QUANTITATIVE RESEARCH METHODS WORKSHOP
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, which quantify the strength of the confounder-treatment and the confounder-outcome association, respectively. For the former, we propose using the Bhattacharyya coefficient, which measures the covariate overlap and, together with the treatment proportion, leads to a uniquely identifiable and easily computable propensity score distribution. For the latter, we propose a sensitivity parameter bounded by the R-squared statistic of the regression of the outcome on covariates. Our procedure relies on a parametric propensity score model and a semiparametric restricted mean outcome model but does not require distributional assumptions on the multivariate covariates. LINK TO PAPER
Fan Li is a professor in the Departments of Statistical Science, and Biostatistics and Bioinformatics at Duke University. Her primary research interest is causal inference and its intersection with health data science and machine learning. She also works on Bayesian analysis and missing data. She was the editor for Social Science, Biostatistics and Policy of the Annals of Applied Statistics, and an elected fellow of the American Statistical Association and the Institute of Mathematical Statistics (IMS).
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