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From |
May Boggess <mboggess@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Efron and Cumulative hazard |

Date |
13 May 2004 12:44:41 -0500 |

On Thursday, Giorgio wrote: > I've been estimating a cox model with frailty. Unfortunately when I use > the option efron, the cumulative hazard is not an increasing function. Enzo > Coviello has told me that one year ago there was a similar comunication. > Is there still a bug or it does depend on frailty option? > Unfortunately, this is a bug. It occurs when computing the cummulative hazard using the option -efron- (with or without -frailty-) when there are ties of more than two observations in the dataset. This is on our list of things-to-do. In the mean time, here is the way to calculate the cummulative hazard. The formula for the cummulative hazard is on page 150 [ST] stcox (version 8 manual). Let's start with a dataset without ties, so that we are certain we are calculating it correctly. This is the easiest possible case - no covariates. -------------------------------------- clear input t 60 63 66 68 70 77 84 91 94 98 101 105 108 109 112 115 126 143 153 161 164 178 end set seed 12345 gen fail=uniform()>0.5 stset t, fail(fail) sts gen atrisk=n sort _t _d gen mych =sum(_d/atrisk) by _t: replace mych=mych[_N] qui stcox, estimate nohr basech(chbres) qui stcox, estimate nohr basech(chefron) efron list _t _d mych chbres chefron, sepby(_t) -------------------------------------- Now let's add a covariate. This is a little more work. Here I am doing it twice, once for the Breslow method of handling ties, and again for the Efron method: -------------------------------------- clear input t 60 63 66 68 70 77 84 91 94 98 101 105 108 109 112 115 126 143 153 161 164 178 end set seed 12345 gen fail=uniform()>0.5 gen drug=int(uniform()*3+1) stset t, fail(fail) sort _t _d qui stcox drug, estimate nohr basech(chbres) predict xbbres, xb gen expxb=exp(xbbres) gsort -_t -_d gen bot=sum(expxb) sort _t _d by _t: replace bot=bot[1] gen mychbres =sum(_d/bot) by _t: replace mychbres=mychbres[_N] list _t _d mychbres chbres, sepby(_t) qui stcox drug, estimate nohr basech(chefron) efron predict xbef, xb gen expxbef=exp(xbef) gsort -_t -_d gen botef=sum(expxbef) sort _t _d by _t: replace botef=botef[1] gen mychef =sum(_d/botef) by _t: replace mychef=mychef[_N] list _t _d mychef chef chbres, sepby(_t) -------------------------------------- At this point, we should be convinced we are calculating it correctly when there are no ties. So, if you add one more observation, say another 63, you should see that my method still agrees with Stata for both Breslow and Efron. If you then add a third observation at 63, you should see that my method again agrees with Stata for Breslow. The above method for computing the cummulative hazard still works when using the options -frailty() shared()- with -stcox-. --may mmb@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Efron and Cumulative hazard***From:*ricchiuti.g@tiscali.it

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