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 [5] (Estimation of causal effects via principal stratification when some outcomes are truncated by “death”. J Educ Behav Stat 2003;28:353–68) have proposed a methodology to calculate large sample bounds – bounds on the SACE that assume that the exact QOL distribution for each arm is known or that the finite sample size can be ignored – in the case of a randomized experiment. We examine a modification of these bounds in the case where a binary covariate describing each of the subjects is available and assignment to the treatment or control group is ignorable conditional on the covariate. Using a dataset involving an employment training program, we find that the use of the covariate does not substantially change the bounds in this case, although it does weaken the assumptions about the sample and thus make the bounds more widely applicable. However, simulations show that the use of a binary covariate can in some cases dramatically narrow the bounds. Extensions and generalizations to more complicated variants of this situation are discussed, although the amount of computation increases very quickly as the number of covariates and the number of possible values of each covariate increase