Characterizing Estimator-Regime Transitions in Adaptive Enrichment Trials
Abstract
Adaptive enrichment trials that identify responsive subpopulations allocate a fixed sample across them and estimate each one's effect from the resulting data. For a synthetic control design with adaptive recruitment and borrowing of control outcomes, we ask whether a doubly robust family of targeted maximum likelihood estimators should replace its sample mean; the choice can be made largely at the design stage. A crossing condition weighs the bias removed and the efficiency gained by the doubly robust family against the finite-sample inflation of nuisance estimation; an equal-error boundary, located by simulation, separates the families in the plane of sample size and bias. A consistency principle prices recruiting with the wrong family's variance functional. With three and eight simulated subpopulations the boundary's sign prediction for the mean squared error difference holds in 99.6% of 10,302 comparisons decided at two standard errors. A pre-specified selector commits to the doubly robust family where the squared anticipated bias exceeds the net variance term. Recruiting along that family's path costs up to $0.035$ in the area under the receiver operating characteristic curve; recruiting with the sample mean functional and routing only the analysis removes this cost and about nine tenths of its error excess.
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BibTeX
@misc{luo2026characterizing,
title = {{Characterizing Estimator-Regime Transitions in Adaptive Enrichment Trials}},
author = {Xin Luo and Maria Kudela and Margaret Gamalo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00549},
eprint = {2611.00549},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00549},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Characterizing Estimator-Regime Transitions in Adaptive Enrichment Trials
AU - Xin Luo
AU - Maria Kudela
AU - Margaret Gamalo
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00549
UR - https://arxiv.org/abs/2611.00549
AB - Adaptive enrichment trials that identify responsive subpopulations allocate a fixed sample across them and estimate each one's effect from the resulting data. For a synthetic control design with adaptive recruitment and borrowing of control outcomes, we ask whether a doubly robust family of targeted maximum likelihood estimators should replace its sample mean; the choice can be made largely at the design stage. A crossing condition weighs the bias removed and the efficiency gained by the doubly robust family against the finite-sample inflation of nuisance estimation; an equal-error boundary, located by simulation, separates the families in the plane of sample size and bias. A consistency principle prices recruiting with the wrong family's variance functional. With three and eight simulated subpopulations the boundary's sign prediction for the mean squared error difference holds in 99.6% of 10,302 comparisons decided at two standard errors. A pre-specified selector commits to the doubly robust family where the squared anticipated bias exceeds the net variance term. Recruiting along that family's path costs up to $0.035$ in the area under the receiver operating characteristic curve; recruiting with the sample mean functional and routing only the analysis removes this cost and about nine tenths of its error excess.
ER -