Abstract:
Cox proportional hazards (PH) model is one of the
finest techniques in identifying combined effects of several
covariates on the relative risk (hazard). This model assumes
that the hazards of the different strata formed by the levels of
the covariates are proportional. The primary objective of this
paper is to illustrate the usefulness of a global goodness-offit
test proposed by Schoenfeld for testing the PH assumption.
Though several classical methods have been discussed in
previous studies there is no one research paper that compares
Schoenfeld’s method with these. Moreover, programmes
are developed in SAS for constructing this global goodnessof-
fit test. In this paper the proposed test is applied to a real,
large scale data set that involves several covariates, whereas
Schoenfeld has used only a small data set with only one
covariate to illustrate this new test.
Using Kaplan-Meier curves, a preliminary analysis was
conducted on the survival data. Then, a Cox PH model was fitted
to the data. All the methods and residual analysis including the
global goodness-of-fit test indicated that for the data set used
the assumption of PH is violated. However, other than for the
global goodness-of-fit test all other techniques are based on
graphical methods and are thus subjective. Hence, for cases
where the violation of the PH assumption is marginal these
graphical methods may be inadequate to detect this departure.
However, as the global goodness-of-fit test is an objective test
it is recommended as the best among the methods compared.
