Meta-analysis: Difference between revisions

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imported>Robert Badgett
imported>Robert Badgett
(→‎Methods of meta-analysis: reordered sections)
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==Methods of meta-analysis==
==Methods of meta-analysis==
Guidelines are available for the conduct<ref name="CochraneHandbook>The Cochrane Collaboration. [http://www.cochrane-handbook.org/ Cochrane Handbook]</ref> and reporting<ref name="pmid19622511">{{cite journal| author=Moher D, Liberati A, Tetzlaff J, Altman DG, PRISMA Group| title=Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. | journal=Ann Intern Med | year= 2009 | volume= 151 | issue= 4 | pages= 264-9, W64 | pmid=19622511  
Guidelines are available for the conduct<ref name="CochraneHandbook>The Cochrane Collaboration. [http://www.cochrane-handbook.org/ Cochrane Handbook]</ref> and reporting<ref name="pmid19622511">{{cite journal| author=Moher D, Liberati A, Tetzlaff J, Altman DG, PRISMA Group| title=Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. | journal=Ann Intern Med | year= 2009 | volume= 151 | issue= 4 | pages= 264-9, W64 | pmid=19622511  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=19622511 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> of meta-analyses.
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=19622511 }}</ref> of meta-analyses.


===Searching for studies===
===Searching for studies===
Meta-analyses vary in the extent of their searches for underlying studies. <ref name="pmid15095765">{{cite journal| author=Royle P, Milne R| title=Literature searching for randomized controlled trials used in Cochrane reviews: rapid versus exhaustive searches. | journal=Int J Technol Assess Health Care | year= 2003 | volume= 19 | issue= 4 | pages= 591-603 | pmid=15095765  
Meta-analyses vary in the extent of their searches for underlying studies. <ref name="pmid15095765">{{cite journal| author=Royle P, Milne R| title=Literature searching for randomized controlled trials used in Cochrane reviews: rapid versus exhaustive searches. | journal=Int J Technol Assess Health Care | year= 2003 | volume= 19 | issue= 4 | pages= 591-603 | pmid=15095765  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=15095765 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> There is debate on how extensive should be the search for studies as there is are diminishing returns with extensive searching. Some studies suggest limiting searches<ref name="pmid15649836">{{cite journal| author=Stevinson C, Lawlor DA| title=Searching multiple databases for systematic reviews: added value or diminishing returns? | journal=Complement Ther Med | year= 2004 | volume= 12 | issue= 4 | pages= 228-32 | pmid=15649836  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=15095765 }}</ref> There is debate on how extensive should be the search for studies as there is are diminishing returns with extensive searching. Some studies suggest limiting searches<ref name="pmid15649836">{{cite journal| author=Stevinson C, Lawlor DA| title=Searching multiple databases for systematic reviews: added value or diminishing returns? | journal=Complement Ther Med | year= 2004 | volume= 12 | issue= 4 | pages= 228-32 | pmid=15649836
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=15649836 | doi=10.1016/j.ctim.2004.09.003 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid11155831">{{cite journal| author=Fergusson D, Laupacis A, Salmi LR, McAlister FA, Huet C| title=What should be included in meta-analyses? An exploration of methodological issues using the ISPOT meta-analyses. | journal=Int J Technol Assess Health Care | year= 2000 | volume= 16 | issue= 4 | pages= 1109-19 | pmid=11155831  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=15649836 | doi=10.1016/j.ctim.2004.09.003 }}</ref><ref name="pmid11155831">{{cite journal| author=Fergusson D, Laupacis A, Salmi LR, McAlister FA, Huet C| title=What should be included in meta-analyses? An exploration of methodological issues using the ISPOT meta-analyses. | journal=Int J Technol Assess Health Care | year= 2000 | volume= 16 | issue= 4 | pages= 1109-19 | pmid=11155831
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=11155831 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid17443625">{{cite journal| author=Hopewell S, Clarke M, Lefebvre C, Scherer R| title=Handsearching versus electronic searching to identify reports of randomized trials. | journal=Cochrane Database Syst Rev | year= 2007 | volume=  | issue= 2 | pages= MR000001 | pmid=17443625  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=11155831 }}</ref><ref name="pmid17443625">{{cite journal| author=Hopewell S, Clarke M, Lefebvre C, Scherer R| title=Handsearching versus electronic searching to identify reports of randomized trials. | journal=Cochrane Database Syst Rev | year= 2007 | volume=  | issue= 2 | pages= MR000001 | pmid=17443625 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=17443625 | doi=10.1002/14651858.MR000001.pub2 }}</ref> while other studies advocate exhaustive searches<ref name="pmid16085190">{{cite journal| author=Lemeshow AR, Blum RE, Berlin JA, Stoto MA, Colditz GA| title=Searching one or two databases was insufficient for meta-analysis of observational studies. | journal=J Clin Epidemiol | year= 2005 | volume= 58 | issue= 9 | pages= 867-73 | pmid=16085190
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=17443625 | doi=10.1002/14651858.MR000001.pub2 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> while other studies advocate exhaustive searches<ref name="pmid16085190">{{cite journal| author=Lemeshow AR, Blum RE, Berlin JA, Stoto MA, Colditz GA| title=Searching one or two databases was insufficient for meta-analysis of observational studies. | journal=J Clin Epidemiol | year= 2005 | volume= 58 | issue= 9 | pages= 867-73 | pmid=16085190  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16085190 | doi=10.1016/j.jclinepi.2005.03.004 }}</ref><ref name="pmid11237924">{{cite journal| author=Avenell A, Handoll HH, Grant AM| title=Lessons for search strategies from a systematic review, in The Cochrane Library, of nutritional supplementation trials in patients after hip fracture. | journal=Am J Clin Nutr | year= 2001 | volume= 73 | issue= 3 | pages= 505-10 | pmid=11237924
