Appendix I
Proportional Hazards Model
(Sources: Kalbfleisch and Prentice [1], Franses and Paap [2])
A second way to include explanatory variables in a duration model is to scale the hazard function by the function 
, that is,
(I.1) 
where 
denotes an arbitrary, unspecified, baseline hazard function for continuous 
. Again, because the hazard function has to be non-negative, one usually specifies 
as
(I.2) 
If the intercept 
is unequal to 0, the baseline hazard is identified upon a scalar. Here, if one opts for a Weibull or an exponential baseline hazard one again has to restrict 
to 1 to identify the parameters.
The conditional density function of given covariates is
(I.3)
The conditional survivor ...
