A major problem in the analysis of clinical trials is missing data from pat
ients who drop out of the study before the predetermined schedule. Shih and
Quan (1997) proposed a "composite" (or "pattern but not mix") approach to
the problem, which makes simultaneous inference on the conditional mean of
the completers and the probability of completion or dropping out of the tri
al. Their method involves the combination of test statistics for the condit
ional mean and dropout probability. In this paper, we justify the asymptoti
c independence of the test statistics used in Shih and Quan.