Meta-analysis: generic inverse variance method
Generic inverse variance method
A meta-analysis integrates the quantitative findings from separate but similar studies and provides a numerical estimate of the overall effect of interest (Petrie et al., 2003).
It is advised to use one of the following specific meta-analysis procedures for continuous and dichotomous outcome data:
- Meta-analysis: continuous measure
- Meta-analysis: correlation
- Meta-analysis: proportion
- Meta-analysis: relative risk
- Meta-analysis: risk difference
- Meta-analysis: odds ratio
- Meta-analysis: area under ROC curve
If none of the above procedures is applicable or suitable, you can use the "generic inverse variance method" procedure. In this procedure estimates and their standard errors are entered directly into MedCalc. For ratio measures of intervention effect, the data should be entered as natural logarithms (for example as a log Hazard ratio and the standard error of the log Hazard ratio).
In the inverse variance method the weight given to each study is the inverse of the variance of the effect estimate (i.e. one over the square of its standard error). Thus larger studies are given more weight than smaller studies, which have larger standard errors. This choice of weight minimizes the imprecision (uncertainty) of the pooled effect estimate.
How to enter data
The data of different studies can be entered as follows in the spreadsheet:
Studies: a variable containing an identification of the different studies.
- Estimate: a variable containing the estimate of interest reported in the different studies.
- Standard error: a variable containing the Standard error of the estimate reported in the different studies.
Filter: a filter to include only a selected subgroup of studies in the meta-analysis.
- Data are entered as natural logarithms: select this option if the data are entered as natural logarithms, for example as a log Hazard ratio and the standard error of the log Hazard ratio.
- 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 included in the meta-analysis: the estimate and 95% confidence interval.
The pooled value for the estimate, with 95% CI, is given both for the Fixed effects model and the Random effects model.
Fixed and random effects model
Under the fixed effects model, it is assumed that the studies share a common true effect, and the summary effect is an estimate of the common effect size.
Under the random effects model (DerSimonian and Laird) the true effects in the studies are assumed to vary between studies and the summary effect is the weighted average of the effects reported in the different studies (Borenstein et al., 2009).
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 Forest plot shows the estimate (with 95% CI) found in the different studies included in the meta-analysis, and the overall effect with 95% CI.
A funnel plot is a graphical tool for detecting bias in meta-analysis. See Meta-analysis: introduction.
Note that when the option "Data are entered as natural logarithms" was selected (see above), then the Standard Errors on the Y-axis are natural logarithms.
- Borenstein M, Hedges LV, Higgins JPT, Rothstein HR (2009) Introduction to meta-analysis. Chichester, UK: Wiley.
- 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.