Meta-analysis: odds ratio
For a short overview of meta-analysis in MedCalc, see Meta-analysis: introduction.
MedCalc uses the Mantel-Haenszel method (Mantel & Haenszel, 1959) for calculating the weighted pooled odds ratio under the fixed effects model. Next the heterogeneity statistic is incorporated to calculate the summary odds ratio under the random effects model (DerSimonian & Laird, 1986).
How to enter data
The data of different studies can be entered as follows in the spreadsheet:
In this example, in a first study 73 cases were treated with an active substance and of these, 15 had a positive outcome. 23 cases received a placebo and 3 of these had a positive outcome. On the next rows of the spreadsheet follow the data of 4 other studies.
The dialog box for "Meta-analysis: odds ratio" can then be completed as follows:
Studies: a variable containing an identification of the different studies.
- Total number of cases: a variable containing the total number of cases in the intervention groups of the different studies
- Number with positive outcome: a variable containing the number of cases with positive outcome in the intervention groups of the different studies
- Total number of cases: a variable containing the total number of cases in the control groups of the different studies
- Number with positive outcome: a variable containing the number of cases with positive outcome in the control groups of the different studies
A filter to include only a selected subgroup of studies in the meta-analysis.
Filter: a filter to include only a selected subgroup of cases in the graph.
- Forest plot: creates a forest plot.
- Marker size relative to study weight: option to have the size of the markers that represent the effects of the studies vary in size according to the weights assigned to the different studies. You can choose the fixed effect model weights or random effect model weights.
- Plot pooled effect - fixed effects model: option to include the pooled effect under the fixed effects model in the forest plot.
- Plot pooled effect - random effect model: option to include the pooled effect under the random effects model in the forest plot.
- Diamonds for pooled effects: option to represent the pooled effects using a diamond (the location of the diamond represents the estimated effect size and the width of the diamond reflects the precision of the estimate).
- Funnel plot: creates a funnel plot to check for the existence of publication bias. See Meta-analysis: introduction.
The program lists the results of the individual studies: number of positive cases, total number of cases, and the odds ratio with 95% CI.
The pooled odds ratio with 95% CI is given both for the Fixed effects model and the Random effects model. If the value 1 is not within the 95% CI, then the Odds ratio is statistically significant at the 5% level (P<0.05).
The random effects model will tend to give a more conservative estimate (i.e. with wider confidence interval), but the results from the two models usually agree where there is no heterogeneity. See Meta-analysis: introduction for interpretation of the heterogeneity statistics Cohran's Q and I2. When heterogeneity is present the random effects model should be the preferred model.
See Meta-analysis: introduction for interpretation of the different publication bias tests.
Note that when a study reports no events (or all events) in both intervention and control groups the study provides no information about relative probability of the event and is automatically omitted from the meta-analysis (Higgins & Green, 2011).
The results of the different studies, with 95% CI, and the overall effect with 95% CI are shown in a forest plot:
Note that the Odds ratios with 95% CI are drawn on a logarithmic scale.
- Borenstein M, Hedges LV, Higgins JPT, Rothstein HR (2009) Introduction to meta-analysis. Chichester, UK: Wiley.
- DerSimonian R, Laird N (1986) Meta-analysis in clinical trials. Controlled Clinical Trials 7:177-188.
- Higgins JPT, Green S (editors). Cochrane Handbook for Systematic Reviews of Interventions Version 5.1.0 [updated March 2011]. The Cochrane Collaboration, 2011. Available from www.cochrane-handbook.org
- Higgins JP, Thompson SG, Deeks JJ, Altman DG (2003) Measuring inconsistency in meta-analyses. BMJ 327:557-560.
- Mantel N, Haenszel W (1959) Statistical aspects of the analysis of data from the retrospective analysis of disease. Journal of the National Cancer Institute 22:719-748.
- Petrie A, Bulman JS, Osborn JF (2003) Further statistics in dentistry. Part 8: systematic reviews and meta-analyses. British Dental Journal 194:73-78.
Introduction to Meta-Analysis
Michael Borenstein, Larry V. Hedges, Julian P. T. Higgins, Hannah R. Rothstein
This book provides a clear and thorough introduction to meta-analysis, the process of synthesizing data from a series of separate studies. Meta-analysis has become a critically important tool in fields as diverse as medicine, pharmacology, epidemiology, education, psychology, business, and ecology.