Optimal Sample Allocation Under Unequal Costs in Cluster-Randomized Trials

Abstract

Conventional optimal design frameworks consider a narrow range of sampling cost structures that thereby constrict their capacity to identify the most powerful and efficient designs. We relax several constraints of previous optimal design frameworks by allowing for variable sampling costs in cluster-randomized trials. The proposed framework introduces additional design considerations and has the potential to identify designs with more statistical power, even when some parameters are constrained due to immutable practical concerns. The results also suggest that the gains in efficiency introduced through the expanded framework are fairly robust to misspecifications of the expanded cost structure and concomitant design parameters (e.g., intraclass correlation coefficient). The proposed framework is implemented in the R package odr.

More powerful cluster randomized control trials

“…Under the assumption that σ 2 = 1, equations ( 40) and ( 41) are equivalent, which completes this section, as we show that the variance of the treatment effect in Shen and Kelcey (2020) coincides with that in this work.…”

“…Column 6 shows the case where all values are round down to the nearest integer and column 7 shows the case where all values are rounded up. This section presents the equivalence between the variance of the treatment effect in equation ( 4) above, and equation A1 in the Appendix of Shen and Kelcey (2020), which we specify with different sample sizes across treatment conditions at all levels. Table 9 below provides a correspondence between how we define the key parameters, and how Shen and Kelcey (2020) do so.…”

“…Finally, a bit more of algebra leads us to determine that the variance of the treatment effect in Shen and Kelcey (2020), expressed in terms of the paramaters we use, is:…”

“…In the statistics literature, Liu (2003) is a pioneer in considering different costs in a cluster RCT, but the scenarios considered are relatively constrained, allowing only either fixed or variable heterogeneous costs, and constraining the solution to have either the same number of clusters or the same number of units in treatment than control. Shen and Kelcey (2020) has recently relaxed some of these constraints but still requires the number of units to be the same in treatment than in control clusters. Moreover, these papers focus on minimizing costs given a level of power, instead of maximizing power given a maximum cost.…”

Intraclass Correlations for Evaluating the Effects of Teacher Empowerment Programs on Student Educational Outcomes

“…Given a fixed (average) treatment effect and significance level, the statistical power for a three-level experiment, with students nested within teachers nested within schools and the randomization of schools or teachers, is determined by two sets of design parameters (Konstantopoulos, 2008a(Konstantopoulos, , 2008bShen & Kelcey, 2020, 2022c. Specifically, for a three-level cluster-randomized trial, one set of parameters is the variance components, including ICCs and, if applicable, proportions of variance explained by covariates.…”