try this - addressed to medics for the binary response problem

Agresti, A., & Hartzel, J. (2000). Tutorial in biostatistics: strategies
for comparing treatments on a binary response with mulit-centre data.
Statistics in Medicine, 19, 1115-1139.
diana


On Fri, 2
Feb 2001, Doggett, David wrote:

> Amazingly none of the books on meta-analysis I am aware of have anything
> explicit to say about how to meta-analyze a common outcome from several
> studies in which the outcome is a single number, not a comparison; i.e.
> observational or survey data. This would be very useful for summarizing
> morbidities in a set case series studies of the same treatment, or for
> summarizing prevalence or another epidemiological measure among several
> observational studies. Apparently the statisticians think this type of
> calculation is so trivial that they have not bothered to tell us how to do
> it.
>
> I have not had time to verify this, but my first guess is that a suitable
> pooled mean for a continuous variable is obtained as one of the intermediate
> steps in an Analysis of Variance (ANOVA). A test for heterogeneity will
> probably be what is called an omnibus F test. If heterogeneity is found,
> then a random-effects ANOVA might be appropriate.
>
> For dichotomous data (i.e., a proportion), Fleiss presents a method for a
> fixed effects overall proportion (Fleiss JL, Statistical methods for rates
> and proportions, 1981, Wiley & Sons, pp. 138-43). He also shows how to carry
> out a heterogeneity test in the form of a Chi Square test, which is very
> similar to a Q test for heterogeneity. In the event of heterogeneity, I have
> been unable to find an example of a random effects method. One potential
> solution is to use the available dichotomous data random effects
> meta-analysis methods for comparisons (i.e., using effect sizes) but to set
> up a mock control group with a value of zero for each study. However, this
> strategy does not give exactly the same answer as the Fleiss fixed effects
> method; therefore, using this strategy for random effects may also be wrong
> to some degree.
>
> Also, Fleiss does not show how to calculate a confidence interval for the
> fixed effects overall proportion. The typical textbook method of calculating
> the variance for a proportion (v = z * sq rt(pq/n) is known to be a very bad
> approximation for proportions near zero or 1.0. Better methods are available
> (the Wilson score method described in Newcombe RG, Statist. Med., 1998,
> 17:857-72), and it may be acceptable to simply plug in the pooled numerator
> and denominator to this method for a fixed effects confidence interval. The
> random effects calculations have not been worked out for meta-analysis of
> dichotomous data using anything but the inappropriate method of obtaining
> variance above. The problem is that all meta-analysis methods available
> assume a symetrical variance, which is decidedly not the case for
> dichotomous data.
>
> The lack of appropriate methods for dichotomous data is especially
> exasperating, because possibly the majority of data in the medical
> literature is of this type (survival rates, treatment success rates,
> morbidity rates, diagnostic test results, etc.). Where are the statisticians
> when we really need them?
>
> If anyone can shed some light on these problems, please jump in here.
>
> David L. Doggett, Ph.D.
> Senior Medical Research Analyst
> Health Technology Assessment and Information Services
> ECRI, a non-profit health services research organization
> 5200 Butler Pike
> Plymouth Meeting, Pennsylvania 19462, U.S.A.
> Phone: (610) 825-6000 x5509
> FAX: (610) 834-1275
> e-mail: [log in to unmask]
>
>
> -----Original Message-----
> From: Thompson, C. [mailto:[log in to unmask]]
> Sent: Wednesday, January 31, 2001 6:30 AM
> To: [log in to unmask]
> Subject: pooling survey data rather than experimental...
>
>
> my problem is this...
>
> - I have a batch of 15 self report surveys of the barriers to research
> utilisation in healthcare settings
>
> - they each address the same research question, similar populations and
> USE THE SAME SCALE (the 'barriers' scale (Funk et al. 1991).
>
> - the scale is made up of 29 items each of which reports a having a mean
> item score, standard deviation and an associated proportion of people
> viewing the item as a moderate/great barrier to research.
>
> - the surveys are each (individually) small samples but add up to a
> sizeable n=20k or so....
>
> I wish to pool the 15 survey responses to the 29 items to reduce the
> confidence intervals associated with the barrier items. And also as it
> would be nice to present a reasonably 'tight' overview and influence
> anyone else considering doing yet another underpowered survey of self
> reported, perceived, behaviour. I think David Covell (1985) showed how
> unreliable that was regarding info seeking and utilisation!
>
> I have looked at ARCUS biostat's meta analysis suite but to no avail...
> it insists on generating ratio based results.... needing two groups....
> hmmm
>
> Does anyone know of HTA reports or similar which have combined results
> of survey data... or would it be OK just to simply average the means (&
> SDs) from the different studies... maybe I am trying to hard to do
> something sexy with these figures - so simple would be good if poss.
>
> cheers
>
> Carl.
>
> *****************************************
>
> Carl Thompson
> Research Fellow & Chair of Graduate School
> Genesis 6
> Department of Health Studies
> Science Park
> University of York
> York, YO10 5DQ
>
> tel +44 (0) 1904 434115
> fax +44 (0) 1904 434102
> mobile 07939 254 863
> e-mail  [log in to unmask]
>
> *****************************************
>

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        Dr. Diana Kornbrot
        Reader in Mathematical Psychology
        Associate Dean Research, Faculty of Health & Human Sciences
        University of Hertfordshire
        College Lane, Hatfield, Hertfordshire AL10 9AB, UK
voice:  +44 0170 728 4626       fax:    +44 0170 728 5073
email:  [log in to unmask]
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