Optimal allocation of subjects in a cluster randomized trial with fixed number of clusters when the ICCs or costs are heterogeneous over clusters

TL;DR

This paper develops optimal design strategies for cluster randomized trials considering heterogeneous intra-cluster correlation coefficients (ICCs) and sampling costs across clusters, improving trial efficiency when assumptions of uniform ICCs and costs do not hold.

Contribution

It introduces a novel optimal design framework for CRTs with non-constant ICCs and unequal sampling costs, extending traditional methods.

Findings

Optimal designs account for heterogeneity in ICCs and costs.

Numerical examples demonstrate improved efficiency over standard designs.

Framework applicable to real-world CRT planning with variable cluster characteristics.

Abstract

The intra-cluster correlation coefficient (ICC) plays an important role while designing the cluster randomized trials (CRTs). Often optimal CRTs are designed assuming that the magnitude of the ICC is constant across the clusters. However, this assumption is hardly satisfied. In some applications, the precise information about the cluster specific correlation is known in advance. In this article, we propose an optimal design with non-constant ICC across the clusters. Also in many situations, the cost of sampling of an observation from a particular cluster may differ from that of some other cluster. An optimal design in those scenarios is also obtained assuming unequal costs of sampling from different clusters. The theoretical findings are supplemented by thorough numerical examples.