1. You must solve this question by hand! You observed the following
sample (+ denotes right censoring):
1.2,1.8,2.0,2.1+,2.9,3.0+,3.4,4.0+,4.1,14.2
(a) Suppose that this sample comes from an exponential distribution. Find
the maximum likelihood estimator of the parameter of the exponential
distribution. Give a 95% confidence interval for that parameter.
(b) Give a 95% confidence interval for S(4) based on the exponential distri-
bution.
2. In a study designed to assess the time to first exit-site infection (in months) in
patients with renal insufficiency, 43 patients utilized a surgically placed catheter
(Group 1), and 76 patients utilized a percutaneous placement of their catheter
(Group 2). Catheter failure was the primary reason for censoring. Cutaneous
exit-site infection was defined as painful cutaneous exit site and positive cultures,
or peritonitis, defined as a presence of clinical symptoms, elevated peritoneal
dialytic fluid. elevated white blood cell count (100 white blood cells /µl with
>50% neutrophils, and positive peritoneal dialytic fluid cultures. The data are
given on my web site on WEBCT.
(a) Fit a Weibull model to data for both groups. Find the maximum estimates
of parameters, λand γ, and their standard errors.
(b) Test the hypothesis that the shape parameter γfor both groups is equal
1 by the likelihood ratio test.
(c) Find the maximum likelihood estimates and a 95% confidence interval for
the two survival functions at five months after placement of the catheter.
Compare these estimates to those obtained using the product-limit esti-
mator.
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