AIC of a weighted cox regression model (coxphw)

Question

I have to compare three cox-regression models. However, one of these violates the PH assumption. Stratfying the variable did not work because it is already categorical. Thus, weighted cox regression would be suitable. I was wondering wether one can extract AIC of a coxphwmodel from the package coxphw? Using extractAIC(model3)just gave 5. Also, is it even possible to compare the models because they employ different methods?

Update:

I found this article by Smith, Betts, Forbes et al. (2011). They mention this article by Chou and Bentler (1996) and write

Because of the weighting, the weighted Cox hazards model is not a true likelihood approach; therefore, we used the Wald χ2 statistic as a large sample approximation to the likelihood, and used −χ2 + 2 * (number of parameters) of the model, as an approximation of AIC (Chou and Bentler 1996).

Any suggestions?

Answer 1

I don't think it's wise to compare standard Cox models with coxphw-weighted models via AIC. With AIC comparisons among models you need to watch out for possible offsets of reported AIC values by a constant. See the Wikipedia entry. Although I haven't thought this through carefully, I fear that the estimated likelihood implied in the work-around proposed by Smith et al might not be comparable to the partial likelihood from a standard Cox model, particularly with respect to that constant offset. You could examine that issue with models of simulated data, I suppose.

For comparing models with different predictors on the same data set, it's probably best to stick with the same model-fitting approach: all standard Cox or all coxphw. If proportional hazards hold for one Cox model then the coxphw weighting shouldn't matter, as the event-average (standard Cox) and weighted-average (coxphw) models should be pretty much the same. If PH doesn't hold for a Cox model it won't for the coxphw-weighted model either. You just get what might be considered a better "average HR" estimate--of something that, absent PH, isn't really an HR.