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Optimal sampling for design-based estimators of regression models.

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  • 1Department of Statistics, University of Auckland, Auckland, New Zealand.

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Summary
This summary is machine-generated.

Optimal two-phase study designs balance resource limits with data informativeness. Generalized raking estimators offer efficiency gains over inverse-probability weighted (IPW) estimators, with distinct optimal designs for each, impacting regression coefficient estimation.

Keywords:
Neyman allocationgeneralized rakinginfluence functionmodel-assisted samplingoptimal designresidualtwo-phase sampling

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Two-phase study designs are crucial for efficiently collecting data in epidemiological and biostatistical research when resources are limited.
  • These designs involve collecting detailed information on a subcohort while relying on broader data for the main cohort.
  • Optimizing sample selection within these designs is key to maximizing statistical power and minimizing costs.

Purpose of the Study:

  • To explore and derive optimal designs for two-phase studies, focusing on design-based estimators.
  • To compare the efficiencies of different optimal designs, particularly for generalized raking estimators versus inverse-probability weighted (IPW) estimators.
  • To investigate the impact of auxiliary information on optimal design choices in measurement-error settings.

Main Methods:

  • Derivation of a closed-form solution for the optimal design in generalized raking estimators.
  • Comparison of optimal designs for generalized raking and IPW estimators.
  • Analysis of general two-phase designs with continuous or discrete outcomes and variables.

Main Results:

  • Optimal designs for generalized raking and IPW estimators can differ significantly.
  • The optimal design for IPW estimation generally provides near-optimal efficiency for generalized raking estimation.
  • Specific settings may allow for further efficiency improvements beyond the IPW-optimal design for generalized raking.

Conclusions:

  • The choice of optimal design in two-phase studies is highly dependent on the chosen analysis estimator.
  • Generalized raking estimators offer advantages, but their optimal design may not align with the simpler IPW-optimal design.
  • Careful consideration of the interplay between design and analysis is necessary for efficient resource allocation in complex studies.