## Description

## 1. Rinderpest Virus in Rabbits with Missing Data.

Temperatures (temp) were

recorded in a rabbit at various times (time) after the rabbit was inoculated with rinderpest

virus (the data modified from Carter and Mitchell, 1958). Rinderpest (RP) is an infectious

viral disease of cattle, domestic buffalo, and some species of wildlife; it is commonly referred

to as cattle plague.

It is characterized by fever, oral erosions, diarrhea, lymphoid necrosis,

and high mortality.

Time after injection Temperature

(time in hrs) (temp in ◦ F)

24 102.8

32 104.5

48 106.5

56 107.0

NA 107.1

70 105.1

72 103.9

75 NA

80 103.2

96 102.1

(a) Using WinBUGS and properly accounting for the missing data demonstrate that

a linear regression with one predictor (time) gives relatively low Bayesian R2

. What are

estimators of the missing data? Does the 95% Credible Set for the slope contain 0? Comment.

(b) Include time2 (squared time) as the second predictor, making the regression quadratic

in variables, but still linear in coefficients. Show that this regression has a larger Bayesian

R2

. What are the estimators of missing data? Do the 95% Credible Sets for parameters in

the quadratic model contain 0? Comment.

Hint: To have cleaner codes, do the modeling in (a) and (b) in two separate WinBUGS

programs.

## 2. Bladder Cancer Data.

An exercise in the book Pagano and Gauvreau (2000) 1

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.csv|dat|xlsx.

Data are given in WinBUGS format bladderBUGS.csv|dat|xlsx. The starter file bladderc0.odc

contains data and also initial values for parameters and censored observations.

Assume that observed times are exponentially distributed with the rate parameter λi

depending on the covariate group, as

λi = exp{β0 + β1 × groupi}

After β0 and β1 are estimated, since the variable group takes values 0 or 1, the means for

the placebo and treatment times become

µ0 =

1

exp{β0}

= exp{−β0}

µ1 =

1

exp{β0 + β1}

= exp{−β0 − β1},

respectively.

The censored data are modeled as exponentials left truncated by the censoring

time. Use noninformative priors on β0 anmd β1.

(a) Is the 90% Credible Set for µ1 − µ0 all positive?

(b) What is the posterior probability of hypothesis H : µ1 > µ0?

(c) Comment on the benefits of the treatment (a paragraph).

1Bladder cancer data from M Pagano and K Gauvreau, ”Principles of Biostatistics, 2nd Ed. Duxbury

2000. Chapter 21, Exercise 9, page 512.

2