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From |
Ricardo Ovaldia <ovaldia@yahoo.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: conditional logistic |

Date |
Thu, 25 Oct 2007 05:22:26 -0700 (PDT) |

Dear all, I posted this under a different header and did not get a reply. So let me ask the question better. What is the difference between conditional logistic regression grouping on clinic and unconditional logistic regression including clinic as a dummy (indicator) variable? Tha is, what is the difference in model assumptions and parameter estimates? Thank you, Ricardo. --- Ricardo Ovaldia <ovaldia@yahoo.com> wrote: > Thank you Dr. Gould for a thorough and clear > explanation. > > I have a similar problem related to conditional > logistic regression. I have data from a multi-center > (7 clinics) study. I analyzed the data using > conditional logistic grouping on clinic. I was asked > to defend my method, because previous analyses on > these data were performed using indicator variables > or > simply using a robust variance estimator. > > I am planning on using the explanation from Dr. > Gould > post, however, the argument that I would use for > conditional logistic is the same as that presented > for > the indicator variables (dummies) . So I am missing > something, what is the difference? By the way, the > results I obtained using conditional logistic and > dummies are very similar. > > Thank you, > Ricardo > > > > > --- "William Gould, StataCorp LP" <wgould@stata.com> > wrote: > > > Daniel Koralek <dkoralek@unc.edu> writes about > using > > -stcox- on individual > > data where each individual was recruited from one > of > > ten centers. He is > > concerned that which center may influence survival > > because "different foods > > eaten in different regions may influence > nutrients". > > > > He considers three ways of dealing with this > > problem, > > > > . stcox ..., vce(cluster center) > > > (1) > > > > . xi: stcox ... i.center > > > (2) > > > > . stcox ..., stratify(center) > > > (3) > > > > and, of course, he could ignore center altogether > > > > . stcox ... [center completely omitted] > > > (0) > > > > As a matter of notation, let's assume the other > > covariates in the > > models (the ... part) are x1 and x2. > > > > My comments are as follows: > > > > Re solution (0): > > > > This solution assumes center has no effect > and > > Daniel has already > > raised concerns that it does, so the solution > > is inappropriate. > > > > Re solution (1): > > > > This solution also assumes center has no > > effect; it instead > > conservatively handles the situation where > the > > individual patients > > are overly homogeneous, which is to say, not > > independent draws. > > Actually, I didn't say that exactly right for > > the Cox model, but > > what I said implies what what I should have > > said, which is that > > selection of the failures from the risk pools > > at each failure time > > are not independent. > > > > Daniel tried solution (1) and found that the > > standard errors changed, > > but the reported coefficients did not. > > Exactly. Under solution (1), > > because center has no effect, the > coefficients > > estimated the standard > > way are fine, although perhaps inefficient. > > The lack of independence, > > however, means standard errors usually will > be > > understated and > > -vce(cluster center)- handles that. > > > > Re solution (2): > > > > This solution assumes that center does have a > > direct effect on > > survival, and it constrains the effect to be > a > > multiplicative > > shift in the the baseline hazard function. > The > > baseline hazard > > function ho(t) is a function of time, such as > > > > ho(t) > > | . > > | . . . > > |. . . > > | . . > > | . . > > | > > +------------------- time > > > > FYI, the baseline survival function So(t) is > > the integral of > > ho(t), negated and exponentiated. There's > > nothing deep there; > > that's just the mathematical formula for > > calculating one one > > from the other. I switchd to hazard > > functions, however, > > because the hazard function is the natural > > metric for the Cox model. > > The hazard rate for a particular individual > in > > the data at a particular > > time is just ho(t)*exp(X_i*b), where X_i are > > the individual's covariates > > at time t. That's why I said solution (2) > > constrains each center's > > effect to be a multiplicative shift of > ho(t). > > > > Concerning our use of dummy variables for > the > > centers, > > we would like to think that we chose this > > particular functional form > > because it is truly representative of how > the > > different > > foods served in the different centers > > influence the hazard, but > > the fact is that we choose this functional > > form because it is > > convenient; the effect of each center is > > wrapped up in just a > > single coefficient. > > > > This is not a bad approach. > > > > Re solution (2.5): > > > > Alright, I admit that Daniel did not include > a > > solution (2.5), but > > I want to add it; it will help to understand > > solution (2), and > > is often useful in and of itself. > > > > Solution (2) was > > > > . xi: stcox ... i.center > > > (2) > > > > Solution 2.5 is > > > > . xi: stcox ... i.center i.center*x1 > > > (2.5) > > > > In this solution, we assume that center does > > not merely shift > > the hazard function in a multiplicative way, > > we assume that > > center modifies the effect of x1. > > > > Actually, there are a lot of solution > (2.5)'s. > > I could have chosen > > x2 rather than x1, > > > > . xi: stcox ... i.center i.center*x2 > > > === message truncated === Ricardo Ovaldia, MS Statistician Oklahoma City, OK __________________________________________________ Do You Yahoo!? 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**Follow-Ups**:**Re: st: conditional logistic***From:*"David W. Harless" <dwharles@vcu.edu>

**References**:**Re: st: clustering in proportional hazards models with stata/mp 10.0 - conditional logistic***From:*Ricardo Ovaldia <ovaldia@yahoo.com>

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