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

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

Thanks again for your precise answers.

I have now tried to run -punaf- after my -cloglog- analyses. However,
-punaf- encountered a problem.
The error message that comes up is: "expression (log(_b[_cons]))
evaluates to missing".

I assume that this might be connected to my use of the -noconstant-
option in the -cloglog- commands. For analyses where the calculations
are possible to run without the -nocons- option, -punaf- also gives me
reasonable results and no error message.
However, from what I know I have to use this option because of my
fully non-parametric baseline hazard function.

Is it possible that -punaf- has a problem with that or might the error
be due to something else? How could I solve this issue?

Best regards,
Angelo



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


2013/7/21 Roger B. Newson <r.newson@imperial.ac.uk>

> In reply to Angelo's queries:
>
> 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).
>
> B. If you are working with a dataset with 1 observation per person per period, and the outcome variable is binary, then you should use an estimation command that allows for the clustering of person-periods by persons. For instance, you might use -xtgee-, or you might use -logit-, -logistic-, or -cloglog- with an option like -vce(cluster person)-. The interpretation of the population unattributable and attributable fractions will then be the same as when -punaf- is used after binary data. That is to say, the PAF (or PUF) will be the fraction of the binary outcomes equal to 1 that is attributable (or unattributable) to living in Scenario 0 instead of Scenario 1.
>
> C. The WHO definition of a PAF is an extremely simple special case of the -punaf- definition of a PAF, for the special case of a binary outcome variable, a discrete-valued exposure variable with n levels, and no concomitant (or confounder) variables. And the WHO also assumes that "Scenario 0" is the real world that we live in, and that "Scenario 1" is a user-specified ideal scenario (eg a dream scenario where the whole world stopped smoking, or a dream scenario where the current smokers become ex-smokers, or a more realistic dream scenario where only a proportion of the current smokers quit smoking). The P_i specified by the WHO are the proportions of the population at the i'th exposure level in the real world (Scenario 0). And the P'_i are the proportions of the population that would have the i'th exposure level in the dream scenario (Scenario 1). And the RR_i are the relative risks (ie rate ratios) associated with the comparing the ith exposure level to the lowest exposu!
 re level. So, the -punaf- definition is a generalization of the WHO definition. There seems to be some controversy about how best to generalize the concept of a PAF (or a PUF) to the case of a Cox regression. (At least, I had a different idea from Samuelson and Eide.)
>
>
> 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/popgenetics/reph/
>
> Opinions expressed are those of the author, not of the institution.
>
> On 16/07/2013 23:20, Angelo Belardi wrote:
>>
>> 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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