# Design and analysis considerations for cohort stepped wedge cluster randomized trials with a decay correlation structure

## TL;DR

This paper introduces a new correlation decay model for cohort stepped wedge cluster randomized trials, providing methods for accurate estimation, sample size calculation, and power analysis considering the decay structure.

## Contribution

It develops a matrix-adjusted quasi-least squares approach for estimating correlation parameters and intervention effects in decay-structured stepped wedge trials.

## Key findings

- Empirical power estimates align well with predictions in simulations.
- The proposed methods work effectively with as few as 9 clusters.
- Two real trial examples demonstrate the sample size procedure.

## Abstract

A stepped wedge cluster randomized trial is a type of longitudinal cluster design that sequentially switches clusters to intervention over time until all clusters are treated. While the traditional posttest-only parallel design requires adjustment for a single intraclass correlation coefficient, the stepped wedge design allows multiple outcome measurements from the same cluster and so additional correlation parameters are necessary to characterize the within-cluster correlation structure. Although a number of studies have differentiated between the concepts of within-period and between-period correlations, only a few studies have allowed the between-period correlation to decay over time. In this article, we consider the proportional decay correlation structure for a cohort stepped wedge design, and provide a matrix-adjusted quasi-least squares (MAQLS) approach to accurately estimate the correlation parameters along with the marginal intervention effect. We further develop the sample size and power procedures accounting for the correlation decay, and investigate the accuracy of the power procedure with continuous outcomes in a simulation study. We show that the empirical power agrees well with the prediction even with as few as 9 clusters, when data are analyzed with MAQLS concurrently with a suitable bias-corrected sandwich variance. Two trial examples are provided to illustrate the new sample size procedure.