Fit a gamma model and calculate maximum likelihood estimate.

Leukemia free-survival times (in months) for Autologous and Allogeneic Transplants The leukemia-free survival times for the 50 allo transplant patients: 0.030, 0.855, 1.184, 1.283, 1.480, 1.776. 2.138. 0.493, 2.500, 2.763, 2.993. 3.224. 3.421, 4.178. 4.441*, 5.691. 5.855+, 6.941+, 6.941, 7.993*, 8.882 8.882, 9.145*, 11 480, 11.513, 12.105*, 12.796, 12.993*, 13.849*, 16.612*, 17.138* 20.066, 20.329*, 22.368*, 26.776*, 28.717*, 28.717*, 32.928*, 33.783+, 34.211*, 34.770*, 39.539*, 41.118*, 45.033*, 46.053+, 46.941*, 48.289*, 57.401*, 58.322, 60.625+ The leukemia-free survival times for the 51 auto transplant patients: 4.836+ 0.658, 0.822, 1.414, 2.500, 3.322, 3.816, 4.737, 4.934, 5.033, 5.757, 5.855, 5.987, 6.151. 6.217, 6.447", 8.651, 8.717, 9.441+, 10.329 11.480, 12.007, 12.007+, 12.237, 12.401+, 13.059*, 14.474*, 15.000*, 15.461, 15.757, 16.480, 16.711, 17.204+, 17.237, 17.303*, 17.664*, 18.092, 18.092*, 18.750*, 20.625*, 27.730*, 31.184+, 32.434*, 35.921+, 42.237, 44.638*, 46.480*, 23.158, 47.467+, 48.3227, 56.086 + denotes a censored observation. a) For both the allo and auto groups, fit a gamma model to the data. Find the maximum likelihood estimates of a and B. Hint: see the R functions dgamma and pgamma. You need to define the censoring indicator from the information given in the table. b) Find the maximum likelihood estimates of the median survival for both groups, and comment Hint: If to is the median survival time, then S(t,) = 0.5. Use # and a from (a) to find tm. c) Find the standard error of a + 8 for the auto group