Power Calculations for Two-Wave, Change from Baseline to Follow-up Study Designs

Change in a quantitative trait is commonly employed as an endpoint in two-wave longitudinal studies. For example, early phase clinical trials often use two-wave designs with biomarker endpoints to confirm that a treatment affects the putative target treatment pathway before proceeding to larger scale clinical efficacy trials. Power calculations for such designs are straightforward if pilot data from longitudinal investigations of similar duration to the proposed study are available. Often longitudinal pilot data of similar duration are not available, and simplifying assumptions are used to calculate sample size from cross-sectional data, one standard approach being to use a formula based on variance estimated from cross sectional data and correlation estimates abstracted from the literature or inferred from experience with similar endpoints. An implicit assumption of this standard approach is that the variance of the quantitative trait is the same at baseline and follow-up. In practice, this assumption rarely holds, and sample size estimates by this standard formula can be dramatically anti-conservative. Even when longitudinal pilot data for estimating parameters required in sample size calculations are available, sample size calculations will be biased if the interval from baseline to follow-up is not of similar duration to that proposed for the study being designed. In this paper we characterize the magnitude of bias in sample size estimates when formula assumptions do not hold and derive alternative conservative formulas for sample size required to achieve nominal power.