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arXiv · 2602.24131

Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems

Sky Qiu·Susan Gruber·Pamela A. Shaw·Brian D. Williamson·Mark J. van der Laan
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Abstract

In a typical two-phase design, a random sample is drawn from the target population in phase 1, during which only a subset of variables is collected. In phase 2, a subsample of the phase-1 cohort is selected, and additional variables are measured. This setting induces a coarsened data structure on the data from the second phase. We assume coarsening at random, that is, the phase-2 sampling mechanism depends only on variables fully observed. We review existing estimators, including the generalized raking estimator and the inverse probability of censoring weighted targeted maximum likelihood estimation (IPCW-TMLE) along with its extensions that also target the phase-2 sampling mechanism to improve efficiency. We further introduce a new class of estimators constructed within the TMLE framework that are asymptotically equivalent.

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Sky Qiu, Susan Gruber, Pamela A. Shaw, Brian D. Williamson, Mark J. van der Laan. 2026-02-27. Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems. https://arxiv.org/abs/2602.24131

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