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16085190 | doi=10.1016/j.jclinepi.2005.03.004 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid11237924">{{cite journal| author=Avenell A, Handoll HH, Grant AM| title=Lessons for search strategies from a systematic review, in The Cochrane Library, of nutritional supplementation trials in patients after hip fracture. | journal=Am J Clin Nutr | year= 2001 | volume= 73 | issue= 3 | pages= 505-10 | pmid=11237924  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=11237924 }}</ref><ref name="pmid16092960">{{cite journal| author=Crumley ET, Wiebe N, Cramer K, Klassen TP, Hartling L| title=Which resources should be used to identify RCT/CCTs for systematic reviews: a systematic review. | journal=BMC Med Res Methodol | year= 2005 | volume= 5 | issue=  | pages= 24 | pmid=16092960
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=11237924 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid16092960">{{cite journal| author=Crumley ET, Wiebe N, Cramer K, Klassen TP, Hartling L| title=Which resources should be used to identify RCT/CCTs for systematic reviews: a systematic review. | journal=BMC Med Res Methodol | year= 2005 | volume= 5 | issue=  | pages= 24 | pmid=16092960  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16092960 | doi=10.1186/1471-2288-5-24 | pmc=PMC1232852 }}</ref><ref name="pmid16926954">{{cite journal| author=Wilkins T, Gillies RA, Davies K| title=EMBASE versus MEDLINE for family medicine searches: can MEDLINE searches find the forest or a tree? | journal=Can Fam Physician | year= 2005 | volume= 51 | issue=  | pages= 848-9 | pmid=16926954
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16092960 | doi=10.1186/1471-2288-5-24 | pmc=PMC1232852 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid16926954">{{cite journal| author=Wilkins T, Gillies RA, Davies K| title=EMBASE versus MEDLINE for family medicine searches: can MEDLINE searches find the forest or a tree? | journal=Can Fam Physician | year= 2005 | volume= 51 | issue=  | pages= 848-9 | pmid=16926954  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16926954 | pmc=PMC1479531 }}</ref><ref name="pmid12701949">{{cite journal| author=Savoie I, Helmer D, Green CJ, Kazanjian A| title=Beyond Medline: reducing bias through extended systematic review search. | journal=Int J Technol Assess Health Care | year= 2003 | volume= 19 | issue= 1 | pages= 168-78 | pmid=12701949
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16926954 | pmc=PMC1479531 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid12701949">{{cite journal| author=Savoie I, Helmer D, Green CJ, Kazanjian A| title=Beyond Medline: reducing bias through extended systematic review search. | journal=Int J Technol Assess Health Care | year= 2003 | volume= 19 | issue= 1 | pages= 168-78 | pmid=12701949  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=12701949 }}</ref><ref name="pmid18313560">{{cite journal| author=Whiting P, Westwood M, Burke M, Sterne J, Glanville J| title=Systematic reviews of test accuracy should search a range of databases to identify primary studies. | journal=J Clin Epidemiol | year= 2008 | volume= 61 | issue= 4 | pages= 357-364 | pmid=18313560
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=12701949 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid18313560">{{cite journal| author=Whiting P, Westwood M, Burke M, Sterne J, Glanville J| title=Systematic reviews of test accuracy should search a range of databases to identify primary studies. | journal=J Clin Epidemiol | year= 2008 | volume= 61 | issue= 4 | pages= 357-364 | pmid=18313560  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=18313560 | doi=10.1016/j.jclinepi.2007.05.013 }}</ref> including unpublished studies<ref name="pmid17443631">{{cite journal| author=Hopewell S, McDonald S, Clarke M, Egger M| title=Grey literature in meta-analyses of randomized trials of health care interventions. | journal=Cochrane Database Syst Rev | year= 2007 | volume=  | issue= 2 | pages= MR000010 | pmid=17443631
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=18313560 | doi=10.1016/j.jclinepi.2007.05.013 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> including unpublished studies<ref name="pmid17443631">{{cite journal| author=Hopewell S, McDonald S, Clarke M, Egger M| title=Grey literature in meta-analyses of randomized trials of health care interventions. | journal=Cochrane Database Syst Rev | year= 2007 | volume=  | issue= 2 | pages= MR000010 | pmid=17443631  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=17443631 | doi=10.1002/14651858.MR000010.pub3 }}</ref><ref name="pmid11072941">{{cite journal| author=McAuley L, Pham B, Tugwell P, Moher D| title=Does the inclusion of grey literature influence estimates of intervention effectiveness reported in meta-analyses? | journal=Lancet | year= 2000 | volume= 356 | issue= 9237 | pages= 1228-31 | pmid=11072941
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=17443631 | doi=10.1002/14651858.MR000010.pub3 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid11072941">{{cite journal| author=McAuley L, Pham B, Tugwell P, Moher D| title=Does the inclusion of grey literature influence estimates of intervention effectiveness reported in meta-analyses? | journal=Lancet | year= 2000 | volume= 356 | issue= 9237 | pages= 1228-31 | pmid=11072941  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=11072941 | doi=10.1016/S0140-6736(00)02786-0 }}</ref>.
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=11072941 | doi=10.1016/S0140-6736(00)02786-0 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref>.


