---
title: Supplement to Baseline Creatinine Determination Method Impacts Association Between Pediatric Acute Kidney Injury and Clinical Outcomes
author: 


output: 
  word_document:
    reference_docx: word-style-reference-supplement.docx
bibliography: AKI_CKD.bib
csl: american-medical-association-parentheses.csl

header-includes:
- \usepackage{placeins}

---


W. Alton Russell, David Scheinker, Scott M. Sutherland
<br>

# Supplementary methods

**Height imputation:** All available height measurements for all patients between 3 months and 18 years of age were used to develop the regression for imputing height when not available. Height was regressed on age using a third-degree polynomial regression separately for the male and female sexes. For patients who did not have any height measurements in the medical record, the regression was used to estimate their height based on age. For patients with one or more heights in the medical record, but no height measurements within 90 days of admission, the height closest to admission date was considered in the imputation as follows: the change in height from the nearest height measurement to the time of admission was estimated by the regression equation and that estimated difference was added to the nearest height measurement. For patients with a height measurement within 90 days of admission, the regression was not used.

The regression equations were $Y=117.6 + 1180X - 1634 X^2 + 147.0X^3$ for male patients and $119.9 + 10350X - 2066X^2 -136.1X^3$ for female patients, where Y is height in centimeters and X is age in seconds.

**Rationale behind receiver operator characteristic (ROC) analysis:** In the context of diagnosing AKI using the SCr relative increase criteria, sensitivity and specificity of AKI as a predictor of clinical outcomes depends on two things: (1) how many patients test positive (i.e., how many patients have a relative SCr increase over baseline that is more than the threshold of 50%) and (2) how strongly testing positive is correlated with the clinical outcomes being predicted. The baseline determination methods we compared led to very different number of patients testing positive for AKI, making it possible that the relative sensitivity and specificity of AKI as a predictor of clinical outcomes under competing baseline definitions were driven more by differences in how baseline influences AKI incidence than by how baseline influences the association between experiencing a SCr increase over baseline and experiencing clinical outcomes. In fact, visually comparing the plot of AKI incidence in Figure 2 to the sensitivity and specificity of AKI as a predictor of clinical outcomes under baseline alternatives plotted in Figure 3, suggests that AKI incidence is driving the relative predictive performance. The shapes of the sensitivity plots somewhat resemble the incidence plot, particularly if you ignore the imputed baseline method, and the shapes of the specificity plots strongly resemble a vertically mirrored image of the incidence plot. Therefore, we performed ROC analysis as a way of decoupling differences in *the association between increases in SCr over baseline and clinical outcomes* from differences in *AKI incidence*. In ROC analysis, all possible relative increase thresholds are considered simultaneously, making AUROC a measure of discriminative performance that is not influenced by how many patients are considered AKI-positive under the competing baseline determination methods. While we report specificity and sensitivity using the KDIGO relative increase threshold (50% over estimated baseline) due to the clinical importance, we consider AUROC to be a more direct estimate of how baseline determination method influences the association between increases in SCr over baseline and clinical outcomes.

**Analysis code:** The analysis was conducted entirely in the R programming language in an R markdown document, which integrates the analytic code with the paper itself. This was done to facilitate sharing and reproducibility. The first author will share the R markdown files with any researchers who request it. However, the dataset of individual patient data cannot be shared.

# Mathematical relationship between imputed baseline and minimum inpatient GFR

Patients are diagnosed with AKI using the relative increase criteria if $\frac{s}{b} \geq 1.5$, where $s$ is the maximum inpatient creatinine in the first 7 days of hospitalization and $b$ is the baseline. Using the Schwartz bedside GFR equation, the minimum inpatient GFR is $g = \frac{0.413h}{s}$.  It follows that for patients with AKI, $s \geq 1.5b$ and therefore $g \leq \frac{0.413h}{1.5b}$. For the Schwartz bedside baseline method, $b = \frac{0.413h}{g^*}$, where $g^*$ is a reference GFR. Through substitution we derive that $g \leq \frac{g^*}{1.5}$. Therefore, using the Schwartz bedside method with a reference GFR of 120, patients are considered positive for AKI if they have a minimum inpatient GFR below $\frac{120}{1.5} = 80$ mL/min/1.74 m^2^ during the first 7 days of hospitalization. Using the Schwartz bedside method with a reference GFR of 107.4, the minimum GFR must be below $\frac{107.3}{1.5} = 71.5$ mL/min/1.74 m^2^. 

