Doubly Flexible Estimation under Label Shift.

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Many studies require estimating parameters in a target population (Q) with partial data, using a source population (P) with complete data.
• Label shift, where the conditional distribution of covariates given the outcome is constant across populations, is a common scenario.
• Traditional methods often rely on accurate models for covariate-outcome relationships and outcome density ratios, which can be challenging to obtain.

Purpose of the Study:

• To develop a robust estimation procedure for target populations under label shift.
• To propose a method that is doubly flexible to misspecifications in outcome regression and density ratios.
• To address the difficulties in estimating outcome density ratios when outcome data is absent in the target population.

Main Methods:

• Leveraging the label shift assumption: P(X|Y) is the same in populations P and Q.
• Utilizing standard nonparametric techniques to approximate conditional expectations of covariates given outcomes.
• Developing an estimation procedure that does not require explicit modeling of the outcome regression or density ratios.

Main Results:

• The proposed method offers greater flexibility than doubly robust methods by allowing misspecification in both outcome regression and density ratios.
• The estimation procedure effectively utilizes information from the source population (P) to infer parameters in the target population (Q).
• Large sample theory for the proposed estimator is developed and validated through simulations and a real-world application.

Conclusions:

• The novel estimation approach provides a powerful tool for handling label shift problems, particularly when direct estimation of density ratios is infeasible.
• The method's double flexibility to model misspecification enhances its applicability in diverse real-world scenarios, including clinical medicine and policy research.
• The study demonstrates the practical utility of the proposed method through its application to the MIMIC-III database.