Due  5/6/2009 12:00 noon

Versions of the Stanford heart transplant data:

1. Data up to 4/1/1974 (103 patients). (SAS book)
2. Data up to 2/14/1980 but only include those who did receive a 
   transplant (184 patients, in R stanford2).
3. Data up to 2/14/1980 for all patients admitted. In the appendix of 
   Kleinbaum: Survival Analysis. (249 patients). But age missing for non-transplant
   subjects.
   A online version is at 
  http://www-stat.stanford.edu/~olshen/hrp262spring01/spring01Assignments/stanf.txt



(1) Fit a weibull regression model with age, age-square and t5 as covariates. with data set #2
(patients live only 1 day or less can cause problem, my suggestion: delete those cases with
survival less than 5 days)

(2) Fit the Cox ph regression model (use data #2 above) with   
     covariates:  age,  age-square, and t5,  

Based on the above Cox model, give (plot) the estimated/predicted survival curve/cumulative hazard curve for 
a transplant patient with age = 45, t5 = 1.3

(3) Fit the Cox model with covariates: age and age-square  (no t5). (with data set #2 above)

predict each patient's survival time by the median of his/her survival curve.

Plot the age vs. median survival from fitted model. 
Also a plot of real data vs age, 
Finally a plot of predicted median from the AFT weibull model in 1.

Comment on each of the above results you got. [not just a SAS output]
Does the Cox model results in general agree with the Weibull model?

(4)  With 103 patients, repeat the analysis similar to our SAS book p. 139
     but include age-square in the covariate. 
     Also try a term of interaction between age and plant.
     Comment on the results.