RE: st: stcox in case the ph-assumption is rejected

[Cameron McIntosh <cnm100@hotmail.com>]

Yuval,
Lambert, P.C., & Royston, P. (2009). Further development of flexible parametric models for survival analysis. The Stata Journal, 9(2), 265–290.http://www.pauldickman.com/cancerepi/handouts/handouts_survival/Lambert2009.pdf

Cam

> Date: Sun, 8 Jan 2012 20:08:10 +0200
> Subject: Re: st: stcox in case the ph-assumption is rejected
> From: yuval.arbel@gmail.com
> To: statalist@hsphsun2.harvard.edu
> 
> Thanks Maarten, that was very helpful.
> 
> Can you recommend on good econometric books that deal with survival
> analysis, Cox Regressions and Competing-Risk Models? what is the full
> reference for Lambert and Royston (2009)?
> 
> On Sun, Jan 8, 2012 at 11:46 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
> > On Sat, Jan 7, 2012 at 4:54 PM, Yuval Arbel wrote:
> >> Marteen,
> >>
> >> I don't see why -stpm2- does not solve my problem. After all -stpm2-
> >> somewhat relaxes the PH assumption.
> >
> > Unfortunatley, that is incorrect. You seem to be mistaking a Cox model
> > for a exponential model: an exponential model assumes that the
> > baseline hazard function (and the hazard ratios) is constant over
> > time, a Cox model leaves the shape of the baseline hazard completely
> > free, in fact it does not even estimate it, it only asumes that the
> > hazard ratios (the effects of the explanatory variables) are constant
> > over time. This is called the proportional hazard assumption. In this
> > respect -stcox- is extremely similar to -stpm2- with the
> > -scale(hazard) option. Both are part of the general form:
> >
> > h_i(t) = h_0(t)*exp(b1*x1_i +b2*x2_i ...)
> >
> > So the hazard of observation i at time t is some baseline hazard
> > function that depends on time and a multiplier that depends on the
> > characteristics (the xs) of observation i. -stcox- and -stpm2- differ
> > with respect to the baseline hazard: -stcox- leaves the baseline
> > hazard completely free(*), -stpm2- uses a very flexible paramteric
> > function to approximate the the baseline hazard. In principle one
> > could say that -stcox- is a bit more flexible in the baseline hazard
> > as -stpm2-, in practice it is a difference between a very very
> > flexible baseline hazard function (-stcox-) and a very flexible
> > baseline hazard function (-stpm2-) So it is no surprise that you find
> > very similar results. In fact on page 278 of (Lambert and Royston
> > 2009) the authors of -stpm2- note :
> >
> > "The estimated hazard ratios and their 95% confidence intervals are
> > very similar to the Cox model, and in fact, there is no difference up
> > to four decimal places. We have yet to find an example of a
> > proportional hazards model where there is a large difference in the
> > estimated hazard ratios between these two models."
> >
> > Notice that the efects of the xs in both models (in the default
> > parametrization) do not depend on the time: if x1 increases by 1 unit
> > the baseline hazard will increase by a factor exp(b1). This is what is
> > meant with the proportional hazard assumption, and both models make
> > that assumption. You can relax the proportional hazard assumption by
> > adding an interaction term between (some function of) time and an x,
> > which is what the -tvc()- option does, or you can allow the different
> > groups as represented by an x to have their own baseline hazard, which
> > is what the -stratify()- option does. To use your analogy with fixed
> > effects regression, I would say that the stratify option is closest to
> > fixed effects regression.
> >
> > Hope this helps,
> > Maarten (again, _not_ Marteen)
> >
> > (*) See for example section 7 of
> > <http://www.maartenbuis.nl/wp/survival.pdf> on how -stcox- can
> > estimate hazard ratios without estimating the baseline hazard
> > function.
> >
> > Paul Lambert and Patrick Royston (2009) Further development of
> > flexible parametric models for survival analysis. The Stata Journal
> > 9(2):265-290.
> >
> > --------------------------
> > Maarten L. Buis
> > Institut fuer Soziologie
> > Universitaet Tuebingen
> > Wilhelmstrasse 36
> > 72074 Tuebingen
> > Germany
> >
> >
> > http://www.maartenbuis.nl
> > --------------------------
> > *
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> 
> 
> 
> -- 
> Dr. Yuval Arbel
> School of Business
> Carmel Academic Center
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1: yuval.arbel@carmel.ac.il
> e-mail2: yuval.arbel@gmail.com
> 
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