Calculating the power to examine treatment-covariate interactions when planning an individual participant data meta-analysis of randomized trials with a binary outcome

Before embarking on an individual participant data meta-analysis (IPDMA) project, researchers and funders need assurance it is worth their time and cost. This should include consideration of how many studies are promising their IPD and, given the characteristics of these studies, the power of an IPDMA including them. Here, we show how to estimate the power of a planned IPDMA of randomized trials to examine treatment-covariate interactions at the participant level (ie, treatment effect modifiers). We focus on a binary outcome with binary or continuous covariates, and propose a three-step approach, which assumes the true interaction size is common to all trials. In step one, the user must specify a minimally important interaction size and, for each trial separately (eg, as obtained from trial publications), the following aggregate data: the number of participants and events in control and treatment groups, the mean and SD for each continuous covariate, and the proportion of participants in each category for each binary covariate. This allows the variance of the interaction estimate to be calculated for each trial, using an analytic solution for Fisher's information matrix from a logistic regression model. Step 2 calculates the variance of the summary interaction estimate from the planned IPDMA (equal to the inverse of the sum of the inverse trial variances from step 1), and step 3 calculates the corresponding power based on a two-sided Wald test. Stata and R code are provided, and two examples given for illustration. Extension to allow for between-study heterogeneity is also considered.