Estimation of Causal Effects via Principal Stratification When Some Outcomes are Truncated by “Death”

Abstract

The topic of “truncation by death” in randomized experiments arises in many fields, such as medicine, economics and education. Traditional approaches addressing this issue ignore the fact that the outcome after the truncation is neither “censored” nor “missing,” but should be treated as being defined on an extended sample space. Using an educational example to illustrate, we will outline here a formulation for tackling this issue, where we call the outcome “truncated by death” because there is no hidden value of the outcome variable masked by the truncating event. We first formulate the principal stratification ( Frangakis & Rubin, 2002 ) approach, and we then derive large sample bounds for causal effects within the principal strata, with or without various identification assumptions. Extensions are then briefly discussed.

Ten years later: Locating and interviewing children of drug abusers

“…Although the mortality rate is similar to what has been found in other long-term follow-ups of opiate-addicted populations (Hser, et al, 2001;Oppenheimer, et al, 1994;Vaillant, 1988;Woody & Metzger, 1994), it does result in selection bias with respect to those that completed the follow-up interview. This selection bias due to mortality presents challenges for analyzing outcome data gathered from the follow-up interviews of parents (Zhang & Rubin, 2003). Second, intensive locating is costly in terms of time and dollars.…”

Bounds on Average and Quantile Treatment Effects of Job Corps Training on Wages

“…This assumption was originally proposed by Zhang and Rubin (2003) and employed in Zhang et al (2008):…”

Principal Stratification -- Uses and Limitations

“…In this context in which outcomes are effectively censored or truncated due to death, this is really the only comparison that is fair. The principal strati cation approach is thus of considerable importance in addressing these questions as well and a number of papers have provided methods to try to assess this survivor average causal effect when outcomes are truncated due to death (Robins, 1986;Zhang and Rubin, 2003;Rubin, 2006;Frangakis et al, 2007;Imai, 2008;Egleston, 2009;Chiba and Va n d e r We e l e , 2011). A very closely related (essentially isomorphic) problem concerns the analysis of the effect of some treatment or vaccine on a post-infection outcome (e.g.…”