Sample size calculation for randomized trials via inverse probability of response weighting when outcome data are missing at random

Abstract

Randomized trials are an established method to evaluate the causal effects of interventions. Despite concerted efforts to retain all trial participants, some missing outcome data are often inevitable. It is unclear how best to account for missing outcome data in sample size calculations. A standard approach is to inflate the sample size by the inverse of one minus the anticipated dropout probability. However, the performance of this approach in the presence of informative outcome missingness has not been well‐studied. We investigate sample size calculation when outcome data are missing at random given the randomized intervention group and fully observed baseline covariates under an inverse probability of response weighted (IPRW) estimating equations approach. Using M‐estimation theory, we derive sample size formulas for both individually randomized and cluster randomized trials (CRTs). We illustrate the proposed method by calculating a sample size for a CRT designed to detect a difference in HIV testing strategies under an IPRW approach. We additionally develop an R shiny app to facilitate implementation of the sample size formulas.