Title: Simultaneous selection and inference for varying coefficients with zero regions: A soft thresholding approach
Authors: Yi Li - University of Michigan (United States) [presenting]
Abstract: Varying coefficient models have emerged as an important tool to explore dynamic patterns in many scientific areas, such as biomedicine, finance, and epidemiology. An often overlooked aspect, however, is that some varying coefficients may have regions where the effects are zero. In a preoperative opioid use study, it was found that the association between opioid use and pain level only exists among patients with the body mass index between 25 and 30. Detection of no-effect regions of the body mass index, referred to as zero regions, is important for opioid prescription management. However, most existing methods ignore detection of zero regions. To fill this knowledge gap, we propose a new soft-thresholded varying coefficient model, where the varying coefficients are piecewise smooth with zero regions. Our new modeling approach enables us to perform variable selection and detect the zero regions of selected variables simultaneously, obtain point estimates of the varying coefficients with zero regions and construct the associated sparse confidence intervals. We prove the asymptotic properties of the estimator, and our simulation study reveals that the confidence intervals achieve the desired coverage probability. The utility of the method is further demonstrated via extensive simulation studies as well as analysis of the aforementioned preoperative opioid use study.