Meta-Analysis – How to Perform a Meta-Analysis of Studies Without a Control Group

effect-sizeobservational-study

I want to meta-analyse some studies which I've already collected and review. However, the studies did not used control groups, due to the types of questions used. How can I do the meta-analysis or which software can I use?
Briefly my problem is as follows:
I reviewed studies which the goal was to evaluate the perception of certain samples of their own behaviour.
For each study, the proportion of the sample which claims to adopt the behaviour in analysis, is equivalent to the effect size.
Do you have any idea how can I determine the average effect size?
Thank you

Best Answer

This is just a meta-analysis of proportions (or transformed values thereof). A couple articles discussing methods for this are:

Stijnen, T., Hamza, T. H., & Ozdemir, P. (2010). Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046-3067.

Chang, B.-H., Waternaux, C., & Lipsitz, S. (2001). Meta-analysis of binary data: Which within study variance estimate to use? Statistics in Medicine, 20, 1947-1956.

Zhou, X.-H., Brizendine, E. J., & Pritz, M. B. (1999). Methods for combining rates from several studies. Statistics in Medicine, 18, 557-566.

A reproduction of the analyses from Stijnen et al. (2010) using the metafor package in R can be found here: http://www.metafor-project.org/doku.php/analyses:stijnen2010

More examples can be found in the help files of the package. In particular:

http://www.rdocumentation.org/packages/metafor/functions/dat.debruin2009 http://www.rdocumentation.org/packages/metafor/functions/dat.pritz1997

If you intend on using the package, you probably also want to take a look at the paper describing the package in more detail:

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48. http://www.jstatsoft.org/v36/i03/

Related Solutions

Solved – How to calculate weighted Hedges’ g effect size in meta-analysis when some effect sizes share a control group

With regards to common control groups, you may want to check out 16.5.4 of the Cochrane Handbook. To quote a subset of this page:

Approaches to overcoming a unit-of-analysis error for a study that could contribute multiple, correlated, comparisons include the following.

Combine groups to create a single pair-wise comparison (recommended).

Select one pair of interventions and exclude the others.

Split the ‘shared’ group into two or more groups with smaller sample size, and include two or more (reasonably independent) comparisons.

Include two or more correlated comparisons and account for the correlation.

Undertake a multiple-treatments meta-analysis (see Section 16.6).

The recommended method in most situations is to combine all relevant experimental intervention groups of the study into a single group, and to combine all relevant control intervention groups into a single control group. As an example, suppose that a meta-analysis of ‘acupuncture versus no acupuncture’ would consider studies of either ‘acupuncture versus sham acupuncture’ or studies of ‘acupuncture versus no intervention’ to be eligible for inclusion. Then a study comparing ‘acupuncture versus sham acupuncture versus no intervention’ would be included in the meta-analysis by combining the participants in the ‘sham acupuncture’ group with participants in the ‘no intervention’ group. This combined control group would be compared with the ‘acupuncture’ group in the usual way. For dichotomous outcomes, both the sample sizes and the numbers of people with events can be summed across groups. For continuous outcomes, means and standard deviations can be combined using methods described in Chapter 7 (Section 7.7.3.8).

With regards to pooling effect sizes for performing moderator meta analysis. There is a list of SPSS resources here. You might want to get a book like Introduction to Meta-Analysis to provide an overview of some of the many issues and calculations involved.

References

Borenstein, M., Hedges, L.V., Higgins, J.P.T. & Rothstein, H.R. (2011). Introduction to meta-analysis. John Wiley \& Sons

Solved – How to perform meta-analysis comparing different proportional mortality ratios of subgroups

I personally use Comprehensive Meta-Analysis, but if you can calculate the SE for each study then you could use RevMan.

Below I put the results for four fictional studies grouped into two groups:

Groups          Effect size and 95% interval                Test of null (2-Tail)           Heterogeneity                   Tau-squared Tau-squared Tau-squared Tau-squared
Group       Number Studies  Point estimate  Lower limit Upper limit     Z-value P-value     Q-value df (Q)  P-value I-squared       Tau Squared Standard Error  Variance    Tau

Fixed effect analysis                                                                       

G1      2   7.03759108414197E-02    0.017603046885197   0.242332278757674       -3.51044333533216   4.47360144140374E-04        0.258038705280314   1   0.611470803514087   0       0   1.52999712888317    2.34089121439075    0
G2      2   2.88585870247873E-02    7.22732614865208E-03    0.10817723861972        -4.89941436298139   9.61227347051619E-07        4.26059028518016E-02    1   0.83646911862334    0       0   1.45672749793515    2.12205500324041    0
Total within                                        0.300644608132116   2   0.860430611444899                       
Total between                                       0.828447690689994   1   0.362721779796614                       
Overall     4   4.47962294435528E-02    1.68510891696442E-02    0.113723780117822       -5.95810589198247   2.55178167485326E-09        1.12909229882211    3   0.770056131706131   0       0   0.861629557762928   0.742405494810739   0

Mixed effects analysis  Mixed effects analysis  Mixed effects analysis  Mixed effects analysis  Mixed effects analysis  Mixed effects analysis  Mixed effects analysis  Mixed effects analysis  Mixed effects analysis                                      

G1      2   7.03759108414197E-02    0.017603046885197   0.242332278757674       -3.51044333533216   4.47360144140374E-04                                        
G2      2   2.88585870247873E-02    7.22732614865208E-03    0.10817723861972        -4.89941436298139   9.61227347051619E-07                                        
Total within                                                                        
Total between                                       0.828447690689994   1   0.362721779796614                       
Overall     4   4.47962294435528E-02    1.68510891696442E-02    0.113723780117822       -5.95810589198247   2.55178167485326E-09

Best Answer

Related Solutions

Solved – How to calculate weighted Hedges’ g effect size in meta-analysis when some effect sizes share a control group

References

Solved – How to perform meta-analysis comparing different proportional mortality ratios of subgroups

Related Question