Evaluating Martingale and Counting Process-Based Covariance and Correlation Estimators for Multivariate Survival Data

Presented by Jiaying Dong
Masters Candidate in Biostatistics
Plan B Adviser: Benjamin Langworthy

Estimating associations between multiple time to event outcomes is an important yet challenging task in survival analysis due to the presence of censoring and competing risks. Traditional measures of correlation and covariance are not valid in this setting. Langworthy et al. [1] proposed a class of time-indexed estimators based on martingale and counting process methods that account for censoring and competing risk and allow for estimations of covariance and correlation between event types. This project evaluates the performance of these estimators through simulation studies and applies them to real world electronic health record data from M Health Fairview Hospital system.

Simulation scenarios varied by sample size, censoring level, time point, and the presence of competing risks. We accessed bias, standard deviation, and coverage probabilities of bootstrap confidence intervals of the estimators. Both estimators performed well with low bias, stable variance and close to 95% coverage probability. In the clinical data application, we examined associations between orders for lactic acid testing, telemetry monitoring and antibiotic administration following clinical deterioration, using the same estimators. The results demonstrated that these martingale and counting process based estimators can be effectively applied in multivariate survival settings and are capable of handling censoring and competing risks, making them useful tools for analyzing associations between time to event outcomes.