I got a few replies to my inquiry about PAR%. I have also had some
requests for feedback and so am posting the gist of the responses to
the list for those interested. I also saw a piece on the STATA list to
which I had *not* sent a posting). I include this for interest.

Essentially there are two camps: those who say I can and those who say
I  cannot. I tend to go for the arguments against but I found that the
confidence interval on my estimate of Population AR were very
wide,whether I used logistic regression, glm or STATAs xtgee
functions. I did not go as faar as bootstrapping, as suggested by
Kaufman.

The result for me is an exploration of my data and a rapid lesson on
the interpretation of logistic regression and GLM coefficients.
However, I am not sure whether I shall include attributable risk in
the final draft of my paper.

Thanks to all of those who took the time to help me

Regards

Terry


replies received a numbered 1-5



 1.
 I can answer part of your question. If your survey has agenuinely 
 representative sample of the population (!) so thatobese and 
 non-obese are represented in their correct proportions,your   OR
 estimates are probably both unbiased and efficient. Then,  if Ie is
 incidence of diabetes in the exposed (obese) population  and Io the
 incidence in the unexposed (non-obese),   

AttributableRisk  (AR) is Ie - Io, and AR% is (Ie - Io)/Ie. 

By dividing eachelement by Io, this becomes (RR - 1)/RR.Since for 
"rare"conditions, OR approximates to RR, AR% can be estimated   from
anon-cohort study whereas AR itself cannot.   Turning to PAR etc, ifp
is the proportion of the population   which is exposed(i.e.obese), 

PAR = p(Ie - Io), and 

PAR% =   {p(Ie - Io)/(p.Ie + (1 -p).Io)}. 

Again, dividing each element  by   Io gives 

PAR% as {p(RR -1)/ (1 + p(RR - 1)}.  

So, using the OR   approximation to RR, we canestimate PAR% but not
PAR itself.   I'm not sure whether across-sectional survey invalidates
this,   but I don't see why itshould. 

2.
Survey data is such a loose term... do you mean that you have a 
random sample of the population of interest?  This is important as for
PAR you need to know what proportion of your target population is
'exposed'/or is positive for that risk factor (obesity?)

Secondly RR and OR are not cloase in value except in special 
circumstances (when the probability of  the outcome of interest is
'small').   The OR is always higher than RR.  I would suggest that you
do not use it as a proxy else you will overestimate the PAR.

Why not calcalate  RR?  it sounds like you have enough information to
do so.


3.
> the answer is yes you can get an estimate of PAR from a logistic
> model, (with the disclaimer about assuming causality etc).
> 
> Instead of using OR's as proxies for RRs, you can set your risk
> factor to be zero for all people and see how many cases your model
> predicts. The difference between observed and this value is then the
> attributable number. OK, so I use this because I've got continuous
> variables in logistic regression models, but it should work out OK.
> 
> How easy it is to compute depends on a) your model and b) your
> package! I use Stata and have programs available for exactly this
> (giving confidence intervals as well).
> 
> Hope this helps, and isn't too simplified!

4.
Dear Terry

You may have had a lot of replies to this already, but here are my
thoughts for what they are worth.

There is increasing concern about using ORs as proxy for RRs when the
prevalence of the condition is high.  The best way (I think) is to
estimate the prevalence rate ratio rather than the prevalence odds
ratio.  The way to do this is to use a generalised linear model with a
log link rather than the logit link used in logistic regression.  The
exponential of the coefficient then gives you the PRR similar to the
estimation of the odds ratio from a logistic regression equation.

If this makes sense, fine.  If not get back to me and I'll try to dig
out some references and a more detailed explanation.

5.
And this from the Stata list with a reference...
>Simon:
>
>I did this using bootstrapping in Stata.  For description see:
>
>Kaufman JS et al.  Obesity and hypertension prevalence in
>populations of African origin. Epidemiology 1996; 7: 398-405.
>
>Additional references are in the bibliography of this article.
>
>In fact, by coincidence, some of the data for this paper
>came from the TMRU in Jamaica.
>
>I used adjustment based on multivariate modeling, as
>developed, for example by Duebner (e.g. Duebner DC,
>et al.  Logistic model estimation of death attributable
>to risk factors for cardiovascular disease. American
>Journal of Epidemiology 1980; 112: 135-143).
>
>- JK
>
>Jay S. Kaufman, Ph.D, Research Epidemiologist
>Department of Research Planning and Evaluation
>306 Research Office Building, Carolinas Medical Center
>P.O. Box 32861, Charlotte NC 28232-2861
>704-355-0561 (Direct); 704-355-7999 (General); 704-355-1880 (FAX)
>
>
>> Dear Statalisters,
>>
>> I am trying to calculate the 95% CI around the PAR% which is given
>> by the equation
>>
>> PAR = (Pe)*(RR-1)/(Pe)*(RR-1)+1
>>
>> My dilemma is this.  Knowing that the variance of the PAR for a
>> retrospective study is the following
>>
>>  var = [c(b+d)/d(a+c)]squared * [a/c(a+c) + b/d(b+d)]
>>
>> I am at odds how to express this when for instance I the RR is age
>> and sex adjusted.
>>
>> I have checks the ideas website to see if any specific ado files
>> have been written to address this without success.
>>
>> Has anyone written or have used an ado file which calculates the
>> PAR and the 95% CI for this given and adjsuted RR or OR?
>>
>> If not can anyone suggest a text that may deal with this problem
>> that I face.
>>
>> I look forward to your responses.
>>
>> Simon Anderson
>> TMRU
>> Jamaica


*********************************************
Dr Terry Aspray
Wellcome Laboratories
Royal Victoria Infirmary
Newcastle upon Tyne
NE1 4LP
Great Britain

tel +44 (0)191 222 5407 fax +44 (0)191 261 1763


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