8.8 In the Weibull model for survival data, the time to response, T , has pdf f(t) = αλtα−1 e−λtα

for t > 0.

Derive the forms for the hazard function and the survivor function. Investigate how changing the shape parameter α affects the shape of the hazard function. Suppose all individuals in a study share the same shape parameter α, but differ in a set of covariates, x. For the ith individual we assume that the λ-parameter, given by λi, is related to the covariates xi by means of the equation, log λi = β

xi.

Show that the model is a proportional hazards model. Show how it may be fitted to the data as a GLM. Compare and contrast this model with that of Example 8.5.