Estimating treatment effects from observational data under truncation by death using survival-incorporated quantiles
The issue of "truncation by death" commonly arises in clinical research: subjects may die before their follow-up assessment, resulting in undefined clinical outcomes. To address this issue, we focus on survival-incorporated quantiles -- quantiles of a composite outcome combining death and clinical outcomes -- to summarize the effect of treatment. Using inverse probability of treatment weighting (IPTW), we propose an estimator for survival-incorporated quantiles from observational data, applicable to settings of both point treatment and time-varying treatments. We establish consistency and asymptotic normality of the estimator under both the true and estimated propensity scores. While the variance properties of IPTW estimators for the mean have been studied, to our knowledge, this article is the first to show that the IPTW quantile estimator using the estimated propensity score yields lower asymptotic variance than the IPTW quantile estimator using the true propensity score. Extensive simulations show that survival-incorporated quantiles provide a simple and useful summary measure and confirm that using the estimated propensity score reduces the root mean square error. We apply our method to estimate the effect of statins on the change in cognitive function, incorporating death, using data from the Long Life Family Study (LLFS) -- a multicenter observational study of 4953 older adults with familial longevity. Our results indicate no significant difference in cognitive decline between statin users and non-users with a similar age- and sex-distribution at baseline. This study not only contributes to understand the cognitive effects of statins but also provides insights into analyzing clinical outcomes in the presence of death.