Jump to ContentJump to Main Navigation
Show Summary Details
More options …

The International Journal of Biostatistics

Ed. by Chambaz, Antoine / Hubbard, Alan E. / van der Laan, Mark J.

IMPACT FACTOR 2017: 0.840
5-year IMPACT FACTOR: 1.000

CiteScore 2017: 0.97

SCImago Journal Rank (SJR) 2017: 1.150
Source Normalized Impact per Paper (SNIP) 2017: 1.022

Mathematical Citation Quotient (MCQ) 2016: 0.09

See all formats and pricing
More options …

Collaborative Double Robust Targeted Maximum Likelihood Estimation

Mark J. van der Laan / Susan Gruber
Published Online: 2010-05-17 | DOI: https://doi.org/10.2202/1557-4679.1181

Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of a pathwise differentiable parameter of a data generating distribution in a semiparametric model, introduced in van der Laan, Rubin (2006). The targeted maximum likelihood approach involves fluctuating an initial estimate of a relevant factor (Q) of the density of the observed data, in order to make a bias/variance tradeoff targeted towards the parameter of interest. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE has been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is correctly specified, and it is semiparametric efficient if both are correctly specified.In this article we provide a template for applying collaborative targeted maximum likelihood estimation (C-TMLE) to the estimation of pathwise differentiable parameters in semi-parametric models. The procedure creates a sequence of candidate targeted maximum likelihood estimators based on an initial estimate for Q coupled with a succession of increasingly non-parametric estimates for g. In a departure from current state of the art nuisance parameter estimation, C-TMLE estimates of g are constructed based on a loss function for the targeted maximum likelihood estimator of the relevant factor Q that uses the nuisance parameter to carry out the fluctuation, instead of a loss function for the nuisance parameter itself. Likelihood-based cross-validation is used to select the best estimator among all candidate TMLE estimators of Q0 in this sequence. A penalized-likelihood loss function for Q is suggested when the parameter of interest is borderline-identifiable.We present theoretical results for "collaborative double robustness," demonstrating that the collaborative targeted maximum likelihood estimator is CAN even when Q and g are both mis-specified, providing that g solves a specified score equation implied by the difference between the Q and the true Q0. This marks an improvement over the current definition of double robustness in the estimating equation literature.We also establish an asymptotic linearity theorem for the C-DR-TMLE of the target parameter, showing that the C-DR-TMLE is more adaptive to the truth, and, as a consequence, can even be super efficient if the first stage density estimator does an excellent job itself with respect to the target parameter.This research provides a template for targeted efficient and robust loss-based learning of a particular target feature of the probability distribution of the data within large (infinite dimensional) semi-parametric models, while still providing statistical inference in terms of confidence intervals and p-values. This research also breaks with a taboo (e.g., in the propensity score literature in the field of causal inference) on using the relevant part of likelihood to fine-tune the fitting of the nuisance parameter/censoring mechanism/treatment mechanism.

Keywords: asymptotic linearity; coarsening at random; causal effect; censored data; cross-validation; collaborative double robust; double robust; efficient influence curve; estimating function; estimator selection; influence curve; G-computation; locally efficient; loss-function; marginal structural model; maximum likelihood estimation; model selection; pathwise derivative; semiparametric model; sieve; super efficiency; super-learning; targeted maximum likelihood estimation; targeted nuisance parameter estimator selection; variable importance

About the article

Published Online: 2010-05-17

Citation Information: The International Journal of Biostatistics, Volume 6, Issue 1, ISSN (Online) 1557-4679, DOI: https://doi.org/10.2202/1557-4679.1181.

Export Citation

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Jeffrey M. Lackner, James Jaccard, Laurie Keefer, Darren Brenner, Rebecca Firth, Gregory D. Gudleski, Frank Hamilton, Leonard A. Katz, Susan S. Krasner, Chang-Xing Ma, Christopher Radziwon, and Michael D. Sitrin
Gastroenterology, 2018
Joseph Antonelli, Matthew Cefalu, Nathan Palmer, and Denis Agniel
Biometrics, 2018
J. Molina, A. Rotnitzky, M. Sued, and J. M. Robins
Biometrika, 2017, Volume 104, Number 3, Page 561
Romain Pirracchio, John K Yue, Geoffrey T Manley, Mark J van der Laan, and Alan E Hubbard
Statistical Methods in Medical Research, 2016, Page 096228021562733
Cheng Ju, Richard Wyss, Jessica M Franklin, Sebastian Schneeweiss, Jenny Häggström, and Mark J van der Laan
Statistical Methods in Medical Research, 2017, Page 096228021774458
Cheng Ju, Susan Gruber, Samuel D Lendle, Antoine Chambaz, Jessica M Franklin, Richard Wyss, Sebastian Schneeweiss, and Mark J van der Laan
Statistical Methods in Medical Research, 2017, Page 096228021772984
Noemi Kreif, Richard Grieve, Rosalba Radice, Zia Sadique, Roland Ramsahai, and Jasjeet S. Sekhon
Medical Decision Making, 2012, Volume 32, Number 6, Page 750
Brandon Koch, David M. Vock, and Julian Wolfson
Biometrics, 2017
Susan M. Shortreed and Ashkan Ertefaie
Biometrics, 2017
Wei Luo, Yeying Zhu, and Debashis Ghosh
Biometrika, 2017, Page asw068
Noémi Kreif, Susan Gruber, Rosalba Radice, Richard Grieve, and Jasjeet S Sekhon
Statistical Methods in Medical Research, 2016, Volume 25, Number 5, Page 2315
Susan Gruber and Mark J van der Laan
Statistical Methods in Medical Research, 2015, Volume 24, Number 6, Page 1003
Matthew Cefalu, Francesca Dominici, Nils Arvold, and Giovanni Parmigiani
Biometrics, 2017, Volume 73, Number 2, Page 410
Kara E. Rudolph and Mark J. van der Laan
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2016
Machteld Vandecandelaere and Stijn Vansteelandt
Multivariate Behavioral Research, 2016, Page 1
Emma Persson, Jenny Häggström, Ingeborg Waernbaum, and Xavier de Luna
Computational Statistics & Data Analysis, 2017, Volume 105, Page 280
Sheri A. Lippman, Starley B. Shade, Jeri Sumitani, Julia DeKadt, Jennifer M. Gilvydis, Mary Jane Ratlhagana, Jessica Grignon, John Tumbo, Hailey Gilmore, Emily Agnew, Parya Saberi, Scott Barnhart, and Wayne T. Steward
Trials, 2016, Volume 17, Number 1
Karel Vermeulen and Stijn Vansteelandt
Journal of the American Statistical Association, 2015, Volume 110, Number 511, Page 1024
Michelle C. Odden, Ira B. Tager, Ron T. Gansevoort, Stephan J.L. Bakker, Linda F. Fried, Anne B. Newman, Ronit Katz, Suzanne Satterfield, Tamara B. Harris, Mark J. Sarnak, David Siscovick, and Michael G. Shlipak
Annals of Epidemiology, 2013, Volume 23, Number 3, Page 106
Samuel D. Lendle, Bruce Fireman, and Mark J. van der Laan
Journal of Clinical Epidemiology, 2013, Volume 66, Number 8, Page S91
Mark J. van der Laan and Richard J. C. M. Starmans
Advances in Statistics, 2014, Volume 2014, Page 1
Hui Wang, Sherri Rose, and Mark J. van der Laan
Statistics & Probability Letters, 2011, Volume 81, Number 7, Page 792

Comments (0)

Please log in or register to comment.
Log in