Closed-form REML estimators and sample size determination for mixed effects models for repeated measures under monotone missingness

TL;DR

This paper derives closed-form REML estimators and sample size formulas for mixed effects models with repeated measures under monotone missingness, enabling accurate power calculations and covariate adjustments.

Contribution

It introduces explicit formulas for REML and variance estimators in MMRM with monotone missing data, facilitating power analysis and sample size determination.

Findings

Method performs well for normal and nonnormal data in small samples

Provides a simple two-step sample size calculation procedure

Applied to an antidepressant trial for illustration

Abstract

We derive the closed-form restricted maximum likelihood (REML) estimator and Kenward-Roger's variance estimator for fixed effects in the mixed effects model for repeated measures (MMRM) when the missing data pattern is monotone. As an important application of the analytic result, we present the formula for calculating the power of treatment comparison using the Wald t test with the Kenward-Roger adjusted variance estimate in MMRM. It allows adjustment for baseline covariates without the need to specify the covariate distribution in randomized trials. A simple two-step procedure is proposed to determine the sample size needed to achieve the targeted power. The proposed method performs well for both normal and moderately nonnormal data even in small samples (n = 20) in simulations. An anti-depressant trial is analyzed for illustrative purposes.