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From |
Ricardo Ovaldia <[email protected]> |

To |
[email protected] |

Subject |
Re: st: clustering in proportional hazards models with stata/mp 10.0 - conditional logistic |

Date |
Wed, 24 Oct 2007 05:47:12 -0700 (PDT) |

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" <[email protected]> wrote: > Daniel Koralek <[email protected]> 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 > > or even x1 and x2, > > . xi: stcox ... i.center i.center*x1 > i.center*x2 > > Anyway, in this modeling-based approach, we > need to think carefully > about how the different foods served in the > centers effects the shifting > of the baseline hazard function. Is it just a > shift (solution 2), > or do the different foods modify the effect x1 > (solution 2.5), or > something else? > > We also need to appreciate that we are assuming > the SHAPE of the > survivor function is the same across all > centers and that we are > just moving it up and down, multiplicatively. > > > Re solution (3): > > In this solution, we let the baseline hazard be > different for each > center. That is, rather than assuming the > baseline function is > > ho(t) > | . > | . . . > |. . . > | . . > | . . > | > +------------------- time > > for all centers, albeit shifted, we assume > that above picture might > be the baseline function for center 1, and for > center 2, the function > could be completely different: > > ho(t) > | . . . > | . . > |. . . > | . . > | . . . > | > +------------------- time > === message truncated === Ricardo Ovaldia, MS Statistician Oklahoma City, OK __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! 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**Follow-Ups**:**Re: st: conditional logistic***From:*Ricardo Ovaldia <[email protected]>

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