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Abstract:
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Unlike the case for designs with normal, continuous outcomes, the literature on power analyses for designs with binary outcomes is relatively new. The relationship between standardized mean differences and the log odds ratio was previously established and it has provided researchers with a helpful analogy between the effect sizes of designs with continuous outcomes and designs with binary outcomes. This relationship has initiated speculation into whether a similar analogy exists between the power analysis for continuous outcomes and the power analysis for binary outcomes. In this paper, we provide a framework for the analogy and explore the conditions under which the analogy is warranted, if any, in two-level cluster randomized designs with binary outcomes. We base our analysis on two-level cluster designs without covariates and compare the power estimates under two probability metrics for binary data with existing methods based on generalized estimating equations. We provide an empirical example using a cluster-randomized trial from the Quality Preschool for Ghana intervention and discuss how researchers can assess the appropriateness of the analogy in practice.
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