Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data

Takumi Saegusa (), Tianzhou Ma, Gang Li, Ying Qing Chen and Mei-Ling Ting Lee
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Takumi Saegusa: University of Maryland
Tianzhou Ma: University of Maryland
Gang Li: University of California
Ying Qing Chen: Fred Hutchinson Cancer Research Center
Mei-Ling Ting Lee: University of Maryland

Statistics in Biosciences, 2020, vol. 12, issue 3, No 8, 376-398

Abstract: Abstract 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.

Keywords: HIV; Survival analysis; Threshold regression; Variable selection (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s12561-020-09284-1

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