Sample-size calculation for a log-transformed outcome measure.

The outcome measure of interest in clinical trials sometimes requires transformation to the logarithmic scale for analysis. This paper examines sample-size calculation for both independent groups and matched-pairs trials for log-transformed outcomes. For both types of trial, we demonstrate how the calculation can be formulated in terms of a relative treatment effect and a statement of relative variability, both specified on the original scale of measurement. For a comparison of two independent groups, the relative treatment effect is the ratio of group geometric means (or alternatively, group arithmetic means) and the coefficient of variation is used as a summary of relative variability. For a matched-pairs comparison, the appropriate relative treatment effect is the geometric mean of the within-pair ratios, and relative variability can be specified as an upper bound on within-pair ratios under a null hypothesis of the relative effect being equal to 1 (i.e., no difference). We discuss the clinical study that motivated this work and demonstrate the application of the sample-size calculation to this study.