There is not a consensus on what details of searching should be reported in a meta-analysis.<ref name="pmid18586178">{{cite journal| author=Sampson M, McGowan J, Tetzlaff J, Cogo E, Moher D| title=No consensus exists on search reporting methods for systematic reviews. | journal=J Clin Epidemiol | year= 2008 | volume= 61 | issue= 8 | pages= 748-54 | pmid=18586178  
There is not a consensus on what details of searching should be reported in a meta-analysis.<ref name="pmid18586178">{{cite journal| author=Sampson M, McGowan J, Tetzlaff J, Cogo E, Moher D| title=No consensus exists on search reporting methods for systematic reviews. | journal=J Clin Epidemiol | year= 2008 | volume= 61 | issue= 8 | pages= 748-54 | pmid=18586178  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=18586178 | doi=10.1016/j.jclinepi.2007.10.009 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref>
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=18586178 | doi=10.1016/j.jclinepi.2007.10.009 }}</ref>


===Selecting studies for inclusion===
===Selecting studies for inclusion===
Conflict in selection of trials to be included in the meta-analysis can affect the conclusions of a meta-analysis.<ref name="pmid9451274">{{cite journal| author=Egger M, Smith GD| title=Bias in location and selection of studies. | journal=BMJ | year= 1998 | volume= 316 | issue= 7124 | pages= 61-6 | pmid=9451274  
Conflict in selection of trials to be included in the meta-analysis can affect the conclusions of a meta-analysis.<ref name="pmid9451274">{{cite journal| author=Egger M, Smith GD| title=Bias in location and selection of studies. | journal=BMJ | year= 1998 | volume= 316 | issue= 7124 | pages= 61-6 | pmid=9451274  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=9451274 | pmc=PMC2665334 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid8544272">{{cite journal| author=Cook DJ, Reeve BK, Guyatt GH, Heyland DK, Griffith LE, Buckingham L et al.| title=Stress ulcer prophylaxis in critically ill patients. Resolving discordant meta-analyses. | journal=JAMA | year= 1996 Jan 24-31 | volume= 275 | issue= 4 | pages= 308-14 | pmid=8544272  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=9451274 | pmc=PMC2665334 }}</ref><ref name="pmid8544272">{{cite journal| author=Cook DJ, Reeve BK, Guyatt GH, Heyland DK, Griffith LE, Buckingham L et al.| title=Stress ulcer prophylaxis in critically ill patients. Resolving discordant meta-analyses. | journal=JAMA | year= 1996 Jan 24-31 | volume= 275 | issue= 4 | pages= 308-14 | pmid=8544272
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=8544272 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref><ref name="pmid12204023">{{cite journal| author=Goodman SN| title=The mammography dilemma: a crisis for evidence-based medicine? | journal=Ann Intern Med | year= 2002 | volume= 137 | issue= 5 Part 1 | pages= 363-5 | pmid=12204023  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=8544272 }}</ref><ref name="pmid12204023">{{cite journal| author=Goodman SN| title=The mammography dilemma: a crisis for evidence-based medicine? | journal=Ann Intern Med | year= 2002 | volume= 137 | issue= 5 Part 1 | pages= 363-5 | pmid=12204023
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=12204023 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref>
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=12204023 }}</ref>


