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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

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

Date |
Sun, 8 Jan 2012 15:58:47 -0500 |

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 > > -------------------------- > > * > > * For searches and help try: > > * http://www.stata.com/help.cgi?search > > * http://www.stata.com/support/statalist/faq > > * http://www.ats.ucla.edu/stat/stata/ > > > > -- > 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 > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: stcox in case the ph-assumption is rejected***From:*Yuval Arbel <yuval.arbel@gmail.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Alex Gamma <alex.gamma@uzh.ch>

**Re: st: stcox in case the ph-assumption is rejected***From:*Yuval Arbel <yuval.arbel@gmail.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Alex Gamma <alex.gamma@uzh.ch>

**Re: st: stcox in case the ph-assumption is rejected***From:*Yuval Arbel <yuval.arbel@gmail.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Yuval Arbel <yuval.arbel@gmail.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Yuval Arbel <yuval.arbel@gmail.com>

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