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For randomized controlled trials (RCTs) with a single intervention beingmeasured on multiple outcomes, researchers often apply a multiple testingprocedure (such as Bonferroni or Benjamini-Hochberg) to adjust $p$-values. Suchan adjustment reduces the likelihood of spurious findings, but also changes thestatistical power, sometimes substantially, which reduces the probability ofdetecting effects when they do exist. However, this consideration is frequentlyignored in typical power analyses, as existing tools do not easily accommodatethe use of multiple testing procedures. We introduce the PUMP R package as atool for analysts to estimate statistical power, minimum detectable effectsize, and sample size requirements for multi-level RCTs with multiple outcomes.Multiple outcomes are accounted for in two ways. First, power estimates fromPUMP properly account for the adjustment in $p$-values from applying a multipletesting procedure. Second, as researchers change their focus from one outcometo multiple outcomes, different definitions of statistical power emerge. PUMPallows researchers to consider a variety of definitions of power, as some maybe more appropriate for the goals of their study. The package estimates powerfor frequentist multi-level mixed effects models, and supports a variety ofcommonly-used RCT designs and models and multiple testing procedures. Inaddition to the main functionality of estimating power, minimum detectableeffect size, and sample size requirements, the package allows the user toeasily explore sensitivity of these quantities to changes in underlyingassumptions.

Power Under Multiplicity Project (PUMP): Estimating Power, Minimum  Detectable Effect Size, and Sample Size When Adjusting for Multiple Outcomes  in Multi-level Experiments