Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

From |
Yuval Arbel <yuval.arbel@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Sun, 8 Jan 2012 20:08:10 +0200 |

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/

**Follow-Ups**:**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:*Muhammad Anees <anees@aneconomist.com>

**Re: st: stcox in case the ph-assumption is rejected***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: stcox in case the ph-assumption is rejected***From:*Cameron McIntosh <cnm100@hotmail.com>

**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>

- Prev by Date:
**Re: st: Accumulated mean and standard deviation** - Next by Date:
**Re: st: Accumulated mean and standard deviation** - Previous by thread:
**Re: st: stcox in case the ph-assumption is rejected** - Next by thread:
**RE: st: stcox in case the ph-assumption is rejected** - Index(es):