A semi-parametric model that describes the relationship between a time to event response
variable and one or more explanatory variables using a hazard function.
The Cox proportional hazard model is expressed as a hazard function h0(t) +
exp(∑βiXi). The formula expresses the hazard at time t for an
individual with a given set of explanatory variables as the product of two quantities. The
first quantity is h0(t), the baseline hazard function. The second quantity is
the exponent of the linear sum βiXi where the sum is over the p
explanatory variables. An important feature of the proportional hazards model is that the
baseline hazard function is a function of t but does not include the Xs. Therefore, it is
unnecessary to specify the form of the baseline function in estimating the parameters.
Also, the parameters in the second quantity are dependent only on the Xs and are
independent of time. The unknown model parameters are estimated using maximum-likelihood