Although meta-analyses in general are very inclusive, arguments exist for only including the best trials.<ref name="pmid7853053">{{cite journal |author=Slavin RE |title=Best evidence synthesis: an intelligent alternative to meta-analysis |journal=J Clin Epidemiol |volume=48 |issue=1 |pages=9–18 |year=1995 |month=January |pmid=7853053 |doi= |url=http://linkinghub.elsevier.com/retrieve/pii/0895-4356(94)00097-A |issn=}}</ref>
Although meta-analyses in general are very inclusive, arguments exist for only including the best trials.<ref name="pmid7853053">{{cite journal |author=Slavin RE |title=Best evidence synthesis: an intelligent alternative to meta-analysis |journal=J Clin Epidemiol |volume=48 |issue=1 |pages=9–18 |year=1995 |month=January |pmid=7853053 |doi= |url=http://linkinghub.elsevier.com/retrieve/pii/0895-4356(94)00097-A |issn=}}</ref>
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===Statistical methods===
===Statistical methods===
====Measuring consistency of study results====
Consistency can be statistically tested using either the Cochran's ''Q'' or ''I<sup>2</sup>''.<ref name="pmid12958120">{{cite journal |author=Higgins  JP, Thompson SG, Deeks JJ, Altman DG |title=Measuring inconsistency in  meta-analyses |journal=BMJ |volume=327 |issue=7414 |pages=557–60  |year=2003 |month=September |pmid=12958120 |pmc=192859  |doi=10.1136/bmj.327.7414.557 |url=http://bmj.com/cgi/pmidlookup?view=long&pmid=12958120 |issn=}}</ref><ref name="pmid12111919">{{cite journal|  author=Higgins JP, Thompson SG| title=Quantifying heterogeneity in a  meta-analysis. | journal=Stat Med | year= 2002 | volume= 21 | issue= 11 |  pages= 1539-58 | pmid=12111919
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&email=badgett@uthscdsa.edu&retmode=ref&cmd=prlinks&id=12111919  | doi=10.1002/sim.1186 }}</ref> The ''I<sup>2</sup>'' is the "percentage of total variation across studies that is due to heterogeneity rather than chance."<ref name="pmid12958120"/> These numbers are usually displayed for each group of studies on a Forest plot.
In interpreting of the Cochran's ''Q'', heterogeneity exists if its p-value is < 0.05 or possibly if < 0.10<ref name="pmid3802849">{{cite journal |author=Fleiss JL |title=Analysis of data from multiclinic trials |journal=Control Clin Trials |volume=7 |issue=4 |pages=267–75 |year=1986 |month=December |pmid=3802849 |doi= |url= |issn=}}</ref><ref name="pmid1289110">{{cite journal |author=Dickersin  K, Berlin JA |title=Meta-analysis: state-of-the-science  |journal=Epidemiol Rev |volume=14 |issue= |pages=154–76 |year=1992  |pmid=1289110 |doi= |url=http://epirev.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=1289110 |issn=}}</ref>.
The following has been proposed for interpreting ''I<sup>2</sup>'':<ref name="pmid12958120"/>
* Low heterogeneity is ''I<sup>2</sup>'' = 25%
* Moderate heterogeneity is ''I<sup>2</sup>'' = 50%
* High heterogeneity is ''I<sup>2</sup>'' = 75%
or according to the Handbook of the [[Cochrane Collaboration]]:<ref name="urlCochrane Handbook for Systematic Reviews of Interventions">{{cite web |url=http://www.cochrane-handbook.org/  |title=Cochrane Handbook for Systematic Reviews of Interventions  |editor=Higgins JPT, Green S| author= |authorlink= |coauthors=  |date=2008 |format= |work= |publisher=Cochrane Collaboration |pages=  |language= |archiveurl= |archivedate= |quote= |accessdate=2008-10-23}}</ref>
* 0%-40%: might not be important
* 30%-60%: may represent moderate heterogeneity
* 50%-90%: may represent substantial heterogeneity
* 75%-100%: considerable heterogeneity
However, I<sup>2</sup>, even when the value is 0%, can be misleading if the [[confidence interval]]s around the value are not provided.<ref name="pmid17974687">{{cite journal|  author=Ioannidis JP, Patsopoulos NA, Evangelou E| title=Uncertainty in  heterogeneity estimates in meta-analyses. | journal=BMJ | year= 2007 |  volume= 335 | issue= 7626 | pages= 914-6 | pmid=17974687
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&retmode=ref&cmd=prlinks&id=17974687  | doi=10.1136/bmj.39343.408449.80 }} </ref><ref name="pmid19018930">{{cite journal|  author=Ioannidis JP| title=Interpretation of tests of heterogeneity and  bias in meta-analysis. | journal=J Eval Clin Pract | year= 2008 |  volume= 14 | issue= 5 | pages= 951-7 | pmid=19018930
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&retmode=ref&cmd=prlinks&id=19018930  | doi=10.1111/j.1365-2753.2008.00986.x }} </ref>
Statistical methods exist for assessing the importance of subgroups.<ref name="pmid12543843">{{cite journal|  author=Altman DG, Bland JM| title=Interaction revisited: the difference  between two estimates. | journal=BMJ | year= 2003 | volume= 326 |  issue= 7382 | pages= 219 | pmid=12543843
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=12543843 | pmc=PMC1125071 }}</ref>
====Comparing rates of dichotomous outcomes====
====Comparing rates of dichotomous outcomes====
Studies are usually statistically combined by a method such as the DerSimonian and Laird.<ref name="pmid3802833">{{cite journal| author=DerSimonian R, Laird N| title=Meta-analysis in clinical trials. | journal=Control Clin Trials | year= 1986 | volume= 7 | issue= 3 | pages= 177-88 | doi=10.1016/0197-2456(86)90046-2 |pmid=3802833 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=3802833 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> The DerSimonian and Laird weight for pooling studies is a type of inverse variance weight and creates a random effect model.
Studies are usually statistically combined by a method such as the DerSimonian and Laird.<ref name="pmid3802833">{{cite journal| author=DerSimonian R, Laird N| title=Meta-analysis in clinical trials. | journal=Control Clin Trials | year= 1986 | volume= 7 | issue= 3 | pages= 177-88 | doi=10.1016/0197-2456(86)90046-2 |pmid=3802833 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=3802833 }}</ref> The DerSimonian and Laird weight for pooling studies is a type of inverse variance weight and creates a random effect model.


Statistical packages are available from the [[Cochrane Collaboration]] (http://www.cc-ims.net/revman) and for [[R (programming language)]] ([http://cran.r-project.org/web/packages/rmeta/ rmeta] and [http://cran.r-project.org/web/packages/HSAUR2/ HSAUR2]).
Statistical packages are available from the [[Cochrane Collaboration]] (http://www.cc-ims.net/revman) and for [[R (programming language)]] ([http://cran.r-project.org/web/packages/rmeta/ rmeta] and [http://cran.r-project.org/web/packages/HSAUR2/ HSAUR2]).
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=====Studies with groups having zero events=====
=====Studies with groups having zero events=====
Excluding studies with zero events total events (zero-total-event trials) or zero events in one treatment group (zero-event trials) may exaggerate effect sizes.<ref name="pmid17679700">{{cite journal |author=Diamond GA, Bax L, Kaul S |title=Uncertain effects of rosiglitazone on the risk for myocardial infarction and cardiovascular death |journal=Ann. Intern. Med. |volume=147 |issue=8 |pages=578–81 |year=2007 |month=October |pmid=17679700 |doi= |url=http://www.annals.org/cgi/content/full/147/8/578 |issn=}}</ref><ref name="pmid17244367">{{cite journal| author=Friedrich JO, Adhikari NK, Beyene J| title=Inclusion of zero total event trials in meta-analyses maintains analytic consistency and incorporates all available data. | journal=BMC Med Res Methodol | year= 2007 | volume= 7 | issue=  | pages= 5 | pmid=17244367
Excluding studies with zero events total events (zero-total-event trials) or zero events in one treatment group (zero-event trials) may exaggerate effect sizes.<ref name="pmid17679700">{{cite journal |author=Diamond GA, Bax L, Kaul S |title=Uncertain effects of rosiglitazone on the risk for myocardial infarction and cardiovascular death |journal=Ann. Intern. Med. |volume=147 |issue=8 |pages=578–81 |year=2007 |month=October |pmid=17679700 |doi= |url=http://www.annals.org/cgi/content/full/147/8/578 |issn=}}</ref><ref name="pmid17244367">{{cite journal| author=Friedrich JO, Adhikari NK, Beyene J| title=Inclusion of zero total event trials in meta-analyses maintains analytic consistency and incorporates all available data. | journal=BMC Med Res Methodol | year= 2007 | volume= 7 | issue=  | pages= 5 | pmid=17244367
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=17244367 | doi=10.1186/1471-2288-7-5 | pmc=PMC1783664 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> An alternative is to use a continuity correction.<ref name="pmid16596572">{{cite journal| author=Bradburn MJ, Deeks JJ, Berlin JA, Russell Localio A| title=Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. | journal=Stat Med | year= 2007 | volume= 26 | issue= 1 | pages= 53-77 | pmid=16596572  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=17244367 | doi=10.1186/1471-2288-7-5 | pmc=PMC1783664 }}</ref> An alternative is to use a continuity correction.<ref name="pmid16596572">{{cite journal| author=Bradburn MJ, Deeks JJ, Berlin JA, Russell Localio A| title=Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. | journal=Stat Med | year= 2007 | volume= 26 | issue= 1 | pages= 53-77 | pmid=16596572
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16596572 | doi=10.1002/sim.2528 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> Rather than using a constant continuity correction, less bias may occur by correcting with either<ref name="pmid15116347">{{cite journal| author=Sweeting MJ, Sutton AJ, Lambert PC| title=What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. | journal=Stat Med | year= 2004 | volume= 23 | issue= 9 | pages= 1351-75 | pmid=15116347  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=16596572 | doi=10.1002/sim.2528 }}</ref> Rather than using a constant continuity correction, less bias may occur by correcting with either<ref name="pmid15116347">{{cite journal| author=Sweeting MJ, Sutton AJ, Lambert PC| title=What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. | journal=Stat Med | year= 2004 | volume= 23 | issue= 9 | pages= 1351-75 | pmid=15116347
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=15116347 | doi=10.1002/sim.1761 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref>
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=15116347 | doi=10.1002/sim.1761 }}</ref>
* "empirical estimate of the pooled effect size from the remaining studies in the meta-analysis."
* "empirical estimate of the pooled effect size from the remaining studies in the meta-analysis."
* "a function of the reciprocal of the opposite group arm size"
* "a function of the reciprocal of the opposite group arm size"
Line 89: Line 112:


