Time‐dependent summary receiver operating characteristics for meta‐analysis of prognostic studies

Prognostic studies are widely conducted to examine whether biomarkers are associated with patient's prognoses and play important roles in medical decisions. Because findings from one prognostic study may be very limited, meta‐analyses may be useful to obtain sound evidence. However, prognostic studies are often analyzed by relying on a study‐specific cut‐off value, which can lead to difficulty in applying the standard meta‐analysis techniques. In this paper, we propose two methods to estimate a time‐dependent version of the summary receiver operating characteristics curve for meta‐analyses of prognostic studies with a right‐censored time‐to‐event outcome. We introduce a bivariate normal model for the pair of time‐dependent sensitivity and specificity and propose a method to form inferences based on summary statistics reported in published papers. This method provides a valid inference asymptotically. In addition, we consider a bivariate binomial model. To draw inferences from this bivariate binomial model, we introduce a multiple imputation method. The multiple imputation is found to be approximately proper multiple imputation, and thus the standard Rubin's variance formula is justified from a Bayesian view point. Our simulation study and application to a real dataset revealed that both methods work well with a moderate or large number of studies and the bivariate binomial model coupled with the multiple imputation outperforms the bivariate normal model with a small number of studies. Copyright © 2016 John Wiley & Sons, Ltd.