Doubly robust estimation of while-alive estimands in individually-randomized and cluster-randomized trials

Abstract

Randomized trials in chronic disease settings often measure treatment benefit through recurrent non-fatal events that are truncated by death, where conventional summaries either discard recurrences, conflate the treatment effect with survival, or treat death as censoring and forfeit a causal interpretation. While-alive estimands measure event burden per unit time alive, but doubly robust estimation for the exposure-weighted while-alive rate remains undeveloped, particularly in cluster-randomized trials (CRTs). We develop a doubly robust estimator based on a local Nelson-Aalen representation, with augmented estimating equations targeting the marginal hazard of the terminal event and the weighted recurrent event rate among those alive; the estimator accommodates multiple event types through prespecified clinical weights and remains consistent if either the censoring model or the outcome working models are correctly specified. For CRTs, we define a new pair of individual-average and cluster-average estimands under informative cluster size, with inference based on cluster-level influence functions. We establish component-wise double robustness and asymptotic normality, corroborate the theory in simulations, and illustrate the methods with reanalyses of data from two completed randomized trials.