Consider a two-sample situation (Z = 0,1), in which the hazard is exponential: for the continuous…

Consider a two-sample situation (Z = 0,1), in which the hazard is exponential:

for the continuous failure variable T. The time axis is grouped into disjoint

(a) Verify that the resulting discrete model is of the form (2.21) and that the same parameter β

(b) Show that if the grouping intervals are constant so thatmeasures the sample differences.

where c is a positive constant, the discrete model also has the logistic relationship (2.24). For the latter case, note that the log odds ratio is β*, where

(c) Again with constant grouping intervals, show that the model can also be written in the form (2.23) as a mixed discrete and continuous Cox model. Express the relative risk in the discrete model in terms of the relative risk in the continuous model.