Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data
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Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data Takumi Saegusa1 · Tianzhou Ma2 · Gang Li3 · Ying Qing Chen4 · Mei‑Ling Ting Lee2 Received: 1 September 2019 / Revised: 13 April 2020 / Accepted: 10 June 2020 © International Chinese Statistical Association 2020
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
* Takumi Saegusa [email protected] 1
Department of Biostatistics, University of Maryland, College Park, MD 20742, USA
2
Department of Epidemiology and Biostatistics, University of Maryland, College Park, MD 20742, USA
3
Department of Biostatistics, University of California, Los Angeles, CA 90095, USA
4
Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA
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Vol.:(0123456789)
Statistics in Biosciences
1 Introduction In analyzing time-to-event data, the Cox proportional hazards regression model [5] is ubiquitous. Its strong proportional hazards assumption is, however, not always appropriate especially when analyzing a complicated mechanism of survival as is the case for HIV drug adherence studies. Such studies involve complex dynamic process affected by many factors including socioeconomic status and psychological characteristics [2, 8, 16]. Threshold regression (TR) provides an attractive alternative to the Cox model because of its flexibility in modeling [24, 25]. In the TR model, fluctuations of health status over time are represented by an underlying stochastic process and time to the event of interest is defined as the first time the process hits a pre-specified boundary threshold. When the underlying process is the Wiener process, its stochasti
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