Testing differences in response trends across a normalized time domain.

A two-stage mixed model analysis of repeated measurement calculates participant-specific regression slopes relating change in available measurements to associated assessment times, and then the difference between mean regression slopes in two or more treatment groups is tested for significance against the within-groups variability of the participant-specific regression slopes. It is not necessary that all participants have the same schedule or number of repeated measurements. However, when dropouts are included in an "intent to treat" analysis, the shortened treatment exposures for the dropouts substantially increase variability and reduce power of tests for differences in rates of change. Previous work has suggested that normalizing the time scale to unit length for all participants prior to fitting the individual regression equations materially reduces the power attenuation produced by dropouts. This article reports a more detailed evaluation of the enhanced robustness against dropouts that is achieved by rescaling the time dimension. The robust analysis is recognized to be equivalent to weighting ordinary least squares regression on the original time scale by the duration of treatment for each participant. Slope coefficients calculated across a shortened time span for dropouts are less stable, so they are given less weight in defining the (linear) treatment effects.