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

[Angelo Belardi <angelo.belardi@unibas.ch>]

Roger, thanks a lot for the detailed answers and all the effort.

After a discussion with my colleagues, I have a few follow-up
questions on the subject:

A:  In your last reply you spoke about Cox regression. Would these
statements also apply to hazard models with a
non-parametric baseline hazard function (using -cloglog-)?

B: We work with person-period formatted datasets we got from
reorganising our initial data. Does that have an influence on the
results we get out of -punaf- or can the results be interpreted
similarly?

C: How would the resulting AHFs have to be interpreted? Are they
time-independent as suggested by Samuelsen and Eide (2008) in their
Equation 4? And could these be interpreted in line with the WHO
definition of PAFs, as a "proportional reduction in the hazard ratio"?


Best regards and thanks already for any further help
Angelo


References:
- Sven Ove Samuelsen and Geir Egil Eide. 2008. Attributable fractions with
survival data. Statistics in Medicine 2008; 27:1447–1467.
http://onlinelibrary.wiley.com/doi/10.1002/sim.3022/abstract
- WHO definition of population attributable fraction,
http://www.who.int/healthinfo/global_burden_disease/metrics_paf/en/index.html



Angelo Belardi
Ambizione research group (SNSF)
Department of Clinical Psychology and Psychiatry
University of Basel
Missionsstrasse 60/62
CH-4055 Basel, Switzerland
Email: angelo.belardi@unibas.ch





