title: Relative risk regression models with inverse polynomials.
abstract: The proportional hazards model assumes that the log hazard ratio is a linear function of parameters. In the current paper, we model the log relative risk as an inverse polynomial, which is particularly suitable for modeling bounded and asymmetric functions. The parameters estimated by maximizing the partial likelihood are consistent and asymptotically normal. The advantages of the inverse polynomial model over the ordinary polynomial model and the fractional polynomial model for fitting various asymmetric log relative risk functions are shown by simulation. The utility of the method is further supported by analyzing two real data sets, addressing the specific question of the location of the minimum risk threshold.
authors: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada. yning@jhsph.edu
authors: Yang
authors: Y
authors: Ning
authors: Mark
authors: M
authors: Woodward
mesh_terms: D050197:Atherosclerosis / Q000401:mortality; D003198:Computer Simulation; D003920:Diabetes Mellitus / Q000401:mortality; D005919:Glomerular Filtration Rate / Q000502:physiology; D006442:Glycated Hemoglobin / Q000032:analysis; D006801:Humans; D008297:Male; D015233:Models, Statistical; D012306:Risk
chemical_list: D006442:Glycated Hemoglobin
keywords: Cox proportional hazards model; inverse polynomial; minimum risk threshold; relative risk regression