Consider a set of subjects such that the counting process for the th subject represents the number of observed events experienced over time . The sample paths of the process are step functions with jumps of size , with . Let denote the vector of unknown regression coefficients. The multiplicative hazards function for is given by

where

• indicates whether the th subject is at risk at time (specifically, if at risk and otherwise)

• is the vector of explanatory variables for the th subject at time

• is an unspecified baseline hazard function

Refer to Fleming and Harrington (1991) and Andersen et al. (1992). The Cox model is a special case of this multiplicative hazards model, where until the first event or censoring, and thereafter.

The partial likelihood for independent triplets , has the form

where if , and otherwise.