Consistent causal effect estimation under dual misspecification and implications for confounder selection procedures

Abstract

In a previously published article in this journal, Vansteeland et al. [Stat Methods Med Res. Epub ahead of print 12 November 2010. DOI: 10.1177/0962280210387717] address confounder selection in the context of causal effect estimation in observational studies. They discuss several selection strategies and propose a procedure whose performance is guided by the quality of the exposure effect estimator. The authors note that when a particular linearity condition is met, consistent estimation of the target parameter can be achieved even under dual misspecification of models for the association of confounders with exposure and outcome and demonstrate the performance of their procedure relative to other estimators when this condition holds. Our earlier published work on collaborative targeted minimum loss based learning provides a general theoretical framework for effective confounder selection that explains the findings of Vansteelandt et al. and underscores the appropriateness of their suggestions that a confounder selection procedure should be concerned with directly targeting the quality of the estimate and that desirable estimators produce valid confidence intervals and are robust to dual misspecification.

Keywords

collaborative double robustness TMLE collaborative targeted maximum likelihood estimation propensity score confounder selection causal effect causal inference dual misspecification

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References

Robins

. A new approach to causal inference in mortality studies with sustained exposure periods – application to control of the healthy worker survivor effect. Math Model 1986; 7: 1393–1512.

Robins

. addendum to: A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect. [Math Model 1986; 7(9–12): 1393–1512. MR 87m:92078]. Comput Math Appl 1987; 14(9–12): 923–945.

Robins

. Robust estimation in sequentially ignorable missing data and causal inference models. Proc Am Stat Assoc Sec Bayesian Stat Sci 2000, pp. 6–10.

Tan

. Bounded, efficient, and doubly robust estimation with inverse weighting. Biometrika 2008; 94: 1–22.

Tan

. Bounded, efficient and doubly robust estimation with inverse weighting. Biometrika 2010; 97(3): 661–682.

Petersen

Porter

Gruber

. Diagnosing and responding to violations in the positivity assumption. Stat Meth Med Res 2010. Published Online 28 October 2010. DOI: 10.1177/0962280210386207.

van der Laan

Rubin

. Targeted maximum likelihood learning. Int J Biostat 2006; 2(1): article 11.

van der Laan

Gruber

. Collaborative double robust penalized targeted maximum likelihood estimation. Int J Biostat 2010; 6(1): article 17.

Gruber

van der Laan

. A targeted maximum likelihood estimator of a causal effect on a bounded continuous outcome. Int J Biostat 2010; 6(1): article 17.

10.

Gruber

van der Laan

. An application of collaborative targeted maximum likelihood estimation in causal inference and genomics. Int J Biostat 2010; 6(1): article 18.

11.

van der Laan

Rose

. Targeted learning: prediction and causal inference for observational and experimental data, New York: Springer, 2011.

12.

Robins

Rotnitzky

. Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell N, Dietz K and Farewell V (eds) AIDS epidemiology: methodological issues, Boston: Birkhäuser, 1992, pp. 297–331.

13.

Robins

Wang

. Inference for imputation estimators. Biometrika 2000; 87: 113–124.

14.

van der Laan

Robins

. Unified methods for censored longitudinal data and causality, New York: Springer, 2003.

15.

Lee

Lessler

Stuart

. Improved propensity score weighting using machine learning. Stat Med 2009; 29: 337–346.

16.

Schneeweiss

Rassen

Glynn

. Highdimensional propensity score adjustment in studies of treatment effects using health care claims data. Epidemiology 2009; 20: 512–522.

17.

Westreich

Cole

Funk

. The role of the c-statistic in variable selection for propensity scores. Pharmacoepidemiol Drug Saf 2011; 20: 317–320.

18.

Vansteelandt

Bekaert

Claeskens

. On model selection and model misspecification in causal inference. Stat Methods Med Res 2012; 21(1): 7–30.

19.

van der Laan

. Measuring treatment effects using semiparametric models. U.C. Berkeley Division of Biostatistics Working Paper Series 2003. Working Paper 136, September.

20.

Robins

Rotnitzky

. Comment on Inference for semiparametric models: some questions and an answer, by Bickel, P.J. and Kwon, J. Stat Sinica 2001; 11: 920–935.

21.

Porter

Gruber

van der Laan

. The relative performance of targeted maximum likelihood estimators. Int J Biostat 2011; 7(1): article 31.

22.

Stitelman

van der Laan

. Collaborative targeted maximum likelihood for time to event data. Int J Biostat 2010; 6(1): article 21.

23.

Gruber

van der Laan

. Collaborative targeted maximum likelihood estimation. In: WNAR 2011, Spring Meeting, Archorage, AL 6–14 May 2011.