Assumptions of the Cox model, from http://www.stat.ubc.ca/~rollin/teach/643w04/lec/node69.html
Though the Cox model is non-parametric to the extent that no assumptions are made about form of the baseline hazard, there are still a number of important issues which need be assessed before the model results can be safely applied.
First and foremost is the issue of non-informative censoring. To satisfy this assumption, the design of the underlying study must ensure that the mechanisms giving rise to censoring of individual subjects are not related to the probability of an event occurring. For example, in clinical studies, care must be taken that continuation of follow-up not depend on a participants medical condition. Violation of this assumption can invalidates just about any sort of survival analysis, from Kaplan-Meier estimation to the Cox model.
The second key assumption in the Cox model is that of proportional hazards. In a regression type setting this means that the survival curves for two strata (determined by the particular choices of values for the
-variables) must have hazard functions
that are proportional over time (i.e. constant relative hazard).
This can be evaluated
graphically using "log-log" plots in the two-sample comparison case.
In that situation, and also for the Cox model, there are tests that can
be applied to test proportionality. Other references:
http://courses.washington.edu/b515/l17.pdf
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