Sample Size and Power When Designing a Randomized Trial for the Estimation of Treatment, Selection, and Preference Effects

rating participant choice, provides unbiased estimates of the effects of the treatment or intervention (treatment effect), the difference between outcomes for participants who prefer one treatment compared with another (selec-tion effect), and the interaction between participants ’ pref-erences for treatment and the treatment actually received (preference effect). It is important to ensure that such tri-als are adequately powered to estimate these effects. Sam-ple Size Formulas. This paper presents methods for determining the required sample sizes for estimating treat-ment, selection, and preference effects. We demonstrate the changes in sample size as various key parameters are changed. In general, approximately twice as many par-ticipants (in total) are needed to have equivalent power for detecting both treatment and selection/preference effect