Power and sample-size calculations for trials that compare slopes over time: Introducing the slopepower command.

Trials of interventions that aim to slow disease progression may analyze a continuous outcome by comparing its change over time-its slope-between the treated and the untreated group using a linear mixed model. To perform a sample-size calculation for such a trial, one must have estimates of the parameters that govern the between- and within-subject variability in the outcome, which are often unknown. The algebra needed for the sample-size calculation can also be complex for such trial designs. We have written a new user-friendly command, slopepower, that performs sample-size or power calculations for trials that compare slope outcomes. The package is based on linear mixed-model methodology, described for this setting by Frost, Kenward, and Fox (2008, Statistics in Medicine 27: 3717-3731). In the first stage of this approach, slopepower obtains estimates of mean slopes together with variances and covariances from a linear mixed model fit to previously collected user-supplied data. In the second stage, these estimates are combined with user input about the target effectiveness of the treatment and design of the future trial to give an estimate of either a sample size or a statistical power. In this article, we present the slopepower command, briefly explain the methodology behind it, and demonstrate how it can be used to help plan a trial and compare the sample sizes needed for different trial designs.