Problem: Properties of betahat from Cox regression (Exam 2022)

Eksempel

Exam June 2022, problem 3.

The R output below shows some results when estimating a Cox model to a
survival data set of 241 individuals with monoclonal gammopathy of undetermined significance
(MGUS). The fitted model has three covariates: age, sex and mspike. The covariate sex is
binary, whereas the covariates age and mpsike are both continuous. In the data set the values of
the covariate age varies from 34 to 90, and the values for mspike varies from 0.3 to 3.2.

exam_2022_problem3
R commands and R output

Problem

Write down the estimated relative risk function.
Find a confidence interval for the ratio of the hazard rate for a female of age 50 years over
the hazard rate of a female of age 51 years, when the mspike value is the same.
Find a confidence interval for the relative risk function for a male of age 35 years and with
mspike value equal to 1.5.