Optimal Sample Size Calculation in Cost-Effectiveness Longitudinal Cluster Randomized Trials

2026-03-19

AI Summary

This study addresses the limitations of existing cost-effectiveness analyses in longitudinal cluster randomized trials, which often fail to adequately model the complex correlation structure between clinical and cost outcomes, thereby hindering accurate sample size determination. To overcome this, the authors develop a unified sample size calculation framework based on a bivariate linear mixed model for three common designs: parallel, crossover, and stepped wedge. They derive, for the first time, closed-form variance expressions under cost-effectiveness objectives and introduce a standardized ceiling ratio to calibrate willingness-to-pay thresholds. By employing generalized least squares estimation, the approach jointly accounts for within-period, between-period, and inter-outcome correlations. Integrating both locally optimal and MaxiMin robust design strategies, the method substantially enhances the precision and robustness of sample size estimates. Empirical validation using real stepped wedge trial data demonstrates its applicability and efficiency across multiple designs.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Longitudinal cluster randomized trials (L-CRTs) are increasingly used to evaluate the cost-effectiveness of healthcare interventions across multiple assessment periods, yet design methods for powering these trials remain underdeveloped. Existing methods for cost-effectiveness analyses in cluster settings are limited to simple parallel-arm cluster randomized trials with a single follow-up assessment period. These methods cannot accommodate the complex correlation structures in L-CRTs conducted over multiple periods, which require differentiation between within-period and between-period correlations for both clinical and cost outcomes, as well as between-outcome correlations. Moreover, while substantial methodological advances have been made for the design of L-CRTs with univariate outcomes, none specifically address cost-effectiveness objectives where clinical and cost outcomes must be jointly modeled. We provide a design-stage framework for powering cost-effectiveness L-CRTs across three design variants: parallel-arm, crossover, and stepped wedge designs. We derive closed-form variance expressions for the generalized least squares estimator of the average incremental net monetary benefit under a bivariate linear mixed model. We propose a standardized ceiling ratio that adjusts willingness-to-pay for relative outcome variability to inform optimal design. We then develop local optimal designs that maximize statistical power under known correlation parameters and MaxiMin designs that ensure robust performance across parameter uncertainty for all three design variants. Through a real stepped wedge trial data example, we demonstrate the sample size calculation for testing intervention cost-effectiveness under local optimal and MaxiMin designs.

Problem

• longitudinal cluster randomized trials
• cost-effectiveness analysis
• sample size calculation
• correlation structure
• incremental net monetary benefit

Innovation

• longitudinal cluster randomized trials
• cost-effectiveness analysis
• optimal design
• bivariate linear mixed model
• MaxiMin design