What's the appropriate way to compare various survival (streg) models?

[Nick Cain]

Dear Survival Specialists,

After running the estat phtest command and finding that my data is not appropriate for the Cox proportional hazards model, I am trying to determine which of the alternate survival models are most appropriate to my data (e.g., Weibull, log-normal, Gompertz, etc).

Should I compare my survival curve to the various plots and determine the best model a priori or is it appropriate to compare the AICs of these various models after estimation to determine the appropriate functional form?

Thanks!

-nick

[Marcos Almeida]

Hello, Nick Cain,

I'm not at all a "survival specialist". That said, and assuming you in fact performed - estat phtest, detail -, there are many options and "paths" to follow, and several of them are still under the Cox regression "umbrella". To name a few:

A. You may stratify the "guilty" variable.

B. You may go for an extended Cox model (by including a time-dependent variable, splitting the model under heavyside functions, including a function of time, or a mix of these options).


However, if you feel there is call (take it as the "rationale") for a parametric model, perhaps you could apply a generalized gamma regression and, after checking the kappa and sigma, select among an exponential, Weibull or lognormal model.

Finally, please keep in mind that, apart from postestimation plots, you can employ likelihood-ratio tests for comparisons between nested models and, if not, there is always the information criteria, say, an AIC awaiting round the corner...

Hopefully that helps.

Best,

Marcos

[Steve Samuels]

I agree with Marcos about trying to model the non-proportionality. streg is a last choice for me: the number of models is limited; 1) you can't use the the Weibull or exponential models, as these are restrictive cases of the proportional hazards model, which you've already rejected; 2) the remaining functional forms are rather inflexible, but you might get lucky and find one that fits your data. I do like Paul Lambert's stpm2 (SSC), which fits semi-parametric models and can also handle non-proportionality. There's a nice handout describing it at stata.com/meeting/uk09/uk09_lambert_royston.pdf

[Nick Cain]

Hello Marcos and Steve -- and thanks for your comments.

I have improved my dataset by adding more observations and am stepping through the survival analysis again. When I re-run the phtest, detail command only one variable (a control variable) is significant, although the p-value of my primary variable of interest is just above the critical threshold (0.0543).

If the p-values for Global Test are strongly nonsignificant, is it OK to use a proportional hazards model?

Thanks again!

-nick

PS: I am attaching stcoxkm plots as well.stcoxkm_plot.pdf