Power comparison of summary measure, mixed model, and survival analysis methods for analysis of repeated-measures trials

In two-group repeated-measures studies, a traditional statistical approach is to base analysis directly on the observed continuous measurements, using either summary measures or a mixed linear model. In some medical studies, however, an alternate approach has been taken: Declare the occurrence of an "event" when the sequence of measurements crosses a prespecified threshold, and compare the groups with respect to time to event using the log-rank test. This approach is appealing to clinicians, but clearly involves a loss of information and therefore statistical efficiency. The aim of this article is to quantify the degree of power loss in the context of the random line model. We also compare the summary measures approach to the random line approach. In regard to the efficiency loss with the survival analysis approach, we find that the loss ranges, depending on the location of the threshold, from moderate to dramatic. Using an optimally weighted log-rank test in place of the standard log-rank test leads to minimal gain in efficiency. In regard to analysis based on the original continuous measurements, for testing the slope a weighted summary measure appears to be the best overall choice, whereas for testing the intercept the maximum likelihood (ML) approach is typically much more efficient than the summary measures approach, although the efficiency of the ML approach can be compromised in studies with a small number of observation timepoints. These results have obvious implications for the choice of study design and analysis.