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this group. In this situation few would argue that formaldehyde protects
against lung cancer. In other instances, however, such selection bias may
be less obvious.”
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On the other hand, much may be gained by a careful examination of
possible sources of heterogeneity between the results from observational
studies.
Publication and selection bias also plague the meta-analysis of com-
pletely randomized trials. Inconclusive or negative results seldom appear in
print (Götzsche, 1987; Chalmers et al., 1990; Easterbrook et al., 1991)
and are unlikely even to be submitted for publication. One can't analyze
what one doesn't know about.
Similarly, the decision as to which studies to incorporate can dramati-
cally affect the results. Meta-analyses of the same issue may reach opposite
conclusions, as shown by assessments of low-molecular-weight heparin in
the prevention of perioperative thrombosis (Nurmohamed et al., 1992;
Leizorovicz et al., 1992) and of second line antirheumatic drugs in the
treatment of rheumatoid arthritis (Felson et al., 1990; Götzsche et al.,
1992). Meta-analyses showing benefit of statistical significance and clinical
importance have been contradicted later by large randomized trials (Egger
et al., 1997).
Where there are substantial differences between the different studies
incorporated in a meta-analysis (their subjects or their environments), or
substantial quantitative differences in the results from the different trials, a
single overall summary estimate of treatment benefit has little practical
applicability (Horowitz, 1995). Any analysis that ignores this hetero-
geneity is clinically misleading and scientifically naive (Thompson, 1994).
Heterogeneity should be scrutinized, with an attempt to explain it (Bailey,
1987; Berkey et al., 1995; Chalmers, 1991; Victor, 1995).
Bayesian Methods
Bayesian methods can be effective in meta-analyses; see, for example,
Mosteller and Chalmers [1992]. In such situations the parameters of
various trials are considered to be random samples from a distribution of
trial parameters. The parameters of this higher-level distribution are called
hyperparameters, and they also have distributions. The model is called
hierarchical
. The extent to which the various trials reinforce each other is
determined by the data. If the trials are very similar, the variation of the
hyperparameters will be small, and the analysis will be very close to a
classical meta-analysis. If the trials do not reinforce each other, the
conclusions of the hierarchical Bayesian analysis will show a very high
variance in the results.
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Reprinted with permission from the BMJ Publishing Group.
