Covariate-adjusted survival analyses in propensity-score matched samples: imputing potential time-to-event outcomes

Matching on an estimated propensity score is frequently used to estimate the effects of treatments from observational data. Since the 1970s, different authors have proposed methods to combine matching at the design stage with regression adjustment at the analysis stage when estimating treatment effects for continuous outcomes. Previous work has consistently shown that the combination has generally superior statistical properties than either method by itself. In biomedical and epidemiological research, survival or time-to-event outcomes are common. We propose a method to combine regression adjustment and propensity score matching to estimate survival curves and hazard ratios based on estimating an imputed potential outcome under control for each successfully matched treated subject, which is accomplished using either an accelerated failure time parametric survival model or a Cox proportional hazard model that is fit to the matched control subjects. That is, a fitted model is then applied to the matched treated subjects to allow simulation of the missing potential outcome under control for each treated subject. Conventional survival analyses (e.g., estimation of survival curves and hazard ratios) can then be conducted using the observed outcome under treatment and the imputed outcome under control. We evaluated the repeated-sampling bias of the proposed methods using simulations. When using nearest neighbor matching, the proposed method resulted in decreased bias compared to crude analyses in the matched sample. We illustrate the method in an example prescribing beta-blockers at hospital discharge to patients hospitalized with heart failure.