If the subgrouping does not account for all heterogeneity, interaction can be tested with meta-regression to avoid  false-positive results.<ref  name="Cochrane Handbook 9.6.3.1">Higgins  JPT, Green S (editors). [http://www.mrc-bsu.cam.ac.uk/cochrane/handbook/chapter_9/9_6_3_1_is_the_effect_different_in_different_subgroups.htm  9.6.3.1  Is the effect different in different  subgroups?] in ''Cochrane Handbook  for Systematic Reviews of Interventions Version 5.0.2'' [updated  September  2009]. The Cochrane Collaboration, 2009. Available from http:// www.cochrane-handbook.org. </ref><ref name="pmid15160401">{{cite journal| author=Higgins JP, Thompson SG| title=Controlling the risk of spurious findings from meta-regression. | journal=Stat Med | year= 2004 | volume= 23 | issue= 11 | pages= 1663-82 | pmid=15160401  
If the subgrouping does not account for all heterogeneity, interaction can be tested with meta-regression to avoid  false-positive results.<ref  name="Cochrane Handbook 9.6.3.1">Higgins  JPT, Green S (editors). [http://www.mrc-bsu.cam.ac.uk/cochrane/handbook/chapter_9/9_6_3_1_is_the_effect_different_in_different_subgroups.htm  9.6.3.1  Is the effect different in different  subgroups?] in ''Cochrane Handbook  for Systematic Reviews of Interventions Version 5.0.2'' [updated  September  2009]. The Cochrane Collaboration, 2009. Available from http:// www.cochrane-handbook.org. </ref><ref name="pmid15160401">{{cite journal| author=Higgins JP, Thompson SG| title=Controlling the risk of spurious findings from meta-regression. | journal=Stat Med | year= 2004 | volume= 23 | issue= 11 | pages= 1663-82 | pmid=15160401  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&email=badgett@uthscdsa.edu&retmode=ref&cmd=prlinks&id=15160401 | doi=10.1002/sim.1752 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref> Metagression is detailed in a section below.
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&email=badgett@uthscdsa.edu&retmode=ref&cmd=prlinks&id=15160401 | doi=10.1002/sim.1752 }}</ref> Metagression is detailed in a section below.


