A useful monotonic non-linear model with applications in medicine and epidemiology

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.