For the FAS height method, an inequality for $g$ can be found as a function of patient height, and for the FAS age method an expression can be found as a function of height, age and sex. Note that these bounds only apply to the relative increase criteria of the AKI definition; patients who meet the absolute increase criteria will be considered AKI-positive regardless of baseline determination method or minimum inpatient GFR.


#####

# Supplementary tables

**Table S1: Mathematical formulations for baseline SCr determination methods**

| Baseline name | Mathematical formulation for determining baseline serum creatinine ($b$) |
|---------------------|---------------------------|
| Schwartz 120 | $b = \frac{0.413h}{120}$ |
| Schwartz 107 | $b = \frac{0.413h}{107.3}$ |
| FAS height | $b = 3.94 - 0.134h + 0.00176h^2 - 9.84 \times 10^{-6}h^3 + 2.04\times 10^{-8}h^4$ |
| FAS age | $b = 0.21 + 0.57a - 0.0075a^2 + 0.00064a^3 - 0.000016a^4$ if male; |
|         | $b = 0.23 + 0.034a - 0.0018a^2 + 0.00017a^3 - 0.0000051a^4$ if female |
| Lowest |  $b = \min\{ p \in P\}$ |
| Second lowest | $b = \min\{p^* : p^* \in P, p^* > \min \{p \in P\}\}$ |
| Mean    | $b = (\sum_{n=0}^N p_n)/N$ |
| Proximal |  $b = \arg\max_{\{p \in P\}} t_p$ |
| [Empirical]-[imputed] | if $P \neq \emptyset$ then use [empirical], otherwise use [imputed] | 

Where $b$ is the estimated pre-admission baseline serum creatinine, $P$ is the set of serum creatinine values measured in the 92-day period preceding admission, $h$ is the patient's height in cm, $t_p$ is the time of a serum creatinine result, $g$ is the reference glomerular filtration rate, and $a$ is age in years. The FAS height equation was derived from the original equation by substituting height in centimeters divided by 100 in for height in meters. Once baseline was determined, patients were classified as AKI+ during the stay if either of the following criteria were met for any inpatient SCr:

#### $s - min\{ a \in A \} \geq 0.3$ mg/dl  **(absolute increase criteria)**
#### $[\frac{s}{b} > 1.5]$ and $[t_s - t_{admit} < 7$ days$]$ **(relative increase criteria)**

where $s$ is an inpatient serum creatinine measurement, $A$ is the set of serum creatinine measurements from the preceding 48 hours of the hospitalization, $b$ is the estimated pre-admission baseline, $t_s$ is the time of the creatinine measurement and $t_{admit}$ is the time of admission.


#####

**Table S2: AKI-positive patients with an ICD-coded diagnosis by AKI stage**


```{r include = FALSE}
library(data.table)
library(flextable)

dt.AKI_diag_by_stage <- fread("AKI_diag_by_stage.csv")

## FORMAT FLEXTABLE
ts2 <- flextable(dt.AKI_diag_by_stage)
ts2 <- theme_box(ts2)
ts2 <- fontsize(ts2, size = 10, part = "all")
ts2 <- font(ts2, fontname = "Times", part = "all")
ts2 <- align(ts2, align = "left", part = "body")
ts2 <- align(ts2, align = "center", part = "header")
ts2 <- autofit(ts2)
```


`r ts2`
#####

# Supplementary figures


**Figure S1: Mean and standard deviation of baseline serum creatinine by imputation method**

![](baseline_mean_sd_imp_fig.png)

#####

**Figure S2: Matrix showing distribution of imputed baselines (diagonal), correlation scatter plots (lower left), and correlation coefficients (upper right) between each of four imputation methods.** The Schwartz methods shown here are with a reference GFR of 107.3 mL/min/1.73 m^2^. Using a different reference GFR for the Schwartz method can shift the distribution but does not impact correlation with other baseline methods.

