A comparison of methods for designing hybrid type 2 cluster-randomized trials with continuous effectiveness and implementation endpoints

TL;DR

This paper compares five design methods for hybrid type 2 cluster-randomized trials with continuous endpoints, providing theoretical and numerical insights to guide study powering.

Contribution

It offers a comprehensive theoretical and numerical comparison of five methods, including a new R package, to optimize power in hybrid CRTs with continuous outcomes.

Findings

P-value adjustment methods are less powerful than combined outcomes and single 1-DF tests.

Disjunctive 2-DF test is more powerful when treatment effects are unequal.

Single 1-DF test tends to be most powerful when treatment effects are equal.

Abstract

Hybrid type 2 studies are gaining popularity for their ability to assess both implementation and health outcomes as co-primary endpoints. Often conducted as cluster-randomized trials (CRTs), five design methods can validly power these studies: p-value adjustment methods, combined outcomes approach, single weighted 1-DF test, disjunctive 2-DF test, and conjunctive test. We compared these methods theoretically and numerically. Theoretical comparisons of power equations allowed us to identify when one method had more or less power than another globally. We showed that p-value adjustment methods are always less powerful than both the combined outcomes approach and the single 1-DF test, and identified conditions where the disjunctive 2-DF test is less powerful than the single 1-DF test. To further investigate when power advantages shift, we conducted a large-scale numerical study using our novel crt2power R package, which calculates power or sample size for CRTs with two continuous co-primary endpoints using these methods. Across 45,000 input scenarios, we found specific patterns: when treatment effects are unequal, the disjunctive 2-DF test tends to be most powerful; when treatment effects are equal, the single 1-DF test tends to dominate. Together, these comparisons offer practical guidance for powering hybrid type 2 studies.