PHSELECT Procedure

Let denote the vector explanatory variables for the lth individual, and let be the associated weight. Let denote the k distinct, ordered event times. Let denote the multiplicity of failures at ; that is, is the size of the set of individuals that fail at . Let be the risk set at . Using this notation, the following equations describe the partial likelihood functions that PROC PHSELECT uses to estimate .

Breslow Likelihood

If you incorporate weights, the Breslow likelihood becomes

In a stratified analysis, the partial likelihood is the product of the partial likelihood functions for the individual strata.

The regression coefficients are estimated by maximizing the log of the partial likelihood function with respect to .