Primary Submission Category: Randomized Designs and Analyses
On the nonparametric identification of the proportion of always survivors
Authors: Veronica Ballerini, Alessandra Mattei, Fabrizia Mealli,
Presenting Author: Veronica Ballerini*
We often aim to evaluate the treatment effect on an outcome variable that may be censored by a time-to-event intermediate variable, e.g., the effect of a new therapy on patients’ quality of life two years after treatment; such evaluation is possible only if the patients are still alive at the time of measurement. A widely used approach in such scenarios is the principal stratification, which makes it possible to define the Survivor Average Causal Effect (SACE) estimand—i.e., a contrast between potential outcomes for the subgroup of individuals who would have survived under both treatment and control. Recently, time-varying SACE-like estimands have been proposed, focusing on the subgroup of those who would have survived at least until a given time t. For identification, the monotonicity assumption is typically invoked. In this work, we prove that it is always possible to nonparametrically identify the proportion of “always survivors” for at least one time t—and, in continuous time, for an infinite number of times in a given interval—under minimal assumptions and relaxing monotonicity. Specifically, it is possible to prove the identifiability in the time interval bounded by the minima of the potential intermediate time-to-event variables, simply assuming these minima differ. We apply this theoretical framework to a case of safety assessment in RCTs to highlight its practical relevance. Furthermore, we introduce a time-varying estimand for safety analysis in this context.