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A General Implementation of TMLE for Longitudinal Data Applied to Causal Inference in Survival Analysis

Author

Listed:
  • Stitelman Ori M.

    (University of California - Berkeley)

  • De Gruttola Victor

    (Harvard School of Public Health)

  • van der Laan Mark J.

    (University of California - Berkeley)

Abstract

In many randomized controlled trials the outcome of interest is a time to event, and one measures on each subject baseline covariates and time-dependent covariates until the subject either drops-out, the time to event is observed, or the end of study is reached. The goal of such a study is to assess the causal effect of the treatment on the survival curve. We present a targeted maximum likelihood estimator of the causal effect of treatment on survival fully utilizing all the available covariate information, resulting in a double robust locally efficient substitution estimator that will be consistent and asymptotically linear if either the censoring mechanism is consistently estimated, or if the maximum likelihood based estimator is already consistent. In particular, under the independent censoring assumption assumed by current methods, this TMLE is always consistent and asymptotically linear so that it provides valid confidence intervals and tests. Furthermore, we show that when both the censoring mechanism and the initial maximum likelihood based estimator are mis-specified, and thus inconsistent, the TMLE exhibits stability when inverse probability weighted estimators and double robust estimating equation based methods break down The TMLE is used to analyze the Tshepo study, a study designed to evaluate the efficacy, tolerability, and development of drug resistance of six different first-line antiretroviral therapies. Most importantly this paper presents a general algorithm that may be used to create targeted maximum likelihood estimators of a large class of parameters of interest for general longitudinal data structures.

Suggested Citation

  • Stitelman Ori M. & De Gruttola Victor & van der Laan Mark J., 2012. "A General Implementation of TMLE for Longitudinal Data Applied to Causal Inference in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-39, September.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:26
    DOI: 10.1515/1557-4679.1334
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    References listed on IDEAS

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    1. Stitelman Ori M & van der Laan Mark J., 2010. "Collaborative Targeted Maximum Likelihood for Time to Event Data," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-46, June.
    2. Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    3. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    4. Mark J. Laan & Alan Hubbard, 1999. "Locally Efficient Estimation of the Quality-Adjusted Lifetime Distribution with Right-Censored Data and Covariates," Biometrics, The International Biometric Society, vol. 55(2), pages 530-536, June.
    5. 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.
    6. van der Laan Mark J. & Gruber Susan, 2010. "Collaborative Double Robust Targeted Maximum Likelihood Estimation," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-71, May.
    7. Stitelman Ori M & Wester C. William & De Gruttola Victor & van der Laan Mark J., 2011. "Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, March.
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    Cited by:

    1. Iván Díaz & Elizabeth Colantuoni & Daniel F. Hanley & Michael Rosenblum, 2019. "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 439-468, July.
    2. Jincheng Shen & Lu Wang & Jeremy M. G. Taylor, 2017. "Estimation of the optimal regime in treatment of prostate cancer recurrence from observational data using flexible weighting models," Biometrics, The International Biometric Society, vol. 73(2), pages 635-645, June.
    3. Jie Zhu & Blanca Gallego, 2021. "Continuous Treatment Recommendation with Deep Survival Dose Response Function," Papers 2108.10453, arXiv.org, revised Sep 2023.
    4. Mireille E. Schnitzer & Erica E.M. Moodie & Mark J. van der Laan & Robert W. Platt & Marina B. Klein, 2014. "Modeling the impact of hepatitis C viral clearance on end-stage liver disease in an HIV co-infected cohort with targeted maximum likelihood estimation," Biometrics, The International Biometric Society, vol. 70(1), pages 144-152, March.
    5. Kara E. Rudolph & Mark J. Laan, 2017. "Robust estimation of encouragement design intervention effects transported across sites," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1509-1525, November.
    6. Díaz Iván & Rosenblum Michael, 2015. "Targeted Maximum Likelihood Estimation using Exponential Families," The International Journal of Biostatistics, De Gruyter, vol. 11(2), pages 233-251, November.

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