An analytic method for randomized trials with informative censoring: Part II

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 failures. 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 -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 -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 -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.