  For randomized controlled trials (RCTs) with a single intervention being
measured on multiple outcomes, researchers often apply a multiple testing
procedure (such as Bonferroni or Benjamini-Hochberg) to adjust $p$-values. Such
an adjustment reduces the likelihood of spurious findings, but also changes the
statistical power, sometimes substantially, which reduces the probability of
detecting effects when they do exist. However, this consideration is frequently
ignored in typical power analyses, as existing tools do not easily accommodate
the use of multiple testing procedures. We introduce the PUMP R package as a
tool for analysts to estimate statistical power, minimum detectable effect
size, and sample size requirements for multi-level RCTs with multiple outcomes.
Multiple outcomes are accounted for in two ways. First, power estimates from
PUMP properly account for the adjustment in $p$-values from applying a multiple
testing procedure. Second, as researchers change their focus from one outcome
to multiple outcomes, different definitions of statistical power emerge. PUMP
allows researchers to consider a variety of definitions of power, as some may
be more appropriate for the goals of their study. The package estimates power
for frequentist multi-level mixed effects models, and supports a variety of
commonly-used RCT designs and models and multiple testing procedures. In
addition to the main functionality of estimating power, minimum detectable
effect size, and sample size requirements, the package allows the user to
easily explore sensitivity of these quantities to changes in underlying
assumptions.
