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A useful monotonic non‐linear model with applications in medicine and epidemiology
Author(s) -
Royston Patrick
Publication year - 2000
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 - 10.1002/1097-0258(20000815)19:15<2053::aid-sim505>3.0.co;2-6
Subject(s) - monotonic function , epidemiology , computer science , linear model , econometrics , medicine , mathematics , machine learning , mathematical analysis
In medicine and epidemiology monotonic curves are important as models for relations which prior knowledge or scientific reasoning dictate should increase or decrease consistently with the predictor value. An example is the monotonically increasing relation between cigarette consumption and the risk of coronary heart disease. In this paper I propose a new class of monotonic non‐linear models which generalizes the well‐known power and exponential transformations of a covariate. The models are cousins of the Gompertz family of growth curves and include non‐sigmoid and asymmetric sigmoid curves. I explore their properties and illustrate their usefulness in three substantial medical and epidemiological data sets. Copyright © 2000 John Wiley & Sons, Ltd.