Statistics Seminar - Fan Li (Duke) "Sample size and power calculations for causal inference in observational studies"

Title: Sample size and power calculations for causal inference in observational studies

Abstract: This paper investigates the theoretical foundation and develops analytical formulas for sample size and power calculations for causal inference with observational data. By analyzing the variance of an inverse probability weighting estimator of the average treatment effect, we decompose the power calculation into three components: propensity score distribution, potential outcome distribution, and their correlation. We show that to determine the minimal sample size of an observational study, in addition to the standard inputs in the power calculation of randomized trials, it is sufficient to have two parameters: the overlap coefficient and the confounding coefficient, which quantify the strength of the confounder-treatment and the confounder-outcome association, respectively. The overlap coefficient is the Bhattacharyya coefficient of the covariate distribution between two groups; together with the treatment proportion, it leads to a uniquely identifiable and easily computable propensity score distribution. The confounding coefficient is the correlation between the linear propensity score and the potential outcome. Our procedure does not require distributional assumptions on the multivariate covariates. We develop an associated R package and an online calculator. The paper link is here