Quantile-Optimal Treatment Regimes

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Optimal treatment regimes are vital for precision medicine and policy interventions.
• Current methods typically focus on maximizing average population benefit.
• Estimating treatment regimes tailored to individual characteristics is a key challenge.

Purpose of the Study:

• To develop a general framework for estimating the quantile-optimal treatment regime.
• To provide robust estimation without requiring a pre-specified outcome regression model.
• To investigate the asymptotic theory of the proposed estimator.

Main Methods:

• Proposed a novel formulation of the estimator as a solution to an optimization problem.
• Utilized empirical process techniques to analyze asymptotic theory.
• Investigated doubly robust estimation and alternative optimality criteria (Gini's mean difference, weighted quantiles).

Main Results:

• Derived nonstandard convergence rates and non-normal limiting distributions for the estimator.
• Filled a theoretical gap in policy search methods, applicable to mean optimality as well.
• Demonstrated estimator performance through numerical simulations and a real-world HIV+ patient data example.

Conclusions:

• The proposed framework offers a robust approach to estimating quantile-optimal treatment regimes.
• The theoretical findings advance the understanding of policy search methods.
• The methods are applicable to static and dynamic treatment regimes and various optimality criteria.