The following data consists of the times to relapse and the times to death following relapse...

Transcribed Image Text:

The following data consists of the times to relapse and the times to death following relapse of 10 bone marrow transplant patients. In the sample patients 4 and 6 were alive in relapse at the end of the study and patients 7-10 were alive, free of relapse at the end of the study. Suppose the time to relapse had an exponential distribution with hazard rate and the time to death in relapse had a Weibull distribution with parameters and a. Patient Relapse Time (months) Death Time (months) 1234567890 5 11 8 12 12 15 24 33+ 32 45 17 28+ 16+ 16+ 17+ 17+ 19+ 19+ 30+ 30+ + Censored observation (a) Construct the likelihood for the relapse rate A. (b) Construct a likelihood for the parameters 0 and a. (c) Suppose we were only allowed to observe a patients death time if the patient relapsed. Construct the likelihood for 0 and a based on this truncated sample, and compare it to the results in (b). The following data consists of the times to relapse and the times to death following relapse of 10 bone marrow transplant patients. In the sample patients 4 and 6 were alive in relapse at the end of the study and patients 7-10 were alive, free of relapse at the end of the study. Suppose the time to relapse had an exponential distribution with hazard rate and the time to death in relapse had a Weibull distribution with parameters and a. Patient Relapse Time (months) Death Time (months) 1234567890 5 11 8 12 12 15 24 33+ 32 45 17 28+ 16+ 16+ 17+ 17+ 19+ 19+ 30+ 30+ + Censored observation (a) Construct the likelihood for the relapse rate A. (b) Construct a likelihood for the parameters 0 and a. (c) Suppose we were only allowed to observe a patients death time if the patient relapsed. Construct the likelihood for 0 and a based on this truncated sample, and compare it to the results in (b).