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Series Editors: Cynthia Mulrow, MD, MSc and Deborah Cook, MD, MSc

Quantitative Synthesis in Systematic Reviews

Joseph Lau, MD; John P.A. Ioannidis, MD; and Christopher H. Schmid, PhD
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From New England Medical Center and Tufts University School of Medicine, Boston, Massachusetts. For definitions of terms used, see Glossary at end of text. Acknowledgments: The authors thank Drs. Andrew Oxman and Larry V. Hedges for their reviews of and valuable comments on the manuscript and thank the clinical reviewer, Norman J. Wilder. Grant Support: In part by grants R01 HS07782 and R01 HS 08532 from the Agency for Health Care Policy and Research (Drs. Lau and Schmid) and grant T32 AI07389 from the National Institutes of Health (Dr. Ioannidis). Current Author Addresses: Drs. Lau and Schmid: Division of Clinical Care Research, New England Medical Center, 750 Washington Street, Box 63, Boston, MA 02111.

Ann Intern Med. 1997;127(9):820-826. doi:10.7326/0003-4819-127-9-199711010-00008
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The final common pathway for most systematic reviews is a statistical summary of the data, or meta-analysis. The complex methods used in meta-analyses should always be complemented by clinical acumen and common sense in designing the protocol of a systematic review, deciding which data can be combined, and determining whether data should be combined. Both continuous and binary data can be pooled. Most meta-analyses summarize data from randomized trials, but other applications, such as the evaluation of diagnostic test performance and observational studies, have also been developed. The statistical methods of meta-analysis aim at evaluating the diversity (heterogeneity) among the results of different studies, exploring and explaining observed heterogeneity, and estimating a common pooled effect with increased precision. Fixed-effects models assume that an intervention has a single true effect, whereas random-effects models assume that an effect may vary across studies. Meta-regression analyses, by using each study rather than each patient as a unit of observation, can help to evaluate the effect of individual variables on the magnitude of an observed effect and thus may sometimes explain why study results differ. It is also important to assess the robustness of conclusions through sensitivity analyses and a formal evaluation of potential sources of bias, including publication bias and the effect of the quality of the studies on the observed effect.


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Figure 1.
Methodologic choices and their implications in dealing with heterogeneous data in a meta-analysis.
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Figure 2.
An inverted funnel plot to detect publication bias.[20]arrow

This example used data from a meta-analysis of intravenous streptokinase for acute myocardial infarction . The risk ratio for the mortality reduction in each study is plotted against the weight of the study, represented by the sample size. A symmetric triangle is fitted around the pooled estimate ( ) so that it encompasses most of the studies. If small “negative” trials with large variance have been left unpublished, the plot will be asymmetrical: Small published studies will show very large estimates of the treatment effect compared with larger studies that have more conservative results. A symmetrical plot provides reassuring evidence that the treatment effect is similar in studies of small and large variance, whereas an asymmetrical plot suggests possible publication bias. The plot shown here reveals that there are fewer small studies (involving 10 to 100 participants) with risk ratios greater than 0.8 than there are small studies with risk ratios less than 0.8, whereas the numbers of medium and large studies are fairly symmetrical. These results suggest that some small studies with negative findings were not published. Outlier studies may also be readily identified by using this plot.

Grahic Jump Location
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Figure 3.
Standard meta-analysis and cumulative meta-analysis, Left.[47]Right.

A standard meta-analysis plot of the risk ratios for progression to AIDS or death in a comparison of early therapy with zidovudine (treatment group) or deferred therapy with zidovudine (control group) . The point estimates for the risk ratio of each study and the pooled point estimate are shown by the points, and the horizontal lines show the CIs, typically 95% CIs. N is the number of patients in the study. The studies are ordered according to year of publication. As a standard convention, a risk ratio of less than 1 denotes a reduction in the number of events in the treated compared with the control group. The results of a cumulative meta-analysis of the same data. N is the number of patients in the clinical trials. The points and lines represent the point estimates and the 95% CIs of the pooled results after the inclusion of each additional study in the calculations. The CIs typically narrow with the addition of more studies unless substantial heterogeneity exists.

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