Effect modification in settings with "truncation by death".

Epidemiologic studies recruiting individuals with higher-than-population-average mortality can be affected by "truncation by death", whereby the outcome of interest (e.g. quality of life) is considered not to be defined for individuals who die before the end of follow-up. Here, we use the potential outcomes framework and principal stratification to derive conditions under which the survivor average causal effect, an estimand defined for the "always-survivors" stratum, is modified by a variable that represents a possible common cause of survival and the outcome of interest, and by a variable that only affects survival. Further, we show that this principal effect can be expressed as a weighted average of this treatment effect for individuals with each level of these variables, and that these weights depend not only on the relative frequencies of the levels in the total population, but also in the "always-survivors" principal stratum. We also discuss the implications of this work for the transportability of the survivor average causal effect.