====Software====
====Software====
Software available for meta-analysis includes:<ref name="pmid17845719">{{cite journal| author=Bax L, Yu LM, Ikeda N, Moons KG| title=A systematic comparison of software dedicated to meta-analysis of causal studies. | journal=BMC Med Res Methodol | year= 2007 | volume= 7 | issue=  | pages= 40 | pmid=17845719  
Software available for meta-analysis includes:<ref name="pmid17845719">{{cite journal| author=Bax L, Yu LM, Ikeda N, Moons KG| title=A systematic comparison of software dedicated to meta-analysis of causal studies. | journal=BMC Med Res Methodol | year= 2007 | volume= 7 | issue=  | pages= 40 | pmid=17845719  
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&email=badgett@uthscdsa.edu&retmode=ref&cmd=prlinks&id=17845719 | doi=10.1186/1471-2288-7-40 | pmc=PMC2048970 }} <!--Formatted by http://sumsearch.uthscsa.edu/cite/--></ref>
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&email=badgett@uthscdsa.edu&retmode=ref&cmd=prlinks&id=17845719 | doi=10.1186/1471-2288-7-40 | pmc=PMC2048970 }}</ref>
* [http://www.cc-ims.net/revman Review Manager (RevMan)] by the Cochrane Collaboration
* [http://www.cc-ims.net/revman Review Manager (RevMan)] by the Cochrane Collaboration
* [[R (programming language)|R programming language]]:
* [[R (programming language)|R programming language]]:
Line 102: Line 125:
===Displaying results===
===Displaying results===
Study results may be grouped and displayed with a Forest plot.[[Image:Forest plot of target HbA1c for Diabetes Type II showing heterogeneity.jpg|right|thumb|350px|{{#ifexist:Template:Forest plot of target HbA1c for Diabetes Type II showing heterogeneity.jpg/credit|{{Forest plot of target HbA1c for Diabetes Type II showing heterogeneity.jpg/credit}}<br/>|}}'''Forest Plot''' showing meta-analysis of [[randomized controlled trial]]s of differing target glucose control and mortality for [[diabetes mellitus type 2]]. Note the heterogeneity (P<0.05 and high I<sup>2</sup> in circled in red) due to increased death when the [[glycosylated hemoglobin A]] (Hb A1c) target was 6.0% in the ACCORD trial<ref name="pmid18539917">{{cite journal |author=Gerstein HC, Miller ME, Byington RP, ''et al'' |title=Effects of intensive glucose lowering in type 2 diabetes |journal=N. Engl. J. Med. |volume=358 |issue=24 |pages=2545–59 |year=2008 |month=June |pmid=18539917 |doi=10.1056/NEJMoa0802743 |url=http://content.nejm.org/cgi/pmidlookup?view=short&pmid=18539917&promo=ONFLNS19 |issn=}}</ref>]]
Study results may be grouped and displayed with a Forest plot.[[Image:Forest plot of target HbA1c for Diabetes Type II showing heterogeneity.jpg|right|thumb|350px|{{#ifexist:Template:Forest plot of target HbA1c for Diabetes Type II showing heterogeneity.jpg/credit|{{Forest plot of target HbA1c for Diabetes Type II showing heterogeneity.jpg/credit}}<br/>|}}'''Forest Plot''' showing meta-analysis of [[randomized controlled trial]]s of differing target glucose control and mortality for [[diabetes mellitus type 2]]. Note the heterogeneity (P<0.05 and high I<sup>2</sup> in circled in red) due to increased death when the [[glycosylated hemoglobin A]] (Hb A1c) target was 6.0% in the ACCORD trial<ref name="pmid18539917">{{cite journal |author=Gerstein HC, Miller ME, Byington RP, ''et al'' |title=Effects of intensive glucose lowering in type 2 diabetes |journal=N. Engl. J. Med. |volume=358 |issue=24 |pages=2545–59 |year=2008 |month=June |pmid=18539917 |doi=10.1056/NEJMoa0802743 |url=http://content.nejm.org/cgi/pmidlookup?view=short&pmid=18539917&promo=ONFLNS19 |issn=}}</ref>]]
===Measuring consistency of study results===
Consistency can be statistically tested using either the Cochran's ''Q'' or ''I<sup>2</sup>''.<ref name="pmid12958120">{{cite journal |author=Higgins JP, Thompson SG, Deeks JJ, Altman DG |title=Measuring inconsistency in meta-analyses |journal=BMJ |volume=327 |issue=7414 |pages=557–60 |year=2003 |month=September |pmid=12958120 |pmc=192859 |doi=10.1136/bmj.327.7414.557 |url=http://bmj.com/cgi/pmidlookup?view=long&pmid=12958120 |issn=}}</ref><ref name="pmid12111919">{{cite journal| author=Higgins JP, Thompson SG| title=Quantifying heterogeneity in a meta-analysis. | journal=Stat Med | year= 2002 | volume= 21 | issue= 11 | pages= 1539-58 | pmid=12111919
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&email=badgett@uthscdsa.edu&retmode=ref&cmd=prlinks&id=12111919 | doi=10.1002/sim.1186 }}</ref> The ''I<sup>2</sup>'' is the "percentage of total variation across studies that is due to heterogeneity rather than chance."<ref name="pmid12958120"/> These numbers are usually displayed for each group of studies on a Forest plot.
In interpreting of the Cochran's ''Q'', heterogeneity exists if its p-value is < 0.05 or possibly if < 0.10<ref name="pmid3802849">{{cite journal |author=Fleiss JL |title=Analysis of data from multiclinic trials |journal=Control Clin Trials |volume=7 |issue=4 |pages=267–75 |year=1986 |month=December |pmid=3802849 |doi= |url= |issn=}}</ref><ref name="pmid1289110">{{cite journal |author=Dickersin K, Berlin JA |title=Meta-analysis: state-of-the-science |journal=Epidemiol Rev |volume=14 |issue= |pages=154–76 |year=1992 |pmid=1289110 |doi= |url=http://epirev.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=1289110 |issn=}}</ref>.
The following has been proposed for interpreting ''I<sup>2</sup>'':<ref name="pmid12958120"/>
* Low heterogeneity is ''I<sup>2</sup>'' = 25%
* Moderate heterogeneity is ''I<sup>2</sup>'' = 50%
* High heterogeneity is ''I<sup>2</sup>'' = 75%
or according to the Handbook of the [[Cochrane Collaboration]]:<ref name="urlCochrane Handbook for Systematic Reviews of Interventions">{{cite web |url=http://www.cochrane-handbook.org/ |title=Cochrane Handbook for Systematic Reviews of Interventions |editor=Higgins JPT, Green S| author= |authorlink= |coauthors= |date=2008 |format= |work= |publisher=Cochrane Collaboration |pages= |language= |archiveurl= |archivedate= |quote= |accessdate=2008-10-23}}</ref>
* 0%-40%: might not be important
* 30%-60%: may represent moderate heterogeneity
* 50%-90%: may represent substantial heterogeneity
* 75%-100%: considerable heterogeneity
However, I<sup>2</sup>, even when the value is 0%, can be misleading if the [[confidence interval]]s around the value are not provided.<ref name="pmid17974687">{{cite journal| author=Ioannidis JP, Patsopoulos NA, Evangelou E| title=Uncertainty in heterogeneity estimates in meta-analyses. | journal=BMJ | year= 2007 | volume= 335 | issue= 7626 | pages= 914-6 | pmid=17974687
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&retmode=ref&cmd=prlinks&id=17974687 | doi=10.1136/bmj.39343.408449.80 }} </ref><ref name="pmid19018930">{{cite journal| author=Ioannidis JP| title=Interpretation of tests of heterogeneity and bias in meta-analysis. | journal=J Eval Clin Pract | year= 2008 | volume= 14 | issue= 5 | pages= 951-7 | pmid=19018930
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=clinical.uthscsa.edu/cite&retmode=ref&cmd=prlinks&id=19018930 | doi=10.1111/j.1365-2753.2008.00986.x }} </ref>
Statistical methods exist for assessing the importance of subgroups.<ref name="pmid12543843">{{cite journal| author=Altman DG, Bland JM| title=Interaction revisited: the difference between two estimates. | journal=BMJ | year= 2003 | volume= 326 | issue= 7382 | pages= 219 | pmid=12543843
| url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=12543843 | pmc=PMC1125071 }}</ref>


