On a non-proportional hazards regression model for repeated medical random counts

A wholly parametric non-proportional hazards survival model is introduced. The model retains Cox's constant of proportionality as the leading term in the relative risk but permits additional flexibility by modelling the relative risk as a function of time. Covariate effects are modelled on the log odds scale, a choice which is more in keeping with the spirit of the multiple logistic function, rather than on the logarithmic scale, as in the proportional hazards model. Some basic properties of the model are described. A special feature of the model is that, when the proportional hazards model applies, Cox's regression coefficients are easily recovered and the computation of other time dependent quantities of interest is routine. A semi-Markov version of the model is derived to analyse recurrent sequential state processes and this is applied to a study of valvotomies conducted in the Regional Medical Cardiology Centre in Belfast, Northern Ireland. The results obtained are compared with those from the classical proportional hazards analysis.