Robins J M
Department of Epidemiology, Harvard School of Public Health, Boston, Massachusetts 02115, USA.
Lifetime Data Anal. 1995;1(4):417-34. doi: 10.1007/BF00985453.
Consider a randomized trial in which time to the occurrence of a particular disease, say pneumocystic pneumonia in an AIDS trial or breast cancer in a mammographic screening trial, is the failure time of primary interest. Suppose that time to disease is subject to informative censoring by the minimum of time to death, loss to and end of follow-up. In such a trial, the potential censoring time is observed for all study subjects, including failure. In the presence of informative censoring, it is not possible to consistently estimate the effect of treatment on time to disease without imposing additional non-identifiable assumptions. Robins (1995) specified two non-identifiable assumptions that allow one to test for and estimate an effect of treatment on time to disease in the presence of informative censoring. The goal of this paper is to provide a class of consistent and reasonably efficient semiparametric tests and estimators for the treatment effect under these assumptions. The tests in our class, like standard weighted-log-rank tests, are asymptotically distribution-free alpha-level tests under the null hypothesis of no causal effect of treatment on time to disease whenever the censoring and failure distributions are conditionally independent given treatment arm. However, our tests remain asymptotically distribution-free alpha-level tests in the presence of informative censoring provided either of our assumptions are true. In contrast, a weighted log-rank test will be an alpha-level test in the presence of informative censoring only if (1) one of our two non-identifiable assumptions hold, and (2) the distribution of time to censoring is the same in the two treatment arms. We also study the estimation, in the presence of informative censoring, of the effect of treatment on the evolution over time of the mean of repeated measures outcome such as CD4 count.
考虑一项随机试验，其中某种特定疾病的发生时间，比如艾滋病试验中的肺孢子菌肺炎或乳房X光筛查试验中的乳腺癌，是主要关注的失效时间。假设疾病发生时间受到以死亡时间、失访时间和随访结束时间中的最小值进行的信息性删失的影响。在这样的试验中，所有研究对象（包括失效对象）的潜在删失时间都是可观测的。在存在信息性删失的情况下，如果不施加额外的不可识别假设，就不可能一致地估计治疗对疾病发生时间的影响。罗宾斯（1995年）提出了两个不可识别假设，这使得人们能够在存在信息性删失的情况下检验并估计治疗对疾病发生时间的影响。本文的目标是在这些假设下，为治疗效果提供一类一致且合理有效的半参数检验和估计量。我们这类检验，与标准加权对数秩检验一样，在治疗对疾病发生时间无因果效应的原假设下，只要给定治疗组时删失分布和失效分布是条件独立的，就是渐近无分布的α水平检验。然而，只要我们的任何一个假设为真，在存在信息性删失的情况下，我们的检验仍然是渐近无分布的α水平检验。相比之下，加权对数秩检验只有在以下两种情况下才会在存在信息性删失时是α水平检验：（1）我们的两个不可识别假设之一成立，并且（2）两个治疗组的删失时间分布相同。我们还研究了在存在信息性删失的情况下，治疗对重复测量结果均值（如CD4计数）随时间演变的影响的估计。
