(i)State the form of the hazard function for the Cox Regression Model, defining all the terms used. (ii)State two advantages of the Cox Regression Model.
Susanna is studying for an on-line test. She has collected data on past attempts at the test and has fitted a Cox Regression Model to the success rate using three covariates:
Employment Z1 = 0 if an employee, and 1 if self-employed.
Attempt Z2 = 0 if first attempt, and 1 if subsequent attempt.
Study time Z3 = 0 if no study time taken, and 1 if study time taken.
Having analysed the data Susanna estimates the parameters as:
Employment 0.4
Attempt -0.2
Study time 1.15
Bill is an employee. He has taken study time and is attempting the test for the second time. Ben is self-employed and is attempting the test for the first time without taking study time.
(iii)Calculate how much more or less likely Ben is to pass, compared with Bill.
Susanna subsequently discovers that the effect of the number of attempts is different for employees and the self-employed.
(iv)Explain how the model could be adjusted to take this into account.
Sample Solution