Power Estimation in Planning Randomized Two-Arm Pre-Post Intervention Trials with Repeated Longitudinal Outcomes.

Background: Intervention effect on ongoing medical processes is estimated from clinical trials on units (i.e. persons or facilities) with fixed timing of repeated longitudinal measurements. All units start out untreated. A randomly chosen subset is switched to the intervention at the same time point. The pre-post switch change in the outcome between these units and unswitched controls is compared using Generalized Least Squares models. Power estimation for such studies is hindered by lack of available GLS based approaches and normative data.

Methods: We derive Generalized Least Squares variance of the intervention effect. For the commonly assumed compound symmetry correlation structure, this leads to simple power formulas with important optimality properties. To maximize power given a constrained number of total time points, we investigate on the optimal pre-post allocation with the local minimization of variance.

Results: In four examples from nursing home and HIV patients, the Toepltiz within-unit correlation of repeated measures differed from compound symmetry. We applied empirical Toeplitz based calculations for variance of the estimated intervention effect to these examples (each with up to seven longitudinal measures). Unlike what happened under compound symmetry, where power was often maximized with multiple observations being pre-intervention, for these examples, having one pre-intervention measure tended to maximize power. Attempts to approximate the Toeplitz variance structures with compound symmetry (to take advantage of the simpler formulas) resulted in overestimation of power for these examples.

Conclusions: While compound symmetry correlation among repeated within-unit measures leads to simple power estimation formulas, this structure often did not hold. There may be strong underestimation of variance of the intervention effect estimate from incorporating short-term within-unit correlation estimates as a common compound symmetry correlation to approximate an unknown Toeplitz correlation without adequately accounting for the correlation between repeated measures declining with time.