Propensity score matching for treatment delay effects with observational survival data

In observational studies with a survival outcome, treatment initiation may be time dependent, which is likely to be affected by both time-invariant and time-varying covariates. In situations where the treatment is necessary for the study population, all or most subjects may be exposed to the treatment sooner or later. In this scenario, the causal effect of interest is the delay in treatment reception. A simple comparison of those receiving treatment early vs. those receiving treatment late might not be appropriate, as the timing of the treatment reception is not randomized. Extending Lu's matching design with time-varying covariates, we propose a propensity score matching strategy to estimate the treatment delay effect. The goal is to balance the covariate distribution between on-time treatment and delayed treatment groups at each time point using risk set matching. Our simulation study shows that, in the presence of treatment delay effects, the matching-based analyses clearly outperform the conventional regression analysis using the naive Cox proportional hazards model. We apply this method to study the treatment delay effect of 17 alpha-hydroxyprogesterone caproate (17P) for patients with recurrent preterm birth.