On Fri, Feb 5, 2010 at 5:48 PM, Terry Therneau <thern...@mayo.edu> wrote: > Before being helpful let me raise a couple of questions: > > 1. "I know I'm looking at longevity data (which is believed to have a > Gompertz distribution for mammals dying from 'old age')". > I'm not as convinced. The Gompertz is a nice story, but is > confounded by individual risk or 'frailty'. But continue > > 2. "the mortality rate will be higher for 'a' younger ages, higher for > 'b' at older ages, and the assumption of the Cox Proportional Hazards > model is violated a priori, isn't it?" > That is correct. So why exactly are you using coxph to fit the data. > > 3. "Yet I found plenty of Gompertz parameter values that differ, and > lead to differences in survival times detectable by coxph, yet pass the > cox.zph test. Should I assume that cox.zph is insufficiently > sensitive..." > > The Cox model fit a model with an average hazard ratio over time. If > the data satisfies the proportional hazards model, then this is all you > need -- this single number tells you everything. If the data does not, > this does not mean that such an average hazard is invalid, it tells you > that this average is not the whole story and coxph is an > oversimplification. I view this as similar to the fact that if a > distribution is Gaussian then then (mean, var) is sufficient, everything > that you ever wanted to know about the data (percentiles, outliers, ...) > is summed up in those two values. If it's not Gaussian it does not > follow that the mean is worthless, but it isn't a complete story. > If you pick your parameters so that the change in hazard ratio is "not > very large", of course cox.zph will not see it. That's also the case > where an overall average is probably a pretty good summary. > > 4: "coxph(Surv(age) ~ group + group:age)" > This is not how a change in hazard ratio over time is approached. The > program should give an error. For one, why do you assume the change is > linear in time? This is rather rare. You might look at the timedep > package. > > 5. Some actual advice -- if you think it is Gompertzian why not fit a > Gompertz distribution? > I don't see anything in CRAN to directly fit Gompertz,
See the functions 'aftreg' and 'phreg' in the package 'eha'. Göran Broström > but the note > below talks about how to do so approximately with survreg. It's a note > to myself of something to add to the survival package documentation, not > yet done, and to my embarassment the file has a time stamp in 1996. Ah > well. > > Terry Therneau > > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- Göran Broström ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
