Freiman Michael H, Small Dylan S
Int J Biostat. 2014;10(2):143-63. doi: 10.1515/ijb-2013-0039.
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.
在进行旨在进行因果推断的实验或观察性研究时，一个常见问题是“因死亡而删失”，即在实验过程中发生的一个事件导致某些受试者的期望结果值（如生活质量（QOL））未被定义。对此的一种方法是估计幸存者平均因果效应（SACE），它是治疗组和对照组之间平均QOL的差异，只考虑那些无论是否接受感兴趣的治疗都会有明确QOL的个体，其中治疗是由研究人员在实验中施加的，或者在观察性研究的情况下是由受试者施加的。Zhang和Rubin [5]（当一些结果因“死亡”而被截断时，通过主分层估计因果效应。《教育行为统计杂志》2003年；28：353 - 68）提出了一种方法来计算大样本界限——在随机实验的情况下，SACE的界限假设每个组的确切QOL分布是已知的，或者可以忽略有限的样本量。在有描述每个受试者的二元协变量且治疗或对照组的分配在协变量条件下是可忽略的情况下，我们研究了这些界限的一种修正。使用一个涉及就业培训项目的数据集，我们发现协变量的使用在这种情况下并没有实质性地改变界限，尽管它确实弱化了关于样本的假设，从而使界限更广泛适用。然而，模拟表明，二元协变量的使用在某些情况下可以显著缩小界限。讨论了对这种情况更复杂变体的扩展和推广，尽管随着协变量数量和每个协变量可能值的数量增加，计算量增长非常快。