==Variations on meta-analysis==
==Variations on meta-analysis==

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Meta-analysis is defined as "a quantitative method of combining the results of independent studies (usually drawn from the published literature) and synthesizing summaries and conclusions which may be used to evaluate therapeutic effectiveness, plan new studies, etc., with application chiefly in the areas of research and medicine."[1]

A meta-analyses is a subset of systematic reviews in which the results of the studies are numerically pooled.

Standards for the reporting of meta-analyses exist.[2]

Validity of meta-analysis

Studies on the validity of meta-analyses conflict.[3][4][5] Some of the conflict may be due to the methods used to compare the meta-analyses.[6]

Methods of meta-analysis

Guidelines are available for the conduct[7] and reporting[2] of meta-analyses.

Searching for studies

Meta-analyses vary in the extent of their searches for underlying studies. [8] There is debate on how extensive should be the search for studies as there is are diminishing returns with extensive searching. Some studies suggest limiting searches[9][10][11] while other studies advocate exhaustive searches[12][13][14][15][16][17] including unpublished studies[18][19].

There is not a consensus on what details of searching should be reported in a meta-analysis.[20]

Selecting studies for inclusion

Conflict in selection of trials to be included in the meta-analysis can affect the conclusions of a meta-analysis.[21][22][23]

Although meta-analyses in general are very inclusive, arguments exist for only including the best trials.[24]

Assessing the quality of trials

For more information, see: Randomized controlled trial.


Cochrane bias scale

The Cochrane Collaboration uses a six item tool.[25]

Jadad score

The Jadad score may be used to assess quality and contains three items:[26]

  1. Was the study described as randomized (this includes the use of words such as randomly, random, and randomization)?
  2. Was the study described as double blind?
  3. Was there a description of withdrawals and dropouts?

Each question is scored one point for a yes answer. In addition, for questions and 2, a point is added if the method was appropriate and a point is deducted if the method is not appropriate (e.g. not effectively randomized or not effectively double-blinded).

Statistical methods

Measuring consistency of study results

Consistency can be statistically tested using either the Cochran's Q or I2.[27][28] The I2 is the "percentage of total variation across studies that is due to heterogeneity rather than chance."[27] These numbers are usually displayed for each group of studies on a Forest plot.

In interpreting of the Cochran's Q, heterogeneity exists if its p-value is < 0.05 or possibly if < 0.10[29][30].

The following has been proposed for interpreting I2:[27]

  • Low heterogeneity is I2 = 25%
  • Moderate heterogeneity is I2 = 50%
  • High heterogeneity is I2 = 75%

or according to the Handbook of the Cochrane Collaboration:[31]

  • 0%-40%: might not be important
  • 30%-60%: may represent moderate heterogeneity
  • 50%-90%: may represent substantial heterogeneity
  • 75%-100%: considerable heterogeneity

However, I2, even when the value is 0%, can be misleading if the confidence intervals around the value are not provided.[32][33]

Statistical methods exist for assessing the importance of subgroups.[34]

Comparing rates of dichotomous outcomes

Studies are usually statistically combined by a method such as the DerSimonian and Laird.[35] The DerSimonian and Laird weight for pooling studies is a type of inverse variance weight and creates a random effect model.

Statistical packages are available from the Cochrane Collaboration (http://www.cc-ims.net/revman) and for R (programming language) (rmeta and HSAUR2).

Studies with groups having zero events

Excluding studies with zero events total events (zero-total-event trials) or zero events in one treatment group (zero-event trials) may exaggerate effect sizes.[36][37] An alternative is to use a continuity correction.[38] Rather than using a constant continuity correction, less bias may occur by correcting with either[39]

  • "empirical estimate of the pooled effect size from the remaining studies in the meta-analysis."
  • "a function of the reciprocal of the opposite group arm size"

For an example of continuity correction using the second method above:[36]

  • S is the sum of corrections for event and no event cells (usually S=1 in a zero-event trial and S=2 in a zero-total-event trial)
  • R is the ratio of group sizes (R=1 if both groups are the same)
  • For a zero-event trial with equal group sizes
    • The correction in the larger experimental group is R/S*(R + 1). This becomes 1/1*(1 + 1) = 1
    • The correction in the smaller experimental group is 1/S*(R + 1). This becomes 1/1*(1 + 1) = 1
  • For a zero-event-total trial with equal group sizes
    • The correction in the larger experimental group is R/S*(R + 1). This becomes 1/2*(1 + 1) = 0.5
    • The correction in the smaller experimental group is 1/S*(R + 1). This becomes 1/2*(1 + 1) = 0.5

Comparing rates of continuous outcomes

The standardized mean difference (SMD) is used. In the interpretation of SMD, 0.2 represents a small effect, 0.5 a moderate effect, and 0.8 a large effect.[40][41]

Subgroup analysis

There are two types of interactions:[42]

  • Qualitative interaction interaction exists if the direction of effect is reversed in subgroups.
  • Quantitative interaction is when the size of the effect varies but not the direction.

