Structural Nested Mean Models for Assessing Time‐Varying Effect Moderation

This article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment (or exposure) is time varying and so are the covariates said to moderate its effect. Intermediate causal effects that describe time-varying causal effects of treatment conditional on past covariate history are introduced and considered as part of Robins' structural nested mean model. Two estimators of the intermediate causal effects, and their standard errors, are presented and discussed: The first is a proposed two-stage regression estimator. The second is Robins' G-estimator. The results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators, and on the bias-variance trade-off between the two estimators are presented. The methodology is illustrated using longitudinal data from a depression study.

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

[2]  J. Robins,et al.  Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models , 2004 .

[3]  W. Newey,et al.  Semiparametric Efficiency Bounds , 1990 .

[4]  E Goetghebeur,et al.  Practical properties of some structural mean analyses of the effect of compliance in randomized trials. , 1997, Controlled clinical trials.

[5]  Brian D. Ripley,et al.  Modern applied statistics with S, 4th Edition , 2002, Statistics and computing.

[6]  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.

[7]  J. Robins,et al.  Estimating exposure effects by modelling the expectation of exposure conditional on confounders. , 1992, Biometrics.

[8]  William N. Venables,et al.  Modern Applied Statistics with S , 2010 .

[9]  J. Robins.  The control of confounding by intermediate variables. , 1989, Statistics in medicine.

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

[11]  H. Kraemer,et al.  Mediators and moderators of treatment effects in randomized clinical trials. , 2002, Archives of general psychiatry.

[12]  Mark J van der Laan,et al.  History-adjusted marginal structural models for estimating time-varying effect modification. , 2007, American journal of epidemiology.

[13]  Els Goetghebeur,et al.  The Effect of Treatment Compliance in a Placebo‐controlled Trial: Regression with Unpaired Data , 1997 .

[14]  Peter J. Bickel,et al.  INFERENCE FOR SEMIPARAMETRIC MODELS: SOME QUESTIONS AND AN ANSWER , 2001 .

[15]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[16]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[17]  P. Lachenbruch.  Statistical Power Analysis for the Behavioral Sciences (2nd ed.) , 1989 .

[18]  Thomas R Ten Have,et al.  Reducing suicidal ideation and depressive symptoms in depressed older primary care patients: a randomized controlled trial. , 2004, JAMA.

[19]  D. A. Kenny,et al.  The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. , 1986, Journal of personality and social psychology.

[20]  J. Robins.  Correcting for non-compliance in randomized trials using structural nested mean models , 1994 .

[21]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[22]  Kevin G Lynch,et al.  Causal Mediation Analyses with Rank Preserving Models , 2007, Biometrics.

[23]  M. Bruce,et al.  Designing an intervention to prevent suicide: PROSPECT (Prevention of Suicide in Primary Care Elderly: Collaborative Trial) , 1999, Dialogues in clinical neuroscience.

[24]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[25]  C. Glymour,et al.  STATISTICS AND CAUSAL INFERENCE , 1985 .

[26]  Stijn Vansteelandt,et al.  Causal inference with generalized structural mean models , 2003 .

[27]  James M. Robins,et al.  Causal Inference from Complex Longitudinal Data , 1997 .

[28]  Dylan Small,et al.  Defining and Estimating Intervention Effects for Groups that will Develop an Auxiliary Outcome , 2007 .

[29]  Mark J. van der Laan,et al.  History-Adjusted Marginal Structural Models: Time-Varying Effect Modification , 2005 .