Optimal Sample Allocation in Group-Randomized Mediation Studies with a Group-Level Mediator |
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| Authors: | Kyle Cox Benjamin Kelcey |
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| Institution: | 1. University of Cincinnati, Cincinnati, OH, USAcoxk5@mail.uc.edu;3. University of Cincinnati, Cincinnati, OH, USA |
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| Abstract: | We derive sample-allocation formulas that maximize the power of several mediation tests in two-level–group-randomized studies under a linear cost structure and fixed budget. The results suggest that the optimal individual sample size is typically smaller than that associated with the detection of a main effect and is frequently less than 10 under parameter values commonly seen in the literature. However, the optimal sample allocation can be heavily influenced by the group-to-individual cost ratio, the ratio of the treatment-mediator to mediator-outcome path coefficients, and the outcome variance structure. We illustrate these findings with a hypothetical group-randomized trial examining a school-discipline reform policy. To encourage utilization of the sample allocation formulas we implement them in the R package PowerUpR and powerupr Shiny application. |
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| Keywords: | Mediation optimal sample allocation optimal design group-randomized studies multilevel models |
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