Estimation of causal effects via principal stratification when some outcomes are truncated by "death"

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.