Description
1. The following table gives survival data from 30 patients with AML. Two possible
prognostic factors are considered:
x1 =
(
1 if patient ≥ 50 years old
0 otherwise
x2 =
(
1 if cellularity of mallow clot section is 100%
0 otherwise
Table. Survival Times and Data of Two Possible
Prognostic Factors and 30 AML Patients
Survival Time x1 x2 Survival Time x1 x2
18 0 0 8 1 0
9 0 1 2 1 1
28+ 0 0 26+ 1 0
31 0 1 10 1 1
39+ 0 1 4 1 0
19+ 0 1 3 1 0
45+ 0 1 4 1 0
6 0 1 18 1 1
8 0 1 8 1 1
15 0 1 3 1 1
23 0 0 14 1 1
28+ 0 0 3 1 0
7 0 1 13 1 1
12 1 0 13 1 1
9 1 0 35+ 1 0
Assuming cox proportional hazard model and use the exact likelihood to handle
the tie observations. Test if the prognostic factors are significant. Compare the
results with the function “survdiff”.
2. You are given a data set in the file “ass4.csv”. It contains the following variables:
lstay Length of stay of a resident
age Age of a resident
trt Nursing home assignment (1: receive treatment,0: control)
gender Gender (1:male,0:female)
marstat Marital status (1: married,0: not married)
hlstat Health status (2: second best, 5: worst)
cens Censoring indicator (1:censored, 0: discharged)
Use 123457 as the seed number to generate a sample of size 1000 and use this
sample to model the home nursing home duration times, measured by days, as
a function of patient characteristics.
(a) Test if the patient characteristics have no impact on the home duration
times. State all three test values (Wald, likelihood ratio and score).
(b) Based on the individual z-scores, can we remove all covariates which pvalues are greater than 0.05? State the null hypothesis we want to test.
Give all three tests (Wald, likelihood ratio and score) and their p-values.
(c) Based on the simplified model, give a 95% confidence interval on the hazard
ratio of the patient with status=4 compared with those with status=5.
