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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 9 Jan 2012 00:36:23 +0000 |

Maarten gave the reference in the post you are replying to. Nick On Sun, Jan 8, 2012 at 6:08 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote: > 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. >> * * 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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