Sample Size Planning in the Design of Two-Level Randomized Cost-Effectiveness Trials

This study introduces recent advances in statistical power analysis methods and tools for designing and analyzing randomized cost-effectiveness trials (RCETs) to evaluate the causal effects and costs of social work interventions. The article focuses on two-level designs, where, for example, students are nested within schools, with interventions applied either at the school level (cluster design) or student level (multisite design). We explore three statistical modeling strategies—random-effects, constant-effects, and fixed-effects models—to assess the cost-effectiveness of interventions, and we develop corresponding power analysis methods and tools. Power is influenced by effect size, sample sizes, and design parameters. We developed a user-friendly tool, PowerUp!-CEA, to aid researchers in planning RCETs. When designing RCETs, it is crucial to consider cost variance, its nested effects, and the covariance between effectiveness and cost data, as neglecting these factors may lead to underestimated power.