Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis

The Cox proportional hazards model or its discrete time analogue, the logistic failure time model, posit highly restrictive parametric models and attempt to estimate parameters which are specific to the model proposed. These methods are typically implemented when assessing effect modification in survival analyses despite their flaws. The targeted maximum likelihood estimation (TMLE) methodology is more robust than the methods typically implemented and allows practitioners to estimate parameters that directly answer the question of interest. TMLE will be used in this paper to estimate two newly proposed parameters of interest that quantify effect modification in the time to event setting. These methods are then applied to the Tshepo study to assess if either gender or baseline CD4 level modify the effect of two cART therapies of interest, efavirenz (EFV) and nevirapine (NVP), on the progression of HIV. The results show that women tend to have more favorable outcomes using EFV while males tend to have more favorable outcomes with NVP. Furthermore, EFV tends to be favorable compared to NVP for individuals at high CD4 levels.

[1]  D. Collet.  Modelling Survival Data in Medical Research , 2004 .

[2]  Kristin E. Porter,et al.  The Relative Performance of Targeted Maximum Likelihood Estimators , 2011, The international journal of biostatistics.

[3]  S. Keleş,et al.  Statistical Applications in Genetics and Molecular Biology Asymptotic Optimality of Likelihood-Based Cross-Validation , 2011 .

[4]  James M. Robins,et al.  Multiply Robust Inference for Statistical Interactions , 2008, Journal of the American Statistical Association.

[5]  M. J. van der Laan,et al.  Statistical Applications in Genetics and Molecular Biology Super Learner , 2010 .

[6]  D.,et al.  Regression Models and Life-Tables , 2022 .

[7]  Joseph Kang,et al.  Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data , 2007, 0804.2958.

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

[9]  C. J. Stone,et al.  A Course in Probability and Statistics , 1995 .

[10]  J. Robins,et al.  Doubly Robust Estimation in Missing Data and Causal Inference Models , 2005, Biometrics.

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

[12]  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 .

[13]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[14]  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 .

[15]  Mark J van der Laan,et al.  The International Journal of Biostatistics Collaborative Targeted Maximum Likelihood for Time to Event Data , 2011 .

[16]  Mark J. van der Laan,et al.  Application of Time-to-Event Methods in the Assessment of Safety in Clinical Trials , 2009 .

[17]  Mark J van der Laan,et al.  The International Journal of Biostatistics A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome , 2011 .

[18]  D G Altman,et al.  Calculating the number needed to treat for trials where the outcome is time to an event , 1999, BMJ.

[19]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[20]  V. DeGruttola,et al.  Non-nucleoside reverse transcriptase inhibitor outcomes among combination antiretroviral therapy-treated adults in Botswana , 2010, AIDS.

[21]  R. Bender,et al.  Estimating adjusted risk difference (RD) and number needed to treat (NNT) measures in the Cox regression model , 2010, Statistics in medicine.

[23]  J. Robins,et al.  Comment: Performance of Double-Robust Estimators When “Inverse Probability” Weights Are Highly Variable , 2007, 0804.2965.

[24]  Edward L. Melnick,et al.  Modeling Survival Data , 2011, International Encyclopedia of Statistical Science.

[25]  M. J. van der Laan,et al.  The International Journal of Biostatistics Collaborative Double Robust Targeted Maximum Likelihood Estimation , 2011 .

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

[27]  On the interpretation, robustness, and power of varieties of case-only tests of gene-environment interaction. , 2010, American journal of epidemiology.

[28]  M. J. van der Laan,et al.  The International Journal of Biostatistics Targeted Maximum Likelihood Learning , 2011 .

[29]  J. Robins,et al.  Estimating causal effects from epidemiological data , 2006, Journal of Epidemiology and Community Health.

[30]  Michael Rosenblum,et al.  Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model , 2010, The international journal of biostatistics.