A median-based test under informative dropout: the one-sample case.

We consider a clinical trial in which the outcome can be assessed by a continuous measure and where dropouts tend to have poorer efficacy than completers. When each subject can act as his/her own control, efficacy is measured by the difference between the outcome measurements at two times. When all subjects complete the protocol, a paired t-test can be used to test for a treatment effect, i.e., whether or not the mean difference is zero. When a patient does not return for the final evaluation, a measure of efficacy cannot be computed for that subject. Often, data from dropouts are ignored and only the observed pairs are used to analyze the data. When the reason for dropping out is not random, the result may be misleading. In this paper, we assume that (1) the distribution of the measure of efficacy (i.e., the change between two outcome measurements) is Gaussian, (2) dropouts would have worse efficacy than the median if they were observed, and (3) the dropout rate is less than 50%. We propose a median-based t-like statistic using the sample median in place of the sample mean. The variance of the median is estimated using only data from the complete half-sample, i.e., the half-sample with better efficacy. Simulations under five patterns of dropouts are performed to compare the proposed statistic with the paired t-test. The results show that the median-based statistic provides a conservative bound for the test of significance of the treatment. In contrast, because the paired t-test does not preserve its level of significance, except when the dropout mechanism is uniform, the paired t-test should not be used for trials in which dropouts tend to have poorer efficacy than completers.