Kernel-Distance-Based Covariate Balancing

A common concern in observational studies focuses on properly evaluating the causal effect, which usually refers to the average treatment effect or the average treatment effect on the treated. In this paper, we propose a data preprocessing method, the Kernel-distance-based covariate balancing, for observational studies with binary treatments. This proposed method yields a set of unit weights for the treatment and control groups, respectively, such that the reweighted covariate distributions can satisfy a set of pre-specified balance conditions. This preprocessing methodology can effectively reduce confounding bias of subsequent estimation of causal effects. We demonstrate the implementation and performance of Kernel-distance-based covariate balancing with Monte Carlo simulation experiments and a real data analysis.

[1]  Qingyuan Zhao,et al.  Double Robustness for Causal Effects via Entropy Balancing , 2015 .

[2]  Jens Hainmueller,et al.  Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies , 2012, Political Analysis.

[3]  Yuying Xie.  Causal Inference with Covariate Balance Optimization , 2018 .

[4]  Joseph Kang,et al.  Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data , 2007, 0804.2958.

[5]  D. Rubin.  The design versus the analysis of observational studies for causal effects: parallels with the design of randomized trials , 2007, Statistics in medicine.

[6]  S. Erlander.  ENTROPY IN LINEAR PROGRAMS--AN APPROACH TO PLANNING , 1977 .

[7]  H. Kim,et al.  Balance diagnostics after propensity score matching. , 2019, Annals of translational medicine.

[8]  G. Imbens,et al.  Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score , 2000 .

[9]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[10]  K. C. G. Chan,et al.  Globally efficient non‐parametric inference of average treatment effects by empirical balancing calibration weighting , 2016, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[11]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[12]  D. Ghosh,et al.  A Kernel-Based Metric for Balance Assessment , 2018, Journal of causal inference.

[13]  Xinwei Ma,et al.  Robust Inference Using Inverse Probability Weighting , 2018, Journal of the American Statistical Association.

[14]  K. Imai,et al.  Covariate balancing propensity score , 2014 .

[15]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[16]  Kevin P. Josey,et al.  A framework for covariate balance using Bregman distances , 2019, Scandinavian Journal of Statistics.

[17]  Raymond K. W. Wong,et al.  Kernel-based covariate functional balancing for observational studies. , 2018, Biometrika.

[18]  T. Speed,et al.  On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9 , 1990 .

[19]  Gert R. G. Lanckriet,et al.  On the empirical estimation of integral probability metrics , 2012 .

[20]  Whitney K. Newey,et al.  Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators , 2003 .

[21]  Donald B. Rubin,et al.  Bayesian Inference for Causal Effects: The Role of Randomization , 1978 .

[22]  Yuying Xie,et al.  A model averaging approach for estimating propensity scores by optimizing balance , 2019, Statistical methods in medical research.

[23]  D. Rubin.  Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[24]  C. Särndal,et al.  Calibration Estimators in Survey Sampling , 1992 .

[25]  R. Lalonde.  Evaluating the Econometric Evaluations of Training Programs with Experimental Data , 1984 .