Truncation-by-Death

Evaluating quality-of-life (QoL) outcomes in populations with high mortality risk is complicated by truncation by death, since QoL is undefined for individuals who do not survive to the planned measurement time. We propose a framework that jointly models the distribution of QoL and survival without extrapolating QoL beyond death. Inspired by multistate formula tions, we extend the joint characterization of binary health states and mortality to continuous QoL outcomes. Because treatment effects cannot be meaningfully summarized in a single one dimensional estimand without strong assumptions, our approach simultaneously considers both survival and the joint distribution of QoL and survival with the latter conveniently displayed in a simplex. We develop assumption-lean, semiparametric estimators based on efficient influence functions, yielding flexible, root-n consistent estimators that accommodate machine-learning methods while making transparent the conditions these must satisfy. The proposed method is illustrated through simulation studies and two real-data applications.

Analysis of data from randomized controlled trials in vulnerable populations requires special attention when assessing treatment effect by a score measuring, e.g., disease stage or activity together with onset of prevalent terminal events. In reality, it is impossible to disentangle a disease score from the terminal event, since the score is not clinically meaningful after this event. In this work, we propose to assess treatment interventions simultaneously on the terminal event and the disease score in the absence of a terminal event. Our proposal is based on a natural data-generating mechanism respecting that a disease score does not exist beyond the terminal event. We use modern semi-parametric statistical methods to provide robust and efficient estimation of the risk of terminal event and expected disease score conditional on no terminal event at a pre-specified landmark time. We also use the simultaneous asymptotic behavior of our estimators to develop a powerful closed testing procedure for confirmatory assessment of treatment effect on both onset of terminal event and level of disease score in the absence of a terminal event. A simulation study mimicking a large-scale outcome trial in chronic kidney patients as well as an analysis of that trial is provided to assess performance.