Development of biomarker combinations for postoperative acute kidney injury via Bayesian model selection in a multicenter cohort study

Background Acute kidney injury (AKI) is a frequent complication of cardiac surgery. We sought prognostic combinations of postoperative biomarkers measured within 6 h of surgery, potentially in combination with cardiopulmonary bypass time (to account for the degree of insult to the kidney). We used data from a large cohort of patients and adapted methods for developing biomarker combinations to account for the multicenter design of the study. Methods The primary endpoint was sustained mild AKI, defined as an increase of 50% or more in serum creatinine over preoperative levels lasting at least 2 days during the hospital stay. Severe AKI (secondary endpoint) was defined as a serum creatinine increase of 100% or more or dialysis during hospitalization. Data were from a cohort of 1219 adults undergoing cardiac surgery at 6 medical centers; among these, 117 developed sustained mild AKI and 60 developed severe AKI. We considered cardiopulmonary bypass time and 22 biomarkers as candidate predictors. We adapted Bayesian model averaging methods to develop center-adjusted combinations for sustained mild AKI by (1) maximizing the posterior model probability and (2) retaining predictors with posterior variable probabilities above 0.5. We used resampling-based methods to avoid optimistic bias in evaluating the biomarker combinations. Results The maximum posterior model probability combination included plasma N-terminal-pro-B-type natriuretic peptide, plasma heart-type fatty acid binding protein, and change in serum creatinine from before to 0–6 h after surgery; the median probability combination additionally included plasma interleukin-6. The center-adjusted, optimism-corrected AUCs for these combinations were 0.80 (95% CI: 0.78, 0.87) and 0.81 (0.78, 0.87), respectively, for predicting sustained mild AKI, and 0.81 (0.76, 0.90) and 0.83 (0.76, 0.90), respectively, for predicting severe AKI. For these data, the Bayesian model averaging methods yielded combinations with prognostic capacity comparable to that achieved by standard frequentist methods but with more parsimonious models. Conclusions Pending external validation, the identified combinations could be used to identify individuals at high risk of AKI immediately after cardiac surgery and could facilitate clinical trials of renoprotective agents. Electronic supplementary material The online version of this article 10.1186/s40364-018-0117-z) contains supplementary material, which is available to authorized users.

Item S1: R code for the primary analysis.
Note: This code was tailored the code for the data at hand. The user of this code should check each line to ensure that it is appropriate for his/her data. In addition, the user should be aware that aspects of his/her data may complicate the analysis and/or require modifications to sections of the code.
The densities are scaled by the proportion of cases and controls to reflect the prevalence of sustained mild AKI. Abbreviations: AKI = acute kidney injury; max post prob combination = maximum posterior probability combination; median prob combination = median probability combination Figure S2: Distribution of biomarker combinations in the largest center, stratified by sustained mild AKI case status.
In contrast to Figure S1, the distributions are not scaled to reflect the prevalence of mild AKI cases. Abbreviations: AKI = acute kidney injury; max post prob combination = maximum posterior probability combination; median prob combination = median probability combination Figure S3: Distribution of three biomarkers (log plasma NT-proBNP, change in sCr, and log plasma h-FABP) among controls (individuals without sustained mild AKI), stratified by center.
Abbreviations: AKI = acute kidney injury; NT-proBNP = N-terminal-pro-B-type natriuretic peptide, sCr = serum creatinine, h-FABP = heart-type fatty acid binding protein.  Figure S4: Posterior model probability of the combinations selected by the BMA methods across the 1000 bootstrap samples. The first plot corresponds to the maximum posterior probability combination and the second plot corresponds to the median probability combination. "Truncated" means the combination was not considered by the BMA algorithm in that particular bootstrap sample; the truncated value is the minimum posterior model probability in that sample. "Index" indicates the bootstrap sample number. Figure S5: Posterior variable probabilities for each of the candidate predictors across 1000 bootstrap samples. "Index" indicates the bootstrap sample number. Figure S6: Posterior variable probabilities for each of the candidate predictors when each patient was left out in turn (only observations non-missing on all candidate predictors were included). "Index" indicates the (arbitrary) rank order of the patient in the analysis dataset. Figure S7: Performance (in terms of the center-adjusted AUC) of the estimated selected combinations across 1000 bootstrap samples. The first plot corresponds to the AUC for the outcome of sustained mild AKI; the second plot corresponds to the AUC for the outcome of severe AKI. "Index" indicates the bootstrap sample number.
In order to explore the impact of deleting observations with missing data, we compared the results of a multiple imputation analysis to the results of our complete-case analysis. First, we created ten completed datasets via multiple imputation using the R package mice. Then, we compared results across these datasets.
1. Average of non-zero MLEs across maximum posterior model probability combinations: In each completed dataset, we applied BMA and stored the estimates for the maximum posterior model probability combinations. Then, we averaged the estimates across the ten datasets. Below are the results for variables whose average estimate was not zero: we present the number of imputed datasets where the variable was included in the maximum posterior model probability combination and the average estimated odds ratio (averaged on the log scale) across the ten datasets. We also present the complete-case odds ratio estimates for the variables in the complete-case maximum posterior model probability combination (plasma NT-proBNP, plasma h-FABP, and change in serum creatinine; also provided in Table 3 of the paper) for comparison. Comparing the imputation results to those based on the complete-case analysis, we see that the variables in the maximum posterior model probability combination in the complete-case analysis are in the maximum posterior model probability combination in all ten of the imputed datasets. Plasma IL-6, which was not in the maximum posterior model probability combination in the complete-case analysis, but was in the median probability combination in the complete-case analysis, was in the maximum posterior model probability combination in nine out of ten imputed datasets. In addition, the average odds ratio for these variables is similar to those from the complete-case analysis.

Variable
2. We considered two different approaches to summarizing the posterior variable probabilities across imputed datasets. a. Average of posterior variable probabilities across imputations: the table below provides the average posterior variable probabilities for the variables whose posterior variable probability averaged across the ten datasets was above 50%. We also present the posterior variable probability estimates from the complete-case analysis (also provided in Table 3 of the paper) for comparison. Comparing the imputation results to those based on the complete-case analysis, we see that the same variables chosen to be in the median probability combination in the complete-case analysis had an average posterior variable probability above 50% across the imputed datasets. Furthermore, the average posterior variability probability of these variables is similar to that estimated in the complete-case analysis, though the average posterior variable probability for plasma IL-6 is somewhat higher in the imputation analysis.

Variable
b. Below we report the number of imputed datasets where the variable's posterior variable probability was above 50% (for variables who achieved this cutoff in at least one dataset).

Variable # Datasets Log plasma MCP-1
1 Log plasma IL-10 1 Log plasma IL-6 9 Log plasma NT-proBNP 10 Log plasma h-FABP 10 Change in sCr 10 We see that the variables selected to be in the median probability combination in the complete-case analysis (plasma IL-6, plasma NT-proBNP, plasma h-FABP, and change in serum creatinine) had posterior variable probabilities above 50% in nine or more of the imputed datasets.
3. In each imputed dataset, we applied the BMA methods and evaluated the apparent AUC of the selected combinations. We present the average apparent AUC across the ten datasets. For comparison, we also present the apparent AUCs based on the complete-case analysis. We see that the average apparent AUC across the ten imputed datasets is somewhat lower than the apparent AUC from the complete-case analysis (note that these estimates have not been corrected for optimistic bias and so differ from the main results reported in the paper). However, the differences in AUC are generally modest.