An Alternative Doubly Robust Estimation in Causal Inference Model

Abstract

Doubly robust (DR) methods that employ both the propensity score and outcome models are widely used to estimate the causal effect of a treatment and generally outperform those methods only using the propensity score or the outcome model. However, without appropriately chosen the working models, DR estimators may substantially lose efficiency. In this paper, based on the augmented inverse probability weighting procedure, we derive a new estimating equation for the causal effect by the strategy of combining estimating equations. The resulting estimator by solving the new estimating equation retains doubly robust and can improve the efficiency under the misspecification of conditional mean working model. We further show the large sample properties of the proposed estimator under some regularity conditions. Through simulation experiments and a real data analysis, we illustrate that the proposed method is competitive with its competitors, which is in line with those implied by the asymptotic theory.

Keywords

Average treatment effect / Causal effect / Doubly robust method / Estimating equation / Inverse probability weighting / Semiparametric efficiency

References

[1] Austin PC. The performance of different propensity score methods for estimating marginal hazard ratios. Stat. Med., 2013, 32: 2837-2849

[2] Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics, 2005, 61: 962-973

[3] Benkeser D, Carone M, Laan MJVD, Gilbert PB. Doubly robust nonparametric inference on the average treatment effect. Biometrika, 2017, 104: 863-880

[4] Cao W, Tsiatis AA, Davidian M. Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data. Biometrika, 2009, 96: 723-734

[5] Cattaneo MD. Efficient semiparametric estimation of multi-valued treatment effects under ignorability. J. Econom., 2010, 155: 138-154

[6] Dehejia RH, Wahba S. Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. J. Am. Stat. Assoc., 1999, 94: 1053-1062

[7] Firpo S. Efficient semiparametric estimation of quantile treatment effects. Econometrica, 2007, 75: 259-276

[8] Hirano K, Imbens GW, Ridder G. Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 2003, 71: 1161-1189

[9] Imai K, Ratkovic M. Covariate balancing propensity score. J. R. Stat. Soc. Ser. B-Stat. Methodol., 2014, 76: 243-263

[10] Kang J, Schafer J. Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Stat. Sci., 2007, 22: 523-539

[11] LaLonde RJ. Evaluating the econometric evaluations of training programs with experimental data. Am. Econ. Rev., 1986, 76: 604-620

[12] Linden A, Adams JL. Using propensity score-based weighting in the evaluation of health management programme effectiveness. J. Eval. Clin. Pract., 2010, 16: 175-179

[13] Lunceford JK, Davidian M. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Stat. Med., 2004, 23: 2937-2960

[14] Newey WK, McFadden D. Engle R, McFadden D. Large sample estimation and hypothesis testing. Handbook of Econometrics, 1994, Amsterdam: Elsevier 2111-2245

[15] Neyman J. On the application of probability theory to agricultural experiments. Essay on principles, section 9. translation of original 1923 paper, which appeared in roczniki nauk rolniczych. Stat. Sci., 1990, 5: 465-472

[16] Qin J, Zhang B, Leung DH. Efficient augmented inverse probability weighted estimation in missing data problems. J. Bus. Econ. Stat., 2017, 35: 86-97

[17] Ridgeway G, McCaffrey DF. Comment: Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Stat. Sci., 2007, 22: 540-543

[18] Robins J, Rotnitzky A, Zhao L. Estimation of regression coefficients when some regressors are not always observed. J. Am. Stat. Assoc., 1994, 89: 846-866

[19] Robins JM. Association, causation, and marginal structural models. Synthese, 1999, 121: 151-179

[20] Robins JM, Hernan MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology, 2000, 11: 550-560

[21] Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. J. Am. Stat. Assoc., 1995, 90: 106-121

[22] Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika, 1983, 70: 41-55

[23] Rubin DB. Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol., 1974, 66: 688-701

[24] Rubin DB. Randomization analysis of experimental data: the fisher randomization test comment. J. Am. Stat. Assoc., 1980, 75: 591-593

[25] Rubin DB, van der Laan MJ. Empirical efficiency maximization: improved locally efficient covariate adjustment in randomized experiments and survival analysis. Int. J. Biostat., 2008, 4: 1-40

[26] Scharfstein DO, Rotnitzky A, Robins JM. Adjusting for nonignorable drop-out using semiparametric nonresponse models. J. Am. Stat. Assoc., 1999, 94: 1096-1120

[27] Smith JA, Todd PE. Does matching overcome LaLondes critique of nonexperimental estimators?. J. Econom., 2005, 125: 305-353

[28] Tan Z. Comment: Understanding OR. PS and DR. Stat. Sci., 2007, 22: 560-568

[29] Tan Z. Bounded, efficient and doubly robust estimation with inverse weighting. Biometrika, 2010, 97: 661-682

[30] Tsiatis A. Semiparametric Theory and Missing Data, 2006, New York: Springer

[31] Uysal SD. Doubly robust estimation of causal effects with multivalued treatments: an application to the returns to schooling. J. Appl. Econom., 2015, 30: 763-786

[32] van der Laan MJ, Rose S. Targeted Learning: Causal Inference for Observational and Experimental Data, 2011, Berlin: Springer

[33] Vansteelandt S, Bekaert M, Claeskens G. On model selection and model misspecification in causal inference. Stat. Methods Med. Res., 2012, 21: 7-30

[34] Vermeulen K, Vansteelandt S. Bias-reduced doubly robust estimation. J. Am. Stat. Assoc., 2015, 110: 1024-1036

[35] Vermeulen K, Vansteelandt S. Data-adaptive bias-reduced doubly robust estimation. Int. J. Biostat., 2016, 12: 253-282

[36] Wooldridge JM. Inverse probability weighted estimation for general missing data problems. J. Econom., 2007, 141: 1281-1301

Funding

National Natural Science Foundation of China(11771032)