Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems
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.
Cite
@article{arxiv.2602.24131,
title = {Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems},
author = {Sky Qiu and Susan Gruber and Pamela A. Shaw and Brian D. Williamson and Mark J. van der Laan},
journal= {arXiv preprint arXiv:2602.24131},
year = {2026}
}