2013/7/1 Roger B. Newson <r.newson@imperial.ac.uk>
>
> PS I have had a look at the Sauelsen and Eide paper, and would like to make a minor correction. The AHF of Equation 4 looks like the PAF that you would get by using -punaf- after a Cox regression, and is equal (in their notation) to
>
> AHF = 1 - E[exp(beta'Z*)]/E[exp(beta'Z)]
>
> where Z is the covariate vector in the real-world scenario, and Z* is the covariate vector in the fantasy-intervention scenario. If you use -punafcc- after a Cox regression, then you should instead get
>
> PAF = 1 - E[exp(beta'Z*)/exp(beta'Z)]
>
> which is not exactly the same thing. However, whichever formula we use, we should probably use the option -vce(unconditional)- if we use it after a Cox regression, because the covariates at the time of each death are subject to sampling error.
>
>
> Best wishes
>
> Roger
>
> Roger B Newson BSc MSc DPhil
> Lecturer in Medical Statistics
> Respiratory Epidemiology and Public Health Group
> National Heart and Lung Institute
> Imperial College London
> Royal Brompton Campus
> Room 33, Emmanuel Kaye Building
> 1B Manresa Road
> London SW3 6LR
> UNITED KINGDOM
> Tel: +44 (0)20 7352 8121 ext 3381
> Fax: +44 (0)20 7351 8322
> Email: r.newson@imperial.ac.uk
> Web page: http://www.imperial.ac.uk/nhli/r.newson/
> Departmental Web page:
> http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/
>
> Opinions expressed are those of the author, not of the institution.
>
> On 01/07/2013 13:09, Roger B. Newson wrote:
>>
>> Thanks to Carlo for this reference. Yes, the attributable hazard
>> fraction (AHF) in Equation (4) of Samuelsen and Eide (2008) is the same
>> as the population attributable fraction (PAF) produced by -punafcc-
>> after using -stcox-. The confidence interval formulas are a little
>> different. Samuelson and Eide use the percentile bootstrap, whereas the
>> online help for -punafcc- recommends the user to use Shah variances by
>> specifying the option -vce(unconditional)-. You could presumably write a
>> program to use the percentile bootstrap with -punafcc-, though.
>>
>> Best wishes
>>
>> Roger
>>
>> References
>>
>> Sven Ove Samuelsen and Geir Egil Eide. 2008. Attributable fractions with
>> survival data. Statistics in Medicine 2008; 27:1447–1467.
>>
>> Roger B Newson BSc MSc DPhil
>> Lecturer in Medical Statistics
>> Respiratory Epidemiology and Public Health Group
>> National Heart and Lung Institute
>> Imperial College London
>> Royal Brompton Campus
>> Room 33, Emmanuel Kaye Building
>> 1B Manresa Road
>> London SW3 6LR
>> UNITED KINGDOM
>> Tel: +44 (0)20 7352 8121 ext 3381
>> Fax: +44 (0)20 7351 8322
>> Email: r.newson@imperial.ac.uk
>> Web page: http://www.imperial.ac.uk/nhli/r.newson/
>> Departmental Web page:
>> http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/
>>
>>
>> Opinions expressed are those of the author, not of the institution.
>>
>> On 01/07/2013 12:21, Carlo Lazzaro wrote:
>>>
>>> I suppose that Angelo refers to the following reference (access to the
>>> full
>>> text conditional on subscription to Stat Med):
>>>
>>> Samuelsen SO, Eide GE. Attributable fractions with survival data. Stat
>>> Med.
>>> 2008 Apr 30;27(9):1447-67.
>>>
>>> Kind regards,
>>> Carlo
>>> -----Messaggio originale-----
>>> Da: owner-statalist@hsphsun2.harvard.edu
>>> [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Roger B.
>>> Newson
>>> Inviato: lunedì 1 luglio 2013 12:57
>>> A: statalist@hsphsun2.harvard.edu
>>> Oggetto: Re: st: Population attributable fractions (PAFs) in
>>> discrete-time
>>> survival analysis. -punaf-
>>>
>>> Yes, you can use -punaf- after a generalized linear model (GLM) with a
>>> complementary log-log link and a binomial error function. Or after any
>>> other
>>> GLM that gives positive-valued conditional expectations (which includes
>>> proportions and also Gamma and inverse-Gaussian means).
>>>
>>> For proportional-hazard models (and also for case-control data), there
>>> is a
>>> package -punafcc-, which you can also download from SSC, and which
>>> estimates
>>> population attributable hazard factions (after proportional-hazard
>>> regressions), or population attributable fractions (after logit
>>> regressions
>>> on case-control data).
>>>
>>> Angelo has not given the Samuelsen & Eide (2008) reference on PAHFs in
>>> full.
>>> However, I would guess that the PAHFs of that reference would be
>>> either the
>>> same as, or similar to, those produced by -punafcc-. I would very much
>>> like
>>> to know the full reference, so I can read it and find out more.
>>>
>>> I hope this helps.
>>>
>>> Best wishes
>>>
>>> Roger
>>>
>>> Roger B Newson BSc MSc DPhil
>>> Lecturer in Medical Statistics
>>> Respiratory Epidemiology and Public Health Group National Heart and Lung
>>> Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel
>>> Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM
>>> Tel: +44 (0)20 7352 8121 ext 3381
>>> Fax: +44 (0)20 7351 8322
>>> Email: r.newson@imperial.ac.uk
>>> Web page: http://www.imperial.ac.uk/nhli/r.newson/
>>> Departmental Web page:
>>> http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgene
>>>
>>> tics/reph/
>>>
>>> Opinions expressed are those of the author, not of the institution.
>>>
>>> On 01/07/2013 00:13, Angelo Belardi wrote:
>>>>
>>>> Dear All,
>>>>
>>>> I am working on discrete-time proportional hazard models with a
>>>> non-parametric baseline hazard function, using -cloglog- in
>>>> person-period formatted datasets.
>>>>
>>>> I would like to additionally calculate population attributable
>>>> fractions (PAFs) in these models.
>>>> However, I have never worked with PAFs in survival analyses before and
>>>> therefore don't know which functions to use and how to correctly
>>>> interpret the results.
>>>>
>>>> Previously, I calculated PAFs in STATA with the -punaf- package from
>>>> Roger Newson, e.g.
>>>> for logistic regressions.
>>>>
>>>> Can I use -punaf- here as well, just after calculating the estimates
>>>> over -cloglog-?
>>>>
>>>> Or is there another function/package for this situation?
>>>>
>>>> Or would it be better to calculate population attributable hazard
>>>> fractions (PAHFs) as described in Samuelsen & Eide (2008)?
>>>>
>>>>
>>>> Thanks for any help or advice on the subject.
>>>>
>>>> Regards,
>>>> Angelo
>>>>
>>>>
>>>> Ref:
>>>> S. O. Samuelsen, G. E. Eide, Statist. Med. 27, 1447 (2008).
>>>> http://onlinelibrary.wiley.com/doi/10.1002/sim.3022/abstract

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