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Does the survivor function estimated after running a Proportional Hazards model give valid predicted probabilities of an event happening after a number of time periods?

The only source I've found on this question says that Proportional Hazards estimates can only be used to discern the factor that two hazards rates differ by when comparing two different levels of an independent variable. They argue that the survivor function is invalid because proportional hazards models (like Cox) do not estimate an underlying hazard function, and so it is impossible to say what the actual predicted hazard is at any point.

According to this powerpoint, the answer is no.

I haven't been able to find any other sources that agree or disagree with their claim that proportional hazards models are only useful for comparisons among hazard rates.

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  • $\begingroup$ I am perhaps doing something wrong, but your link does not work for me ... ("Server not found") $\endgroup$ – user5644 Dec 11 '11 at 21:11
  • $\begingroup$ Here is the link (note that there are spaces within the link, which causes problems): gseweb.harvard.edu/~faculty/singer/Presentations/9) ALDA Chapters 14 and 15.ppt $\endgroup$ – gung Dec 11 '11 at 22:42
  • $\begingroup$ isites.harvard.edu/icb/… --> Chapters 14 and 15: Fitting Cox Regression Models $\endgroup$ – ocram Dec 12 '11 at 6:58
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It has always been my understanding that the appeal of the Cox proportional hazards model is that there's no estimation of the underlying hazard function, and as such it is unbound from some of the assumptions about the shape of that hazard.

From that, I've asserted that that means you can't use the Cox model to generate estimates of the survival function, only the differences between them, in front of people who should know better and been met with little objection.

For whatever that's worth.

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