Causal inference for semi-competing risks data

Abstract

An emerging challenge for time-to-event data is studying semi-competing risks, namely when two event times are of interest: a non-terminal event time (e.g. age at disease diagnosis), and a terminal event time (e.g. age at death). The non-terminal event is observed only if it precedes the terminal event, which may occur before or after the non-terminal event. Studying treatment or intervention effects on the dual event times is complicated because for some units, the non-terminal event may occur under one treatment value but not under the other. Until recently, existing approaches (e.g., the survivor average causal effect) generally disregarded the timeto-event nature of both outcomes. More recent research focused on principal strata effects within time-varying populations under Bayesian approaches. In this paper, we propose alternative non time-varying estimands, based on a single stratification of the population. We present a novel assumption utilizing the time-to-event nature of the data, which is weaker than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present nonparametric and semi-parametric estimation methods for right-censored data.

A matching framework for truncation by death problems

“…However, even in a carefully designed trial, outcomes for some study participants can be missing, or more precisely, ill-defined, because participants had died prior to date of outcome collection. This problem is known as "truncation by death" (Zhang and Rubin, 2003;Hayden et al, 2005;Egleston et al, 2006;Lee, 2009;Zhang et al, 2009;Ding et al, 2011;Tchetgen Tchetgen, 2014;Wang et al, 2017;Ding and Lu, 2017;Feller et al, 2017;Nevo and Gorfine, 2020).…”

“…As a result, there is a built-in tension between the strength of the assumptions researchers are willing to make and the degree to which causal effects can be identified from the observed data. Ordered by the increasing strength of the assumptions underpinning them, three main approaches have been considered for the SACE: constructing bounds (Zhang and Rubin, 2003;Lee, 2009;Nevo and Gorfine, 2020), conducting sensitivity analyses (Hayden et al, 2005;Egleston et al, 2006;Ding et al, 2011;Ding and Lu, 2017;Nevo and Gorfine, 2020) and leveraging additional assumptions for full identification (Hayden et al, 2005;Zhang et al, 2009;Ding et al, 2011;Ding and Lu, 2017;Feller et al, 2017;Wang et al, 2017).…”

Modeling semi‐competing risks data as a longitudinal bivariate process

“…Beyond the usual challenges of time-to-event analyses (i.e., structuring covariate effects, handling functions of time, and accommodating various forms of censoring and truncation), key challenges that arise in the analysis of semi-competing risks data are: (i) respecting the terminal event as a competing risk and (ii) structuring dependence between 𝑇 1 and 𝑇 2 . In the statistical literature, numerous frameworks for the analysis of semi-competing risks data have been proposed, including: methods grounded in causal inference (Egleston et al, 2006;Tchetgen Tchetgen, 2014;Nevo and Gorfine, 2020); methods based on structuring dependence via a copula (Fine et al, 2001;Peng and Fine, 2007;Li and Peng, 2015); the use of illness-death models (Xu et al, 2010;Lee et al, 2017Lee et al, , 2015; and the recently proposed cross-quantile residual ratio (Yang and Peng, 2016). While additional review details are provided in Section A.1 of the Supporting Information, we note that these methods either: (i) view dependence as a statistical nuisance, and not a potential source of new clinical knowledge; or (ii) focus on the role of the nonterminal event as a risk factor for the terminal event, thereby reframing the nonterminal event away from being an outcome of interest.…”