Estimation of the causal effect of a time-varying exposure on the marginal mean of a repeated binary outcome. Commentary. Authors' reply

We provide sufficient conditions for estimating from longitudinal data the causal effect of a time-dependent exposure or treatment on the marginal probability of response for a dichotomous outcome. We then show how one can estimate this effect under these conditions using the g-computation algorithm of Robins. We also derive the conditions under which some current approaches to the analysis of longitudinal data, such as the generalized estimating equations (GEE) approach of Zeger and Liang, the feedback model techniques of Liang and Zeger, and within-subject conditional methods, can provide valid tests and estimates of causal effects. We use out methods to estimate the causal effect of maternal stress on the marginal probability of a child's illness from the Mothers' Stress and Children's Morbidity data and compare out results with those previously obtained by Zeger and Liang using a GEE approach.

[1]  J M Robins,et al.  Correction for non-compliance in equivalence trials. , 1998, Statistics in medicine.

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

[3]  J. Robins,et al.  G-Estimation of the Effect of Prophylaxis Therapy for Pneumocystis carinii Pneumonia on the Survival of AIDS Patients , 1992, Epidemiology.

[4]  J. Robins.  Estimation of the time-dependent accelerated failure time model in the presence of confounding factors , 1992 .

[5]  J. Kalbfleisch,et al.  A Comparison of Cluster-Specific and Population-Averaged Approaches for Analyzing Correlated Binary Data , 1991 .

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

[7]  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 .

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

[9]  A. Gallant,et al.  Semi-nonparametric Maximum Likelihood Estimation , 1987 .

[10]  J M Robins,et al.  Identifiability, exchangeability, and epidemiological confounding. , 1986, International journal of epidemiology.

[11]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[12]  K Y Liang,et al.  Longitudinal data analysis for discrete and continuous outcomes. , 1986, Biometrics.

[13]  P. Holland.  Statistics and Causal Inference , 1985 .

[14]  P. Rosenbaum.  The Consequences of Adjustment for a Concomitant Variable that Has Been Affected by the Treatment , 1984 .

[15]  P. Rosenbaum.  From Association to Causation in Observational Studies: The Role of Tests of Strongly Ignorable Treatment Assignment , 1984 .

[16]  Sheldon M. Ross,et al.  Stochastic Processes , 1982 .

[17]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[18]  N. Laird.  Nonparametric Maximum Likelihood Estimation of a Mixing Distribution , 1978 .

[19]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

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

[21]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[22]  J. Robins,et al.  Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models , 2000 .

[23]  J. Robins.  Causal Inference from Complex Longitudinal Data , 1997 .

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

[25]  Scott L. Zeger,et al.  Feedback Models for Discrete and Continuous Time Series , 1991 .

[26]  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.

[27]  J. 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” , 1987 .

[28]  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 .

[29]  Gary Chamberlain,et al.  Chapter 22 Panel data , 1984 .

[30]  Donald B. Rubin,et al.  Bayesian Inference for Causal Effects: The Role of Randomization , 1978 .