Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems

• URL: http://arxiv.org/abs/2602.24131v1
• Date: Fri, 27 Feb 2026 16:08:41 GMT
• Title: Efficient Targeted Maximum Likelihood Estimators for Two-Phase Design Problems
• Abstract summary: In a two-phase design, a random sample is drawn from the target population in phase 1, during which only a subset of variables is collected.<n>In phase 2, a subsample of the phase-1 cohort is selected, and additional variables are measured.<n>We assume coarsening at random, that is, the phase-2 sampling mechanism depends only on variables fully observed.
• Score: 3.6210754412846318
• License: http://creativecommons.org/licenses/by/4.0/
• 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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