Designing three-level cluster randomized trials to assess treatment effect heterogeneity

Abstract

Summary Cluster randomized trials often exhibit a three-level structure with participants nested in subclusters such as health care providers, and subclusters nested in clusters such as clinics. While the average treatment effect has been the primary focus in planning three-level randomized trials, interest is growing in understanding whether the treatment effect varies among prespecified patient subpopulations, such as those defined by demographics or baseline clinical characteristics. In this article, we derive novel analytical design formulas based on the asymptotic covariance matrix for powering confirmatory analyses of treatment effect heterogeneity in three-level trials, that are broadly applicable to the evaluation of cluster-level, subcluster-level, and participant-level effect modifiers and to designs where randomization can be carried out at any level. We characterize a nested exchangeable correlation structure for both the effect modifier and the outcome conditional on the effect modifier, and generate new insights from a study design perspective for conducting analyses of treatment effect heterogeneity based on a linear mixed analysis of covariance model. A simulation study is conducted to validate our new methods and two real-world trial examples are used for illustrations.

Health equity considerations in pragmatic trials in Alzheimer's and dementia disease: Results from a methodological review

“… 37 Methodology for detecting treatment‐effect heterogeneity in cluster randomized trials is the topic of ongoing research. 38 , 39 …”

“…However, recent methodological results have revealed that detecting treatment‐effect heterogeneity in cluster randomized trials may not always require larger sample sizes than detecting the average treatment effect 37 . Methodology for detecting treatment‐effect heterogeneity in cluster randomized trials is the topic of ongoing research 38,39 …”

“…37 Methodology for detecting treatment-effect heterogeneity in cluster randomized trials is the topic of ongoing research. 38,39 Finally, while equity considerations are context dependent, it is insufficient to only consider age and sex. Given the evidence of outcome-related inequities by race/ethnicity, education, socioeconomic status, and social capital, equity-relevant trials should carefully consider PROGRESS-Plus factors in their objectives, design, analysis and reporting, particularly in circumstances where there is disproportionate need or unequal impacts on equity-relevant groups.…”

Models for cluster randomized designs using ranked set sampling

“…Watson et al investigated the impact of small sample sizes on the performance of a three‐arm parallel CRD 21 . Li et al 22 constructed a three‐level CRD with two covariates to assess treatment effect heterogeneity. Recent developments in CRDs and up to date references can be found in review papers 23,24 …”

Maximin optimal cluster randomized designs for assessing treatment effect heterogeneity

“…Although the power analysis of the treatment-by-covariate interaction test has been relatively well-studied in individually randomized trials, 3,4,5 related methods for power analysis in CRTs have only received recent attention with the goal to enable a rigorous understanding of how system-level innovations may differentially impact outcomes for important subpopulations. 6,7,8,9,10 With a pre-specified effect modifier, Yang et al 8 developed an analytical sample size and power formula to test the treatmentby-covariate interaction, making it possible to power CRTs a priori for confirmatory HTE analyses. Similar to designing conventional CRTs to study the average treatment effect, the intracluster correlation coefficient (ICC) of the outcome, or outcome-ICC, plays an essential role in determining the power and necessary sample size for the HTE test.…”