cox ph

[Matt Piercy]

I have a question about interpretation of cox model vs weibull (or other parametric model). I have fitted the data to both and the weibull has a lower Akaike information criterion. Does this make it a better model? The Cox PH test is not rejected and the Weibull shape parameter (1/p in stata) is not 1 (i.e. no constant hazard or mathematically exponential dist). Is the lower AIC better or is there more to it? I know there is an extra assumption in Weibull about the baseline hazard function which is not fitted in Cox but is the model otherwise better? Second in a couple of books I have read about the Cox-Oates test, which tests (as I understand it) whether the hazard function is constant i.e. Cox appropriate. I queried stata on this and they don't provide this test, but it seems equivalent (to me at least) as to whether the shape parameter is 1. Can you comment please?

[George Ford]

I don't think AIC comparison is useful. Different likelihood functions; non-nested models.

If you use different distributions (log-normal, log-logistic, Gompertz) in streg, I suspect you can AIC-compare those.

stcoxgof is your ado for Cox-Oates.

The two approaches are different. You'd need to think about how and which one you prefer for your specific purpose.

[Matt Piercy]

Thanks George. I gathered the AIC was not useful as the models were too different. I was not aware of the stcoxgof. Thanks for that.

[Matt Piercy]

I tried out the coxgof and compared it to the cox-oates in the book 'Analysis of Survival Data' by Cox and Oates (Chapman and Hall published 1984). They use it to test exponential distribution in Weibull i.e. shape =1. Is the cox-oates test appropriate for cox model?

[Matt Piercy]

I think I have got it now. Cox-Oates is a measure of whether the baseline hazard function is different in the two groups in the coxgof command. It is based on the score test which is 1st deriv of log likelihood function, and the p-value is the standard normal of this (i.e. c-o is a z stat). In the example in the book they use it to test whether the shape parameter =1 i.e. baseline hazard = ongoing hazard. It could be used to test a cox model if there are two groups to see if the hazard is different and as the hazard is assumed to be constant this would be the same thing.