TABLE OF CONTENTS A proportional hazards model possesses the property that different individuals have hazard functions that are proportional to one another, i.e., h( t x 1)/ h( tx 2), the ratio of hazard functions for two individuals with covariates x ? 1 = [ x 11, x 12, , x 1 p] and x ? 2 = [ x 21, x 22, , x 2 p, does not vary with time t. This implies that, given a set of covariates x, the hazard function can be written as:
where g(x) is a function of x and h o( t) can be regarded as a baseline hazard function for an individual for whom g( x) = 1. The model forces the hazard ratio between two individuals to be constant over time since:
If the relative risk function g is taken as the exponential, additive effects on the log-linear scale are obtained. The effects of covariates are such that the baseline hazard function, h o( t), is modified multiplicatively by covariates (including group indicators), so that the hazard function for an individual patient is:
Although specifying a parametric form for h o( t) is straightforward, such a modelling approach has been rendered largely obsolete since Cox (1972) proposed a model...
