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Relative risk regression models with inverse polynomials
Author(s) -
Ning Yang,
Woodward Mark
Publication year - 2013
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5761
Subject(s) - inverse , mathematics , polynomial , bounded function , hazard , polynomial regression , function (biology) , log linear model , polynomial and rational function modeling , statistics , regression analysis , linear model , mathematical analysis , chemistry , geometry , organic chemistry , evolutionary biology , biology
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. Copyright © 2013 John Wiley & Sons, Ltd.