Causal inference in longitudinal studies with history-restricted marginal structural models.

A new class of Marginal Structural Models (MSMs), History-Restricted MSMs (HRMSMs), was recently introduced for longitudinal data for the purpose of defining causal parameters which may often be better suited for public health research or at least more practicable than MSMs (6, 2). HRMSMs allow investigators to analyze the causal effect of a treatment on an outcome based on a fixed, shorter and user-specified history of exposure compared to MSMs. By default, the latter represent the treatment causal effect of interest based on a treatment history defined by the treatments assigned between the study's start and outcome collection. We lay out in this article the formal statistical framework behind HRMSMs. Beyond allowing a more flexible causal analysis, HRMSMs improve computational tractability and mitigate statistical power concerns when designing longitudinal studies. We also develop three consistent estimators of HRMSM parameters under sufficient model assumptions: the Inverse Probability of Treatment Weighted (IPTW), G-computation and Double Robust (DR) estimators. In addition, we show that the assumptions commonly adopted for identification and consistent estimation of MSM parameters (existence of counterfactuals, consistency, time-ordering and sequential randomization assumptions) also lead to identification and consistent estimation of HRMSM parameters.

[1]  J. Robins.  A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods. , 1987, Journal of chronic diseases.

[2]  Aad van der Vaart,et al.  The Cross-Validated Adaptive Epsilon-Net Estimator , 2006 .

[3]  J. Robins.  A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[4]  Mark J. van der Laan,et al.  Causal effects in longitudinal studies: Definition and maximum likelihood estimation , 2006, Comput. Stat. Data Anal..

[5]  Mark J. van der Laan,et al.  Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms in Estimation , 2004 .

[6]  M. J. Laan,et al.  Construction of Counterfactuals and the G-computation Formula , 2002 .

[7]  S. Dudoit,et al.  Unified Cross-Validation Methodology For Selection Among Estimators and a General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities and Examples , 2003 .

[8]  M. J. Laan,et al.  Double Robust Estimation in Longitudinal Marginal Structural Models , 2006 .

[9]  Locally Efficient Estimation of Nonparametric Causal Effects on Mean Outcomes in Longitudinal Studies , 2003 .

[10]  J. Robins,et al.  Marginal Structural Models and Causal Inference in Epidemiology , 2000, Epidemiology.

[11]  Marshall M Joffe,et al.  History-Adjusted Marginal Structural Models and Statically-Optimal Dynamic Treatment Regimens , 2005 .

[12]  M. Joffe,et al.  Administration of parenteral iron and mortality among hemodialysis patients. , 2004, Journal of the American Society of Nephrology : JASN.

[13]  Luke Clancy,et al.  Cause-specific mortality and the extended effects of particulate pollution and temperature exposure. , 2003, Environmental health perspectives.

[14]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[15]  Mark J. van der Laan,et al.  Nonparametric causal effects based on marginal structural models , 2007 .

[16]  James M. Robins,et al.  Unified Methods for Censored Longitudinal Data and Causality , 2003 .

[17]  Mark J. van der Laan,et al.  G-computation estimation for causal inference with complex longitudinal data , 2006, Comput. Stat. Data Anal..

[18]  James M. Robins,et al.  Association, Causation, And Marginal Structural Models , 1999, Synthese.

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

[20]  James M. Robins,et al.  Marginal Structural Models versus Structural nested Models as Tools for Causal inference , 2000 .

[21]  U. Epa.  Air Quality Criteria for Particulate Matter , 1996 .

[22]  James M. Robins,et al.  Coarsening at Random: Characterizations, Conjectures, Counter-Examples , 1997 .

[23]  Barbara Sternfeld,et al.  Effects of Physical Activity and Body Composition on Functional Limitation in the Elderly: Application of the Marginal Structural Model , 2004, Epidemiology.

[24]  D. Rubin.  [On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9.] Comment: Neyman (1923) and Causal Inference in Experiments and Observational Studies , 1990 .

[25]  Mark J. van der Laan,et al.  Why prefer double robust estimators in causal inference , 2005 .