meta-analyses of this (and all other) form are very straightforward
conceptually if you adopt a BAYESIAN approach, though actually
programming the model is currently possibly somewhat more
involved than for non-Bayesian alternatives. BUGS (downloadable
from the MRC Biostatistics unit in Cambridge) is free, suitable, and
has examples, tutorials etc available.
> 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
> 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]
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