Re: st: Once more - combining confidence intervals?

[Alan Kelly <akelly@gemini.tcd.ie>]

Thanks Roger for your reply (copied below).

You mention that I may not have provided enough information in my 
original request - admittedly I gave only what information I felt was 
directly relevant.  However, from your comments its clear that more 
information would have been helpful.

The context of the question is a national capture-recapture 
prevalence estimation exercise for a particular condition based on 
lists (3) of individuals who have contact with the 3 separate 
agencies.  Hence the use of the standard log-linear modelling 
approach to estimate the total number of of individuals in the 
population.

As I mentioned in my first email (copied below) the global fit (all 
ages, both sexes) was very poor due to heterogeneity (which can arise 
for a number of reasons, but may be due in part to differential 
probabilities of 'capture' by the different agencies for different 
age/sex groups.  Stratification has improved the goodness of fit of 
the model(s) in each strata.  The chosen model generates an estimate 
of the population size for the given age/sex group (say males 15 - 24 
years) and an associated 95% confidence interval.  In practice, I 
have 3 age bands by both sexes to give 6 estimates of the respective 
numbers (and CIs) with this condition in the corresponding strata. 
The individual point estimates can be added to give an estimate of 
the total across all ages and both sexes.  The difficulty arises from 
the need to derive a confidence interval for this estimate of the 
total based on the available 6 confidence intervals.  Individuals 
with this condition are by no means typical of their age/sex class in 
the population as a whole (fortunately!) as the condition is 
relatively rare.
So my question stands ...is there a sensible strategy for combining 
lower and upper bounds to the individual CIs?
Any suggestions very welcome...
Alan Kelly


Reply from Roger Harbord
________________________

I think part of the reason for lack of response may have been lack of 
clarity or information in the query, but I'll give it a go:

I assume you really meant a (weighted) average of the prevalences 
rather than a sum of the prevalences.  But if the sample you're using 
in your model is representative of the population (i.e. a simple 
random sample), I would have thought you could simply fit the same 
model without stratification.  If not, how about weighting the sample 
according to known population demographics and using the -svy- 
commands, e.g.  -svyprop- or possibly -svylogit- ?

I think you're right that summing individual lower and upper 
confidence intervals will certainly not give the right answer!

Seeing as a prevalence is simply a proportion (with the disease at a 
given time), I'm not entirely clear why you're using log-linear 
models rather than logistic ones, or indeed simply estimating 
proportions and CIs using -ci- if its a simple random sample, but 
that's another matter - maybe there's more than one disease state..?

Hope this helps
(if not try providing more information - see
http://www.stata.com/support/statalist/faq/#noanswer
),

Roger.

----------------------------------------------------
Roger Harbord     mailto:roger.harbord@bristol.ac.uk
Department of Social Medicine, University of Bristol


Original question:

> Dear all,
> Following stratified modelling (log-linear) to derive a population
> prevalence, I have a number of point prevalence estimates and their
> associated confidence intervals for various age/sex groups (15 - 24
> years, 25 - 34 years and 35 - 54 years for males and females separately).
> I need to have an estimate of the prevalence for the entire 15 - 54
> population.  Fitting a global model produces a very poor fit (due to
> heterogeneity).  Summing the point estimates to obtain an overall
> prevalence seems reasonable. However, although I have seen this done,
> summing the individual lower and upper confidence intervals to give a CI
> for the total prevalence does not seem intuitive to me...for a start,
> the  individual age/sex standard errors are based on different numbers of
> individuals. Any suggestions as to how I could tackle the above would be
> appreciated. best wishes,
Alan Kelly

+-------------------------------------------------------+
 Dr. Alan Kelly          E-mail akelly@mail.tcd.ie
 Biostatistician           Phone:  +353-1-608 1385 or 608 1087
		  Fax:      +353-1-403 1211 or 403 1212



Director of the Small Area Health Research Unit 
Department of Community Health & General Practice 
Trinity Center for Health Sciences
AMNCH
Tallaght Hospital
Dublin 24
Ireland 

 http://www.tcd.ie/Community_Health/SAHRU/index.html
+--------------------------------------------------------+
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