Using Ant Colony Optimization to Identify Optimal Sample Allocations in Cluster-Randomized Trials

Abstract

When designing cluster-randomized trials (CRTs), one important consideration is determining the proper sample sizes across levels and treatment conditions to cost-efficiently achieve adequate statistical power. This consideration is usually addressed in an optimal design framework by leveraging the cost structures of sampling and optimizing the sampling ratios across treatment conditions and levels of the hierarchy. Traditionally, optimization is done through the first-order derivative approach by setting the first-order derivatives equal to zero to solve for the optimal design parameters. However, the first-order derivative method is incapable of properly handling the optimization task when statistical power formulas are complex, such as those for CRTs detecting mediation effects under the joint significance test. The current study proposes using an ant colony optimization (ACO) algorithm to identify optimal allocations. We evaluate the algorithm’s performance for CRTs detecting main and mediation effects. The results show that the ACO algorithm can identify optimal sample allocations for CRTs investigating main effects with the same design efficiency as those identified through the first-order derivative method. Furthermore, it can efficiently identify optimal sample allocations for CRTs investigating mediation effects under the joint significance test. We have implemented the proposed methods in the R package odr.

Keywords:

• Ant colony optimization
• cluster-randomized trials
• optimal sample allocation
• optimal design
• statistical power

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The R codes, inputs and outputs of this paper are available at https://osf.io/yptc4/.

Additional information

Funding

This paper was based in part on work supported by the Spencer Foundation with grants (#202000198 and # 202300277).