Longitudinal Outcomes Truncated by Death: Causal Estimands and Bayesian Estimators

Abstract

In randomized controlled trials with longitudinal outcomes, death before the end of follow-up poses a fundamental challenge: after death, the outcome is no longer a real-valued measurement. This complicates the definition and interpretation of causal estimands, particularly when treatment may affect both survival and longitudinal outcomes. We review existing estimands for longitudinal outcomes truncated by death and clarify the assumptions required for their identification and estimation. We show that these estimands fall into two broad classes, distinguished by whether they require additional assumptions to compare longitudinal outcomes beyond death. Such assumptions may be inappropriate in chronic diseases, either because i) death and longitudinal outcomes are driven by the same underlying biological process or ii) the relative desirability of survival with poor function versus death may depend on individual preferences. We compare the behavior of the estimands in a simulation study using Bayesian estimators and illustrate their use with data from a randomized controlled trial in amyotrophic lateral sclerosis. We argue that, in the presence of death truncation, pairing the survivor average causal effect with the restricted mean survival time estimand provides an interpretable characterization of treatment effects on longitudinal and survival outcomes.