Estimation of local treatment under the binary instrumental variable model

Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper, we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges for causal estimation with a binary outcome, and show that surprisingly, it can be more difficult than the case with a continuous outcome. We propose novel modeling and estimating procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness or efficiency. Our approach is illustrated via simulation studies and a real data analysis.

[1]  Judea Pearl,et al.  On the Testability of Causal Models With Latent and Instrumental Variables , 1995, UAI.

[2]  D. Rubin,et al.  Principal Stratification in Causal Inference , 2002, Biometrics.

[3]  A. Goldberger.  STRUCTURAL EQUATION METHODS IN THE SOCIAL SCIENCES , 1972 .

[4]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1994 .

[5]  J. Robins,et al.  On falsification of the binary instrumental variable model , 2016, Biometrika.

[6]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[7]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1995 .

[8]  J. Robins,et al.  Congenial Causal Inference with Binary Structural Nested Mean Models , 2017 .

[9]  T. Richardson.  Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality , 2013 .

[10]  Markus Frölich,et al.  Nonparametric IV Estimation of Local Average Treatment Effects with Covariates , 2002, SSRN Electronic Journal.

[11]  Eric Tchetgen Tchetgen,et al.  Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables , 2016, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[12]  James M. Robins,et al.  DOUBLY ROBUST INSTRUMENTAL VARIABLE REGRESSION , 2012 .

[13]  Vanessa Didelez,et al.  Assumptions of IV methods for observational epidemiology , 2010, 1011.0595.

[14]  Elizabeth L. Ogburn,et al.  Doubly robust estimation of the local average treatment effect curve , 2015, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[15]  Frank Windmeijer,et al.  Instrumental Variable Estimators for Binary Outcomes , 2009 .

[16]  J. Angrist,et al.  Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings , 1999 .

[17]  Alberto Abadie.  Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models , 2002 .

[18]  Zhiqiang Tan,et al.  Regression and Weighting Methods for Causal Inference Using Instrumental Variables , 2006 .

[19]  Alberto Abadie.  Semiparametric instrumental variable estimation of treatment response models , 2003 .

[20]  Illtyd Trethowan.  Causality , 1938 .

[21]  James M. Robins,et al.  Transparent Parametrizations of Models for Potential Outcomes , 2012 .

[22]  Xiao-Li Meng,et al.  Multiple-Imputation Inferences with Uncongenial Sources of Input , 1994 .

[23]  Philip G. Wright,et al.  The tariff on animal and vegetable oils , 1928 .

[24]  Thomas S. Richardson,et al.  Identification and estimation of causal effects with outcomes truncated by death , 2016, Biometrika.

[25]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[26]  James M. Robins,et al.  On Modeling and Estimation for the Relative Risk and Risk Difference , 2015, 1510.02430.

[27]  J. Robins,et al.  Instruments for Causal Inference: An Epidemiologist's Dream? , 2006, Epidemiology.