Sample size calculations for multilevel factorial longitudinal cluster randomised trials

2025-08-03

AI Summary

Existing sample size methods are inadequate for longitudinal cluster-randomized trials (e.g., stepped-wedge, cluster-randomized crossover designs) that simultaneously assess main effects of individual-level and cluster-level interventions, as well as their interaction. Method: We propose the first general analytical framework for sample size calculation in hierarchical factorial longitudinal designs, integrating linear mixed-effects models with variance decomposition to derive closed-form expressions for statistical power targeting individual-level, cluster-level, and interaction effects. The method flexibly accommodates diverse longitudinal cluster-randomized designs and explicitly quantifies power for interaction testing. Contribution/Results: Applied to the SharES breast cancer education trial, our approach accurately estimated required sample sizes for all effects, demonstrating improved design rigor and statistical efficiency in complex multilevel intervention studies. This framework enhances the feasibility and validity of evaluating both main and interactive intervention effects in pragmatic cluster-randomized trials.

Technology Category

• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

Typically, trials investigate the impact of either an individual-level intervention on participant outcomes, or the impact of a cluster-level intervention on participant outcomes. Factorial designs consider two (or more) treatments for each of two (or more) different factors. In factorial trial designs, trial units (individuals or clusters) are each randomised to a level of each of the treatments; these designs allow assessment of the interactions between different interventions. Recently, there has been growing interest in the design of trials that jointly assess the impact of individual- and cluster-level interventions (i.e. multi-level interventions); requiring the development of methodology that accommodates randomisation at multiple levels. While recent work has developed sample size methodology for variants combining standard cluster randomisation and individual randomisation, that work does not apply to longitudinal cluster randomised trial designs such as the stepped wedge design or cluster randomised crossover design. Here we present dedicated sample size methodology for "split-plot factorial longitudinal cluster randomised trials" with continuous outcomes: allowing for joint assessment of individual-level and cluster-level interventions that allows for the impact of the cluster-level intervention to be assessed using any longitudinal cluster randomised trial design. We show how the power to detect given effects of the individual-level intervention, the cluster-level intervention, and the interaction between the two depends on standard results for individually-randomised trials and longitudinal cluster randomised trials. We apply these results to the SharES trial, which considered the effects of a patient- and clinician-level interventions for patients with breast cancer on patient knowledge about the risks and benefits of treatment.

Problem

• Develop sample size methods for multilevel factorial longitudinal trials
• Assess interactions between individual and cluster level interventions
• Apply methodology to trials like stepped wedge designs

Innovation

• Split-plot factorial longitudinal cluster randomised trials
• Joint assessment of individual and cluster interventions
• Power analysis for multi-level intervention effects