Propensity score weighting methods for causal subgroup analysis with time-to-event outcomes

Evaluating causal effects of an intervention in pre-specified subgroups is a standard goal in comparative effectiveness research. Despite recent advancements in causal subgroup analysis, research on time-to-event outcomes has been lacking. This article investigates the propensity score weighting method for causal subgroup survival analysis. We introduce two causal estimands, the subgroup marginal hazard ratio and subgroup restricted average causal effect, and provide corresponding propensity score weighting estimators. We analytically established that the bias of subgroup-restricted average causal effect is determined by subgroup covariate balance. Using extensive simulations, we compare the performance of various combinations of propensity score models (logistic regression, random forests, least absolute shrinkage and selection operator, and generalized boosted models) and weighting schemes (inverse probability weighting, and overlap weighting) for estimating the causal estimands. We find that the logistic model with subgroup-covariate interactions selected by least absolute shrinkage and selection operator consistently outperforms other propensity score models. Also, overlap weighting generally outperforms inverse probability weighting in terms of balance, bias and variance, and the advantage is particularly pronounced in small subgroups and/or in the presence of poor overlap. We applied the methods to the observational Comparing Options for Management: PAtient-centered REsults for Uterine Fibroids study to evaluate the causal effects of myomectomy versus hysterectomy on the time to disease recurrence in a number of pre-specified subgroups of patients with uterine fibroids.