Abstract
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.
Highlights
Sample size is a critical design consideration when planning a randomized controlled trial (RCT)
2.3 Stage 1: Slope and variance parameter estimation slopepower uses the mixed command with the restricted maximum-likelihood option to fit a linear mixed model relating the outcome to time since study entry, using data supplied by the user
We have presented a new command, slopepower, that can be used to perform samplesize or power calculations for trials that compare rates of change in an outcome over time. slopepower can be used for any continuous clinical trial outcome that is expected to change at a constant rate over time and where a treatment is expected to slow that rate
Summary
Sample size is a critical design consideration when planning a randomized controlled trial (RCT). Specifying the treatment-effect variance formula from such an LMM for a sample-size calculation requires knowledge of all the parameters that govern between- and withinsubject variability in outcomes, which are often unknown In such situations, one can use data from any relevant previously conducted longitudinal studies to estimate these parameters. We introduce a new package, slopepower, that translates a two-stage approach for estimating these parameters and performing sample-size calculations (Frost, Kenward, and Fox 2008; Frost et al 2017) into a user-friendly command, appropriate for planning two-arm parallel trials comparing slopes where the treatment is expected to slow disease progression by a constant amount throughout follow-up and where the outcome is expected to change linearly over time.
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