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


From   [email protected]
To   [email protected]
Subject   Re: st: Re: interpretation of exponentiated coefficients (cloglog)
Date   Wed, 6 Jul 2005 16:53:36 EDT

Good idea Jose. In the meantime you can create a short post estimation  
command that provides the related RR's. 
 
Don't forget that cloglog can be used to model binary or  
grouped/proportional data in a manner similar to that of logistic and probit. At  times a binary 
model calls for a cloglog -- or even loglog -- link to obtain  the "best" 
model, as defined by various GOF tests including AIC and BIC  statistics. cloglog 
has other uses than with survival concerns. 
 
Joe Hilbe
=========================
 
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´┐Ż 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
>

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