Causal effects on non-terminal event time with application to antibiotic usage and future resistance

Comparing future antibiotic resistance levels resulting from different antibiotic treatments is challenging because some patients may survive only under one of the antibiotic treatments. We embed this problem within a semi-competing risks approach to study the causal effect on resistant infection, treated as a non-terminal event time. We argue that existing principal stratification estimands for such problems exclude patients for whom a causal effect is well-defined and is of clinical interest. Therefore, we present a new principal stratum, the infected-or-survivors (ios). The ios is the subpopulation of patients who would have survived or been infected under both antibiotic treatments. This subpopulation is more inclusive than previously defined subpopulations. We target the causal effect among these patients, which we term the feasible-infection causal effect (FICE). We develop large-sample bounds under novel assumptions, and discuss the plausibility of these assumptions in our application. As an alternative, we derive FICE identification using two illness-death models with a bivariate frailty random variable. These two models are connected by a cross-world correlation parameter. Estimation is performed by an expectation-maximization algorithm followed by a Monte Carlo procedure. We apply our methods to detailed clinical data obtained from a hospital setting.