![](imputed_bl_pairwise_fig.png)




#####


**Figure S3: Imputed baseline SCr by age (left) and by height (right).** Scatterplots showing individual patients with smoothed conditional mean plotted as line overtop. On the 'by height' plot, points are completely masked by the trendlines for all imputation methods besides FAS Age because those methods are calculated as functions of height. On the 'by age' plot, the points for 'FAS age' appear as two lines that separate for older ages, which represents the different functions applied to male and female patients which are similar for children but separate in adolescence.

![](imputed_by_age_height_fig.png)



#####

**Figure S4, incidence by imputation method among all patients**

![](p_inc_imputed_fig.png)

#####

**Figure S5: Sensitivity and specificity for AKI and clinical outcomes based on universal imputation method.** The sensitivity and specificity for predicting each clinical outcome (application of an ICD AKI code, development of post-hospitalization CKD, and mortality) is shown for each of the five baseline determination methods with 95% confidence intervals.

![](sens_spec_imp_fig.png)

#####

**Fig. S6: ROC curves for AKI and clinical outcomes based on universal imputation method (top) and AUROC of AKI as predictor of clinical outcomes under alternative SCr universal imputation methods with 95% confidence intervals (bottom).** AUROC curves for AKI as predictor of the three clinical outcomes according to baseline imputation method are shown. The AUROC curves were constructed by varying the relative increase threshold. Abbreviations: AKI, acute kidney injury; ROC, receiver operator characteristic curve; CKD, chronic kidney disease

![](ROC_and_AUC_imp_fig.png)



#####

**Figure S7, Matrix showing distribution of imputed baselines (diagonal), correlation scatter plots (lower left), and correlation coefficients (upper right) between four empirical methods and three imputed methods for patients with measured preadmission SCr.** Ridges in the density plots for the empirical methods are artifacts of SCr being reported as rounded to the nearest 0.1 mg/dL.




![](bl_pairwise_with_preSCr_fig.png)

#####

**Figure S8, Distribution of Estimated GFR implied by empirical baseline across methods**. GFR estimated using Schwartz bedside equation. Mean and standard deviation shown by point and solid lines. For reference, GFR of 107.3 (blue) and 120 (red) are shown using dashed lines.

![](bl_gfr_empirical.png)



#####

**Figure S9, incidence by baseline method for patients with measured preadmission SCr**

![](p_inc_preScr_fig.png)

#####

**Figure S10, incidence by baseline method for "empirical first" and universal imputation methods**

![](p_inc_empfirst_fig.png)


#####



**Figure S11, Sensitivity and specificity for AKI and clinical outcomes for empirical-first and universal imputation methods.** The sensitivity and specificity for predicting each clinical outcome (application of an ICD AKI code, development of post-hospitalization CKD, and mortality) is shown for each method ("X") with 95% confidence intervals (vertical bars). The uncertainty range around specificity point estimates ranged from 1.0% -- 3.1%, making the error bars difficult to see.

![](sens_spec_empfirst_fig.png)


#####

**Figure S12, Sensitivity analysis showing ROC curves (top) and AUROC (bottom) for AKI as a predictor of clinical outcomes based on baseline method for patients age 1 year -- 18 years of age with measured pre-admission SCr.** This was run as a sensitivity analysis to assess the impact of including patients as young as 3 months of age in the primary analysis. Patients between 3 months and 12 years of age are often assessed for AKI using these methods, but the imputation methods were developed and recommended for patients at least one year old.

![](ROC_and_AUC_over12mo_fig.png)



#####

**Figure S13, empirical cumulative distribution function for the interval between the first and last post-discharge SCr qualifying patients as developing post-hospitalization CKD** The interval between qualifying labs was at least [1, 7, 30, 60, 90] days apart for [94%, 85%, 72%, 65%, 60%] of patients classified as developing post-hospitalization CKD.

![](cdf_time_between_poststay_GFR.png)

#####

**Figure S14, ROC curves for AKI as a predictor of clinical outcomes based on baseline method for patients with measured pre-admission SCr with thresholds corresponding to each AKI stage indicated.**

![](ROC_with_stages.png)