.06 (0.95, 1.18) 0.64 (0.18, 2.06) 1.10 (0.89, 1.37) 0.91 (0.82, 1.01)
Rivaroxaban 15 mg vs 1.61 (0.50, 5.69) 1.58 (0.48, 5.64) 1.62 (0.50, 5.75) 1.66 (0.51, 5.88) 1.57 (0.49, 5.58) 1.73 (0.52, 6.21) 1.43 (0.44, 5.07)
Rivaroxaban 20 mg vs 0.93 (0.75, 1.16) 0.91 (0.72, 1.14) 0.94 (0.74, 1.18) 0.96 (0.77, 1.19) 0.91 (0.73, 1.12) 0.58 (0.16, 1.90) 0.83 (0.69, 1.00)
Warfarin vs 1.12 (1.00, 1.26) 1.10 (0.96, 1.26) 1.13 (0.99, 1.30) 1.16 (1.04, 1.29) 1.10 (0.99, 1.22) 0.70 (0.20, 2.26) 1.21 (1.00, 1.46)

Forest plots, NOAC vs NOAC

noac <- unique(D[treatment != "Warfarin", treatment])
for (i in 1:length(noac)) {
  forest(relative.effect(results, noac[i], noac[1:length(noac) != i]))
}

Diagnostics

summary(results)
## $measure
## [1] "Log Odds Ratio"
## 
## $summaries
## 
## Iterations = 5010:30000
## Thinning interval = 10 
## Number of chains = 4 
## Sample size per chain = 2500 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                                  Mean      SD  Naive SE Time-series SE
## d.Warfarin.Apixaban_5_mg     -0.11624 0.05847 0.0005847      0.0005987
## d.Warfarin.Dabigatran_110_mg -0.09461 0.06795 0.0006795      0.0007573
## d.Warfarin.Dabigatran_150_mg -0.12557 0.06852 0.0006852      0.0006751
## d.Warfarin.Edoxaban_30_mg    -0.14707 0.05323 0.0005323      0.0006062
## d.Warfarin.Edoxaban_60_mg    -0.09213 0.05294 0.0005294      0.0005313
## d.Warfarin.Rivaroxaban_15_mg  0.36889 0.61858 0.0061858      0.0062678
## d.Warfarin.Rivaroxaban_20_mg -0.19007 0.09645 0.0009645      0.0009920
## 
## 2. Quantiles for each variable:
## 
##                                 2.5%      25%      50%      75%     97.5%
## d.Warfarin.Apixaban_5_mg     -0.2296 -0.15494 -0.11644 -0.07654 -0.001855
## d.Warfarin.Dabigatran_110_mg -0.2286 -0.14116 -0.09423 -0.04873  0.036934
## d.Warfarin.Dabigatran_150_mg -0.2590 -0.17157 -0.12615 -0.07944  0.008336
## d.Warfarin.Edoxaban_30_mg    -0.2511 -0.18312 -0.14708 -0.11150 -0.042363
## d.Warfarin.Edoxaban_60_mg    -0.1949 -0.12774 -0.09230 -0.05635  0.012399
## d.Warfarin.Rivaroxaban_15_mg -0.8165 -0.03943  0.35947  0.76733  1.623675
## d.Warfarin.Rivaroxaban_20_mg -0.3760 -0.25527 -0.19058 -0.12383 -0.003099
## 
## 
## $DIC
##     Dbar       pD      DIC 
## 14.79001 13.15944 27.94945 
## 
## attr(,"class")
## [1] "summary.mtc.result"

Sampler diagnostics.

gelman.plot(results)

gelman.diag(results)
## Potential scale reduction factors:
## 
##                              Point est. Upper C.I.
## d.Warfarin.Apixaban_5_mg              1          1
## d.Warfarin.Dabigatran_110_mg          1          1
## d.Warfarin.Dabigatran_150_mg          1          1
## d.Warfarin.Edoxaban_30_mg             1          1
## d.Warfarin.Edoxaban_60_mg             1          1
## d.Warfarin.Rivaroxaban_15_mg          1          1
## d.Warfarin.Rivaroxaban_20_mg          1          1
## 
## Multivariate psrf
## 
## 1
plot(results)

autocorr.plot(results$samples)

Assess the degree of heterogeneity and inconsistency.

anohe <- mtc.anohe(network, n.adapt=nAdapt, n.iter=nIter, thin=thin)
summary(anohe)
## Analysis of heterogeneity
## =========================
## 
## Per-comparison I-squared:
## -------------------------
## 
##                  t1                t2  i2.pair  i2.cons incons.p
## 1     Apixaban_5_mg          Warfarin  0.00000  0.00000       NA
## 2 Dabigatran_110_mg Dabigatran_150_mg       NA       NA       NA
## 3 Dabigatran_110_mg          Warfarin       NA       NA       NA
## 4 Dabigatran_150_mg          Warfarin       NA       NA       NA
## 5    Edoxaban_30_mg    Edoxaban_60_mg 83.76690 37.19692       NA
## 6    Edoxaban_30_mg          Warfarin 80.09397 18.12514       NA
## 7    Edoxaban_60_mg          Warfarin  0.00000  0.00000       NA
## 8 Rivaroxaban_15_mg          Warfarin       NA       NA       NA
## 9 Rivaroxaban_20_mg          Warfarin       NA       NA       NA
## 
## Global I-squared:
## -------------------------
## 
##   i2.pair i2.cons
## 1       0       0
plot(anohe)
## Analysis of heterogeneity -- convergence plots
## Unrelated Study Effects (USE) model:

## Unrelated Mean Effects (UME) model:

## Consistency model: