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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Sun, 8 Jan 2012 10:46:30 +0100 |

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/

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

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