Relative risk regression models with inverse polynomials

Authors

  • Yang Ning,

    Corresponding author
    • Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada
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  • Mark Woodward

    1. George Institute for Global Health, University of Sydney, Sydney, Australia
    2. Department of Epidemiology, Johns Hopkins University, Baltimore, Maryland, U.S.A.
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Correspondence to: Yang Ning, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada.

E-mail: yning@jhsph.edu

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. Copyright © 2013 John Wiley & Sons, Ltd.

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