Question

Based on data reported on the International Bone Marrow Transplant Registry, the survival function for a person given an HLA-identical sibling transplant for refractory multiple myeloma is given by

x	S(x)
Months post transplant	Survival probability
0≤x<6	1.00
6≤x<12	0.65
12≤x<18	0.45
18≤x<24	0.35
24≤x<30	0.30
30≤x<36	0.25
36≤x<42	0.15
42≤x<48	0.10
48≤x<54	0.06
x≥54	0

                       

1. Find the probability mass function for the time to death for a refractory multiple myeloma bone marrow transplant patient, denoted by X.

Pmf =

2. Find the hazard rate of X.

(c) Find the median time to death and the 75^th percentile of X.

Answer 1

We will start solving this example by finding Cumulative Distribution Function(C.D.F.)

Hazard rate is also called as Failure rate.