The assumptions behind Cox regression are similar to other types of generalized linear models. Nevertheless, there are some additional assumptions that need to be tested, such as the hazards being proportional and the failure times not being tied.
More information help stcox postestimation
Checklist
Time-to-event outcome
The y-variable has to reflect time-to-event.
Independence of errors
Data should be independent, i.e. not derived from any dependent samples design, e.g. before-after measurements/paired samples.
Correct model specification
Your model should be correctly specified. This means that the x-variables that are included should be meaningful and contribute to the model. No important (confounding) variables should be omitted (often referred to as omitted variable bias).
No multicollinearity
Multicollinearity may occur when two or more x-variables that are included simultaneously in the model are strongly correlated with each another. Actually, this does not violate the assumptions, but is does create greater standard errors which makes it harder to reject the null hypothesis.
