Statistics for Maintenance Modelling: Proportional Hazards and Accelerated Life Models

# Case Study 2 - Analysis of Survival Data for Cancer Patients¤

The main objective is to compare the effects of the two treatments upon survival time, but in doing so one must take into account other factors that may also influence survival. What actually needs to be studied here is the joint effect of the various factors (i.e. treatment and covariates) in the experiment on survival time.

As a first step in model fitting, a simple proportional hazards model was used, namely h(t; y) = h0(t) g(y) = . This is called an exponential PH model where the baseline hazard is a constant of (see The Hazard Function for the Weibull Distribution screen in the Continuous Lifetime Distributions 1 session). We start with a model involving all of the covariates. This can be done by associating a vector y = (y1, y2, ... , y7) with each individual, where:

- y1 = Performance status
- y2 = Age
- y3 = Months since entry into study
- y4 = 1 if tumor type is squamus, 0 otherwise
- y5 = 1 if tumor type is small, 0 otherwise
- y6 = 1 if tumor type is adeno, 0 otherwise
- y7 = 0 if treatment is test, 1 if it is standard