Meta-analysis: continuous measure
For a short overview of meta-analysis in MedCalc, see Meta-analysis: introduction.
For meta-analysis of studies with a continuous measure (comparison of means between treated cases and controls), MedCalc uses the Hedges g statistic as a formulation for the standardized mean difference under the fixed effects model. Next the heterogeneity statistic is incorporated to calculate the summary standardized mean difference under the random effects model (DerSimonian & Laird, 1986).
The standardized mean difference Hedges g is the difference between the two means divided by the pooled standard deviation, with a correction for small sample bias:
where Γ is the Gamma function.
How to enter data
The data of different studies can be entered as follows in the spreadsheet:
In this example, in a first study 40 cases were treated and the mean of the parameter of interest was 23.52 with a standard deviation of 1.38. In 40 control cases the mean was 20.12 with standard deviation of 3.36. On the next rows of the spreadsheet follow the data of 4 other studies.
The dialog box for "Meta-analysis: continuous measure" can then be completed as follows:
Studies: a variable containing an identification of the different studies.
Intervention groups & Control groups:
Number of cases, Mean, Standard deviation: variables containing the number of cases, mean and standard deviation observed in the different studies, in the intervention groups and control groups respectively.
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, the standardized mean difference (SMD) with 95% CI.
The total Standardized Mean Difference with 95% CI is given both for the Fixed effects model and the Random effects model.
If the value 0 is not within the 95% CI, then the SMD is statistically significant at the 5% level (P<0.05).
Cohen's rule of thumb for interpretation of the SMD statistic is: a value of 0.2 indicates a small effect, a value of 0.5 indicates a medium effect and a value of 0.8 or larger indicates a large effect.
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.
The results of the different studies, with 95% CI, and the overall standardized mean difference with 95% CI is shown in the following forest plot:
- 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.
- Hedges LV, Olkin I (1985) Statistical methods for meta-analysis. London: Academic Press.
- Higgins JP, Thompson SG, Deeks JJ, Altman DG (2003) Measuring inconsistency in meta-analyses. BMJ 327:557-560.
- 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.