Simple Power and Sample Size Estimation for Non-Randomized Longitudinal Difference in Differences Studies

Abstract

Intervention effects on continuous longitudinal normal outcomes are often estimated in two-arm pre-post interventional studies with b≥1 pre- and k≥1 post-intervention measures using “Difference-in-Differences” (DD) analysis. Although randomization is preferred, non-randomized designs are often necessary due to practical constraints. Power/sample size estimation methods for non-randomized DD designs that incorporate the correlation structure of repeated measures are needed. We derive Generalized Least Squares (GLS) variance estimate of the intervention effect. For the commonly assumed compound symmetry (CS) correlation structure (where the correlation between all repeated measures is a constantρ) this leads to simple power and sample size estimation formulas that can be implemented using pencil and paper. Given a constrained number of total timepoints (T), having as close to possible equal number of pre-and post-intervention timepoints (b=k) achieves greatest power. When planning a study with 7 or less timepoints, given large ρ(ρ≥0.6) in multiple baseline measures (b≥2) or ρ≥0.8 in a single baseline setting, the improvement in power from a randomized versus non-randomized DD design may be minor. Extensions to cluster study designs and incorporation of time invariant covariates are given. Applications to study planning are illustrated using three real examples with T=4 timepoints and ρ ranging from 0.55 to 0.75.