MacMillan-CSAP Workshop on Quantitative Research Methods: José Zubizarreta, “Stable Weights that Balance Covariates for Causal Inference and Estimation with Incomplete Outcome Data”
“Stable Weights that Balance Covariates for Causal Inference and Estimation with Incomplete Outcome Data”
Speaker: José Zubizarreta, Assistant Professor in the Division of Decision, Risk, and Operations (DRO) at Columbia Business School and in the Statistics Department at Columbia University
Abstract: Weighting methods that adjust for observed covariates, such as inverse probability weighting, are widely used for causal inference and estimation with incomplete outcome data. Part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes, or a variety of population means for several variables. However, this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings. To address these limitations, this paper presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher. This method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions, such as variances and correlations and also, for example, the quantiles of interactions of pairs and triples of observed covariates, thus balancing entire two- and three-way marginals. Since the weighting method is based on a well-defined convex optimization problem, duality theory provides insight into the behavior of the variance of the optimal weights in relation to the level of covariate balance adjustment, answering the question, how much does tightening a balance constraint increases the variance of the weights? Also, the weighting method runs in polynomial time so relatively large data sets can be handled quickly. An implementation of the method is provided in the new package sbw for R. This paper shows some theoretical properties of the resulting weights and illustrates their use by analyzing both a data set from the 2010 Chilean earthquake and a simulated example.
José R. Zubizarreta is an assistant professor in the Division of Decision, Risk, and Operations (DRO) at Columbia Business School and in the Statistics Department at Columbia University. Before joining DRO, he completed his PhD in statistics at The Wharton School at the University of Pennsylvania in 2013, focusing on optimal designs for observational studies using mathematical programming. Since then, his methodological research has been on optimal multivariate matching, instrumental variable estimation, regression discontinuity designs, and stable weight adjustment for covariates, among others. His applied work has included the evaluation of medical interventions relevant to preterm babies in Latin America and the US, and assessing the effectiveness of for-profit and not-for-profit schools in his home country, Chile. José is the winner of the Kenneth Rothman Award for the best paper published in Epidemiology in 2013.