Methods for the Design of Cluster Randomized Trials

Abstract

When designing a randomized trial the power calculation is an important consideration. Under-powered trials can lead to null results due to insufficient information and over-powered trials waste time and resources. This dissertation focuses on analytical derivation of power calculation formulas in scenarios where simulation of power would be time consuming. We aim to provide practical and intuitive power calculation methods relevant to complex designs and missing data settings. First, our focus is on stepped-wedge cluster randomized trials (SW-CRTs), where a cluster-level intervention is rolled out in a sequential fashion. The order in which clusters cross-forward from a control to an intervention is determined by randomization. Chapter 1 explores power calculation for SW-CRTs when cluster sizes vary. Variance estimators for the intervention effect are derived under a standard linear mixed effect model incorporating cluster size variation. In this setting, the power of the design depends on the randomization sequence. We propose efficient algorithms to identify upper and lower bounds of the power across all randomization sequences, and obtain an approximation to the expected power based only on knowledge of the cluster size mean and coefficient of variation. Chapter 2 is dedicated to power calculation for SW-CRTs with binary outcomes under a logistic model fitted by generalized estimating equations. We describe general methods that incorporate variable cluster sizes and complex correlation structures, which allow the correlation among outcomes in the same cluster to change over time and with intervention status. In Chapter 3, we switch attention to individual and cluster randomized trials with missing outcome data. We explore sample size calculation when outcome data are missing at random given the randomized intervention group and fully observed auxiliary covariates under an inverse probability of response weighted estimating equations approach. Using M-estimation theory, we derive formulas for sample size calculation using large sample variances. These formulas are simplified to provide insight into how weighting influences sample size in practical missing data settings.