2. Bladder Cancer Data. An exercise in the book Pagano and Gauvreau (2000) 2 features data on 86 patients who after surgery were assigned to placebo or chemotherapy (thiopeta). Endpoint was the time to cancer recurrence (in months). Variables are: time, group (0 - placebo, 1- chemotherapy), and observed (0 - recurrence not observed, 1 - recurrence observed). This data is given in files bladerc. cav | dat |xlsx. Data are given in WinBUGS format bladderBUGS . cav| dat |x1sx. The starter file bladderco. odc contains data and also initial values for parameters and censored observations. Students should understand that these formats are equivalent, and be able to convert one into the other as needed. Assume that observed times are exponentially distributed with the rate parameter A; depending on the covariate group, as As = exp{Bo + 81 x group,} After Po and 1 are estimated, since the variable group takes values 0 or 1, the means for the placebo and treatment times become Ho = exp { Bo} = exp{ -Bo} 1 exp {Bo + B1} = exp{-Bo - B1}, respectively. The censored data are modeled as exponentials left truncated by the censoring time. Use noninformative priors on So and B1. (a) Is the 90% Credible Set for #1 - #o all positive? (b) What is the posterior probability of hypothesis H : #1 > Ho? (c) Comment on the benefits of the treatment (a paragraph). "Bladder cancer data from M Pagano and K Gauvreau, "Principles of Biostatistics, 2nd Ed. Duxbury 2000. Chapter 21, Exercise 9, page 512