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Biostatistics. 2016 Jan;17(1):165-77. doi: 10.1093/biostatistics/kxv028. Epub 2015 Jul 29.

Double robust and efficient estimation of a prognostic model for events in the presence of dependent censoring.

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Faculté de pharmacie, Université de Montréal, Montréal, Québec H3C 3J7, Canada
The Department of Biostatistics and the Center for Biostatistics in AIDS Research at Harvard T.H. Chan School of Public Health, Boston, MA 02115, USA.


In longitudinal data arising from observational or experimental studies, dependent subject drop-out is a common occurrence. If the goal is estimation of the parameters of a marginal complete-data model for the outcome, biased inference will result from fitting the model of interest with only uncensored subjects. For example, investigators are interested in estimating a prognostic model for clinical events in HIV-positive patients, under the counterfactual scenario in which everyone remained on ART (when in reality, only a subset had). Inverse probability of censoring weighting (IPCW) is a popular method that relies on correct estimation of the probability of censoring to produce consistent estimation, but is an inefficient estimator in its standard form. We introduce sequentially augmented regression (SAR), an adaptation of the Bang and Robins (2005. Doubly robust estimation in missing data and causal inference models. Biometrics 61, 962-972.) method to estimate a complete-data prediction model, adjusting for longitudinal missing at random censoring. In addition, we propose a closely related non-parametric approach using targeted maximum likelihood estimation (TMLE; van der Laan and Rubin, 2006. Targeted maximum likelihood learning. The International Journal of Biostatistics 2 (1), Article 11). We compare IPCW, SAR, and TMLE (implemented parametrically and with Super Learner) through simulation and the above-mentioned case study.


Inverse probability of censoring weighting; Longitudinal; Marginal structural model; Prediction; Targeted maximum likelihood estimation; Targeted minimum loss-based estimation

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