Meta-analysis: continuous measure

Command:

Statistics Meta-analysis Continuous measure

Description

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).

Under the fixed effects model, it is assumed that all studies come from a common population, and that the effect size (Standardized Mean Difference, SMD) is not significantly different among the different trials. This assumption is tested by the "Heterogeneity test". If this test yields a low P-value (P<0.05), then the fixed effects model may be invalid. In this case, the random effects model may be more appropriate, in which both the random variation within the studies and the variation between the different studies is incorporated.

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 and Laird).

The standarized mean difference Hedges g is the difference between the two means divided by the pooled standard deviation, with an adjustment for small sample bias.

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 23 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.

Required input

The dialog box for "Meta-analysis: continuous measure" can then be completed as follows:

Results

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. If the test of heterogeneity is statistically significant (P<0.05), like in the example, then more emphasis should be placed on the random effects model.

Graph

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:

Literature

• DerSimonian R, Laird N (1986) Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177-188. [Abstract]
• Petrie A, Bulman JS, Osborn JF (2003) Further statistics in dentistry. Part 8: systematic reviews and meta-analyses. British Dental Journal, 194:73-78. [Abstract]

See also

• Odds ratio