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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 > 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] > David Braunholtz Department of Public Health & Epidemiology Public Health Building University of Birmingham Birmingham B15 2TT E-Mail: [log in to unmask] Tel: 0121-414-7495 FAX: 0121-414-7878