Concerning the problem of a random effects method for getting a summary
prevalence rate and confidence interval from several different centers or
studies, there were several suggestions. Hanan Bell, Bruce Guthrie and
David Braunholtz suggested Bayesian and hierarchical modelling methods.
While I believe a Bayesian method would be best, I am hoping to find a
cookbook frequentist method that is accessible to the nonstatistician.
Diana Kornblut provided some Agresti references that discuss frequentist
methods for binary outcome trials at multiple centers or from multiple
studies. Unfortunately these trial result methods are not helpful. The
situation we are concerned with is much simpler than the situation with
trial results. Trials have two binary outcomes at each center, the
treatment proportion (successes, survival, whatever) and the control
proportion. Trial methods are concerned with comparing these two
proportions by the odds ratio, rate ratio or difference between them.
We are concerned with the situation of only a single proportion at each
center, the prevalence rate. There is no within-center or within-study odds
ratio, rate ratio or difference. One has only a single proportion from each
center, and one wants to combine them and get a confidence interval. But
the straight pooling of the samples assumes fixed effects (i.e., all the
centers serve identical populations) and weights by sample size. A more
conservative approach would be to calculate the unweighted mean of the
various prevalence rates and give the range. But there must be a more
elegant but still reasonably simple random effects frequentist method for
getting a summary prevalence rate and confidence interval.
This would seem to be something found in the epidemiology literature.
However, that literature has not been as concerned with random effects
methods and meta-analysis methods as the trial literature. If anyone knows
of such a method, please inform the rest of us.
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
http://www.ecri.org
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