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From |
"josemaria" <[email protected]> |

To |
<[email protected]> |

Subject |
st: Re: interpretation of exponentiated coefficients (cloglog) |

Date |
Tue, 5 Jul 2005 12:35:30 -0300 |

Dear Statalisters: if the eform is to be introduced in cloglog (and in its use in glm) , it should be very well explained what result we obtain, and I think the explanations of David and Stephen helped very much. But I would see as useful to have an option in order to obtain the corresponding relative risk (p/q), without first using predict and then using display . Regards, Jos� Maria Jose Maria Pacheco de Souza, Professor Titular Departamento de Epidemiologia/Faculdade de Saude Publica, USP Av. Dr. Arnaldo, 715 01246-904 - S. Paulo/SP - Brasil fones (11)3082-3886; (11)3066-7724; (11)3768-8612; (11)3714-2403 fax (11)3082-2920; (11)3714-2403 ----- Original Message ----- From: "Stephen P. Jenkins" <[email protected]> Sent: Tuesday, July 05, 2005 5:33 AM Subject: st: interpretation of exponentiated coefficients (cloglog) > > Date: Mon, 4 Jul 2005 10:49:52 +0100 > > From: "David Harrison" <[email protected]> > > Subject: RE: st: interpretation of exponentiated coefficients > > > > I don't think the -eform- could ever be "not appropriate" for > > a GLM... it is just easier to interpret with some link > > functions than others. In the case of -cloglog-, if we take > > the easiest case of a binary variable, the exponentiated > > coefficient would be: > > > > - -log(1-p)/-log(1-q) > > > > where p is the probability of the outcome given our binary > > variable is true and q is the probabilty of the outcome given > > our binary variable is false. As far as I know, this has no > > name. By comparison, the relative risk would be p/q, and the > > odds ratio (p/(1-p))/(q/(1-q)). > > > > There does seem to be some relationship with hazards, as the > > cumulative hazard function is -log(1-F(t)), where F(t) is the > > distribution function of the time to an event. If the outcome > > Y is the probability that this event happens before a fixed > > time t then you have P(Y=1) = P(T<t) = F(t) and the -eform- > > of the -cloglog- model is the ratio of the cumulative hazard > > functions for this event, evaluated at t. I still wouldn't > > really call this a hazard ratio. > > The -cloglog- model is the discrete time (a.k.a. grouped data or > interval-censored) model representation of the continuous time > proportional hazard model (see entry -discrete- in the [ST] manual). > The beta (regression slope) coefficients estimated in the -cloglog- > model are the beta (regression slope) coefficients from the underlying > PH model. exp(beta_k) for the k_th regressor is indeed a "hazard > ratio". > > Given this important interpretation, and since most people probably use > -cloglog- for hazard regression applications, I've been asking StataCorp > to add the eform option to -cloglog- for years (at User Group meetings). > > It hasn't been implemented perhaps because one can also now estimate a > -cloglog- model by ML using -glm- and get eform coefficients that way. > But that is not a very good reason because we can also estimate a > -logit- model using -glm- and get eform coefficients ... and yet, of > course, we can get odds ratios directly via -logistic-. > > I would support addition of an eform option to -cloglog-. > > > Stephen > * * 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: interpretation of exponentiated coefficients (cloglog)***From:*"Stephen P. Jenkins" <[email protected]>

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