A matching framework for truncation by death problems

Abstract

Even in a carefully designed randomized 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, known as truncation by death, means that the treated and untreated are no longer balanced with respect to covariates determining survival. To overcome this problem, researchers often utilize principal stratification and focus on the Survivor Average Causal Effect (SACE). The SACE is the average causal effect among the subpopulation that will survive regardless of treatment status. In this paper, we present a new approach based on matching for SACE identification and estimation. We provide an identification result for the SACE that motivates the use of matching to restore the balance among the survivors. We discuss various practical issues, including the choice of distance measures, possibility of matching with replacement, post-matching crude and model-based SACE estimators, and non-parametric tests. Our simulation results demonstrate the flexibility and advantages of our approach. Because the cross-world assumptions needed for SACE identification can be too strong and are unfalsifiable, we also present sensitivity analysis techniques and illustrate their use in real data analysis. Finally, a recent alternative for SACE that does not demand cross-world unfalsifiable assumptions targets the conditional separable effects. We show how our approach can also be utilized to estimate these causal effects.

A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies

“…The aforementioned selection bias resembles the issue of truncation by death (Rubin, 2006;Hayden et al, 2005;Egleston et al, 2007;Zehavi and Nevo, 2021). One solution employs the principal stratification approach (Frangakis and Rubin, 2002) to focus instead on the SACE, which compares the outcome under different treatment levels among the sub-population who would have survived regardless of treatment assignment.…”

“…Therefore, we do not know which participants would have survived until time t regardless of their treatment assignment and cannot identify HR C (t) from the observed data using standard identification assumptions (e.g., randomization and SUTVA). Usually, point-identification of the SACE entails strong assumptions (Hayden et al, 2005;Zehavi and Nevo, 2021) that are unlikely to hold in our setup (Martinussen et al, 2020). Therefore, to avoid making strong and implausible assumptions, we focus on a sensitivity analysis approach.…”

“…The SACE is the effect of treatment on a non-survival outcome among the sub-population that would have survived under either treatment arm. The SACE is not point-identified under standard assumptions, prompting researchers to often center their efforts around sensitivity analysis methods (Hayden et al, 2005;Egleston et al, 2007;Zehavi and Nevo, 2021).…”

The Subtype-Free Average Causal Effect for Heterogeneous Disease Etiology

“…To study etiologic heterogeneity, researchers often use a multinomial regression model in which being healthy or having each of the disease subtypes form the possible values of the outcome. However, the multinomial regression parameters do not correspond to well-defined causal effects, because the multinomial regression parameters are equivalent to the parameters obtained from a series of logistics regressions, each comparing one disease subtype to the healthy controls, resulting in selection bias (Nevo et al, 2021). This form of bias is not limited to subtype comparisons and is not unique to multinomial regression.…”

“…More generally, competing events create a challenge in making causal statements. Section 4.2 reviews related approaches and considers their applicability in our setup (Young et al, 2020;Stensrud et al, 2020;Nevo et al, 2021).…”