st: Population attributable fractions (PAFs) in discrete-time survival analysis. -punaf-

[<S.Jenkins@lse.ac.uk>]

As part of his reply to Angelo Belardi <angelo.belardi@unibas.ch>, 
Roger Newson <r.newson@imperial.ac.uk> wrote:
 
> A. You can indeed use -punaf- after -cloglog-. (Or you should be able to
> do so - let me know if you have any problems.) However, the
> interpretation of the attributable and unattributable fractions will
> then be similar to the interpretation of these parameters when you use
> - -punaf- after -logit- or -logistic-. It is probably not a good idea to
> use -punafcc- after -cloglog-. And -punafcc- should probably not be used
> after -logit- or -logistic-, except if your data are from a case-control
> study (for which -punafcc- was written). After a Cox regression, you may
> use either -punaf- or -punafcc-, depending on what kind of population
> unattributable and attributable fractions you wanted to estimate (ie my
> kind or Samuelson and Eider's kind).

My understanding is that Angelo is using -cloglog- to fit the discrete-time  proportional hazard model, i.e. the analogue of the Cox model - which is for continuous survival times -- for interval -censored survival time data. The estimated coefficients on the predictors from the -cloglog- model are exactly the coefficients from the underlying continuous time model, and exp(coeff) is the corresponding hazard ratio. 
Given this context, why is it not a good idea to use -punaf- after -cloglog-? Could you please clarify?

Stephen
------------------
Stephen P. Jenkins <s.jenkins@lse.ac.uk> 

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