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d patients 7–10 were alive, free of relapse at the end of the study. ppose the time to relapse had an exponential distribution with hazard e 1 and the time to death in relapse had a Weibull distribution with rameters 0 and a. Relapse Time (months) Patient Death Time (months) 1 5 11 2 8 12 3 12 15 33* 45 4 24 32 17 28+ 7 16+ 16+ 8. 17+ 17+ 9 19+ 19+ 10 30+ 30+ + Censored observation

d patients 7–10 were alive, free of relapse at the end of the study. ppose the time to relapse had an exponential distribution with hazard e 1 and the time to death in relapse had a Weibull distribution with rameters 0 and a. Relapse Time (months) Patient Death Time (months) 1 5 11 2 8 12 3 12 15 33* 45 4 24 32 17 28+ 7 16+ 16+ 8. 17+ 17+ 9 19+ 19+ 10 30+ 30+ + Censored observation

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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  1. 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 lambda and the time to death in relapse had a Weibull distribution with parameters theta and alpha

(a) Construct the likelihood for the relapse rate lambda.

(c) Suppose we were only allowed to observe a patients death time if the patient relapsed. Construct the likelihood for theta and alpha based on this truncated sample

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 λ and the time to death in relapse had a Weibull distribution with parameters θ and α. | Patient | Relapse Time (months) | Death Time (months) | |---------|-----------------------|---------------------| | 1 | 5 | 11 | | 2 | 8 | 12 | | 3 | 12 | 15 | | 4 | 24 | 33+ | | 5 | 32 | 45 | | 6 | 17 | 28+ | | 7 | 16+ | 16+ | | 8 | 17+ | 17+ | | 9 | 19+ | 19+ | | 10 | 30+ | 30+ | + Censored observation
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 λ and the time to death in relapse had a Weibull distribution with parameters θ and α. | Patient | Relapse Time (months) | Death Time (months) | |---------|-----------------------|---------------------| | 1 | 5 | 11 | | 2 | 8 | 12 | | 3 | 12 | 15 | | 4 | 24 | 33+ | | 5 | 32 | 45 | | 6 | 17 | 28+ | | 7 | 16+ | 16+ | | 8 | 17+ | 17+ | | 9 | 19+ | 19+ | | 10 | 30+ | 30+ | + Censored observation
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