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Exploration of Heterogeneous Treatment Effects via Concave Fusion
Shujie Ma1, Jian Huang2, Zhiwei Zhang1
1Department of Statistics, University of California at Riverside, Riverside, California 92521, USA.
Abstract:
Understanding treatment heterogeneity is essential to the development of precision medicine, which seeks to tailor medical treatments to subgroups of patients with similar characteristics. One of the challenges of achieving this goal is that we usually do not have a priori knowledge of the grouping information of patients with respect to treatment effect. To address this problem, we consider a heterogeneous regression model which allows the coefficients for treatment variables to be subject-dependent with unknown grouping information. We develop a concave fusion penalized method for estimating the grouping structure and the subgroup-specific treatment effects, and derive an alternating direction method of multipliers algorithm for its implementation. We also study the theoretical properties of the proposed method and show that under suitable conditions there exists a local minimizer that equals the oracle least squares estimator based on a priori knowledge of the true grouping information with high probability. This provides theoretical support for making statistical inference about the subgroup-specific treatment effects using the proposed method. The proposed method is illustrated in simulation studies and illustrated with real data from an AIDS Clinical Trials Group Study.
Insights
This study introduces a new method to identify patient subgroups and their specific treatment effects, advancing precision medicine. The approach effectively estimates treatment heterogeneity without prior patient grouping knowledge.
Area of Science:
- Biostatistics
- Computational Biology
- Precision Medicine
Background:
- Precision medicine requires tailoring treatments to patient subgroups.
- Identifying these subgroups and their unique treatment responses is challenging due to unknown grouping information.
Purpose of the Study:
- To develop a statistical method for estimating subgroup structures and treatment effects.
- To address the challenge of unknown patient grouping in heterogeneous treatment effect analysis.
Main Methods:
- A heterogeneous regression model with subject-dependent coefficients for unknown groupings.
- A concave fusion penalized method for estimating grouping and subgroup-specific effects.
- An alternating direction method of multipliers algorithm for implementation.
Main Results:
- The proposed method accurately estimates patient groupings and subgroup-specific treatment effects.
- Theoretical analysis shows the method's consistency with oracle estimators under ideal conditions.
- The approach was validated through simulations and real-world AIDS Clinical Trials Group data.
Conclusions:
- This novel penalized regression approach effectively identifies patient subgroups and their distinct treatment effects.
- The method provides a robust framework for statistical inference in precision medicine.
- It advances the goal of tailoring medical treatments to specific patient populations.
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