Sharp bounds on the causal effects in randomized experiments with “truncation-by-death”

Many randomized experiments suffer from the “truncation-by-death” problem where potential outcomes are not defined for some subpopulations. For example, in medical trials, quality-of-life measures are only defined for surviving patients. In this article, I derive the sharp bounds on causal effects under various assumptions. My identification analysis is based on the idea that the “truncation-by-death” problem can be formulated as the contaminated data problem. The proposed analytical techniques can be applied to other settings in causal inference including the estimation of direct and indirect effects and the analysis of three-arm randomized experiments with noncompliance.