Takumi Saegusa, Tianzhou Ma, Gang Li, Ying Qing Chen, Mei-Ling Ting Lee
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Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data.
The threshold regression model is an effective alternative to the Cox proportional hazards regression model when the proportional hazards assumption is not met. This paper considers variable selection for threshold regression. This model has separate regression functions for the initial health status and the speed of degradation in health. This flexibility is an important advantage when considering relevant risk factors for a complex time-to-event model where one needs to decide which variables should be included in the regression function for the initial health status, in the function for the speed of degradation in health, or in both functions. In this paper, we extend the broken adaptive ridge (BAR) method, originally designed for variable selection for one regression function, to simultaneous variable selection for both regression functions needed in the threshold regression model. We establish variable selection consistency of the proposed method and asymptotic normality of the estimator of non-zero regression coefficients. Simulation results show that our method outperformed threshold regression without variable selection and variable selection based on the Akaike information criterion. We apply the proposed method to data from an HIV drug adherence study in which electronic monitoring of drug intake is used to identify risk factors for non- adherence.
期刊介绍:
Statistics in Biosciences (SIBS) is published three times a year in print and electronic form. It aims at development and application of statistical methods and their interface with other quantitative methods, such as computational and mathematical methods, in biological and life science, health science, and biopharmaceutical and biotechnological science.
SIBS publishes scientific papers and review articles in four sections, with the first two sections as the primary sections. Original Articles publish novel statistical and quantitative methods in biosciences. The Bioscience Case Studies and Practice Articles publish papers that advance statistical practice in biosciences, such as case studies, innovative applications of existing methods that further understanding of subject-matter science, evaluation of existing methods and data sources. Review Articles publish papers that review an area of statistical and quantitative methodology, software, and data sources in biosciences. Commentaries provide perspectives of research topics or policy issues that are of current quantitative interest in biosciences, reactions to an article published in the journal, and scholarly essays. Substantive science is essential in motivating and demonstrating the methodological development and use for an article to be acceptable. Articles published in SIBS share the goal of promoting evidence-based real world practice and policy making through effective and timely interaction and communication of statisticians and quantitative researchers with subject-matter scientists in biosciences.