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Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models

Author

Listed:
  • Petersen Maya

    (Division of Biostatistics, University of California, Berkeley, CA, USA)

  • Schwab Joshua

    (Division of Biostatistics, University of California, Berkeley, CA, USA)

  • Gruber Susan

    (Department of Epidemiology, Harvard School of Public Health, Boston, MA, USA)

  • Blaser Nello

    (Institute of Social and Preventive Medicine (ISPM), University of Bern, Bern, Switzerland)

  • Schomaker Michael

    (Centre for Infectious Disease Epidemiology & Research, University of Cape Town, Cape Town, South Africa)

  • van der Laan Mark

    (Division of Biostatistics, University of California, Berkeley, CA, USA)

Abstract

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.

Suggested Citation

  • Petersen Maya & Schwab Joshua & Gruber Susan & Blaser Nello & Schomaker Michael & van der Laan Mark, 2014. "Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models," Journal of Causal Inference, De Gruyter, vol. 2(2), pages 147-185, September.
    • Handle: RePEc:bpj:causin:v:2:y:2014:i:2:p:39:n:1
    DOI: 10.1515/jci-2013-0007
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    References listed on IDEAS

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    1. Murphy S.A. & van der Laan M.J. & Robins J.M., 2001. "Marginal Mean Models for Dynamic Regimes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1410-1423, December.
    2. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    3. James Robins & Andrea Rotnitzky & Stijn Vansteelandt, 2007. "Discussions," Biometrics, The International Biometric Society, vol. 63(3), pages 650-653, September.
    4. Sally Picciotto & Miguel A. Hernán & John H. Page & Jessica G. Young & James M. Robins, 2012. "Structural Nested Cumulative Failure Time Models to Estimate the Effects of Interventions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 886-900, September.
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    Cited by:

    1. Kristin A. Linn & Eric B. Laber & Leonard A. Stefanski, 2017. "Interactive -Learning for Quantiles," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 638-649, April.

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