Large Sample Bounds on the Survivor Average Causal Effect in the Presence of a Binary Covariate with Conditionally Ignorable Treatment Assignment

A common problem when conducting an experiment or observational study for the purpose of causal inference is “censoring by death,” in which an event occurring during the experiment causes the desired outcome value – such as quality of life (QOL) – not to be defined for some subjects. One approach to this is to estimate the Survivor Average Causal Effect (SACE), which is the difference in the mean QOL between the treated and control arms, considering only those individuals who would have had well-defined QOL regardless of whether they received the treatment of interest, where the treatment is imposed by the researcher in an experiment or by the subject in the case of an observational study. Zhang and Rubin [