If the subgrouping accounts for all heterogeneity, interaction can be sought using an inverse-variance method for a fixed-effect model.[43]

If the subgrouping does not account for all heterogeneity, interaction can be tested with meta-regression to avoid false-positive results.[43][44] Metagression is detailed in a section below.

Software

Software available for meta-analysis includes:[45]

Displaying results

Study results may be grouped and displayed with a Forest plot.

(CC) Photo: Robert Badgett
Forest Plot showing meta-analysis of randomized controlled trials of differing target glucose control and mortality for diabetes mellitus type 2. Note the heterogeneity (P<0.05 and high I2 in circled in red) due to increased death when the glycosylated hemoglobin A (Hb A1c) target was 6.0% in the ACCORD trial[47]

Variations on meta-analysis

Cumulative meta-analysis

Cumulative meta-analysis has been used to show that 25 off 33 randomized controlled trials of streptokinase not necessary[48] and have shown the delay in adoption of evidence by experts[49].

Cumulative meta-analyses may be prone to false positive results due to repeated tests of statistical significance.[50]

Individual patient data meta-analysis

An individual patient data meta-analysis is "where analyses are done using original data and outcomes for each person enrolled in relevant studies; these results are then pooled in one analysis as if patients were in a single large study."[51]

Individual patient data meta-analysis (IPD meta-analysis) may have more long lasting results than other meta-analyses.[52]

Meta-regression

Meta-regression allows simultaneous comparison of multiple sources of heterogeneity.[53][54][55][56]

Meta-regression can also analyze subgroups.[43]A permutation test may reduce the chance of a false positive subgroup analysis.[44]

When analyzing a meta-regression of dichotomous independent variables, the "results of meta-regression analyses are most usefully expressed as ratios of odds ratios (or risk ratios)."[7]

Meta-regression can be performed with the rmeta package[57] of the R programming language as described by Everitt and Hothorn[58][59].

Examples of meta-regression analysis are:

  1. McAlister FA, Wiebe N, Ezekowitz JA, Leung AA, Armstrong PW (2009). "Meta-analysis: beta-blocker dose, heart rate reduction, and death in patients with heart failure.". Ann Intern Med 150 (11): 784-94. PMID 19487713.
  1. Briel M, Ferreira-Gonzalez I, You JJ, Karanicolas PJ, Akl EA, Wu P et al. (2009). "Association between change in high density lipoprotein cholesterol and cardiovascular disease morbidity and mortality: systematic review and meta-regression analysis.". BMJ 338: b92. DOI:10.1136/bmj.b92. PMID 19221140. PMC PMC2645847. Research Blogging.
  1. Emerging Risk Factors Collaboration. Erqou S, Kaptoge S, Perry PL, Di Angelantonio E, Thompson A et al. (2009). "Lipoprotein(a) concentration and the risk of coronary heart disease, stroke, and nonvascular mortality.". JAMA 302 (4): 412-23. DOI:10.1001/jama.2009.1063. PMID 19622820. Research Blogging.


Network meta-analysis

A network meta-analysis[60] and Bayesian hierarchical models[61] pool studies in order to compare to treatments that have not been directly compared.[62] Network meta-analyses are commonly not well performed[63]and can have misleading conclusions.[64][65][66] Network meta-analyses have been conducted by the Cochrane Collaboration.[67][68]

Network meta-analyses can be conducted with Bugs and OpenBugs software.

Meta-analysis of diagnostic tests

Standards exists for the meta-analysis of diagnostic tests.[69][70] The traditional summary receiver operating characteristic curve (SROC curve) should be replaced by either the hierarchical summary receiver operating characteristic curve(HSROC curve).[70][71] or bivariate random-effects model.[72] Discussions of HSROC and bivariate random-effects meta-analysis are available.[73][72] An example of a meta-analysis using bivariate mixed-effects binomial regression model is available.[74] Examples of using the HSROC and diagnostic odds ratio are available.[75]

Factors associated with higher quality meta-analyses

Meta-analyses by the Cochrane Collaboration tend to be of higher quality.[76]

Individual data meta-analyses, in which the records from individual patients are pooled together into one dataset, tend to have more stable conclusions.[52]

Factors associated with lower quality meta-analyses

About a third of meta-analyses that happen to precede large randomized controlled trials will conflict with the results of the trial.[3]

Conflict of interest

Meta-analyses produced with a conflict of interest are more likely to interpret results as positive.[77]

Small study effect and publication bias

The small study effect is the observation that small studies tend to report more positive results.[78][79] This is especially a threat when the original studies in a meta-analysis are less than 50 patients in size.[80]

Publication bias against negative studies is part of the small study effect and may threaten the validity of meta-analyses that are positive and all the studies included within the meta-analysis are small.[81][82]

In performing a meta-analysis, a file drawer[83]or a funnel plot analysis[82][84] may help detect underlying publication bias among the studies in the meta-analysis.

Outcome reporting bias

Meta-analyses in which a smaller proportion of included trials provide raw data for inclusion in the meta-analysis are more likely to be positive.[85] This may be due a bias against reporting negative results.[86]

Problems with meta-analyses

Obsolescence

The conclusions of meta-analyses may be mitigated by research published after the search date of the meta-analysis. This may occur by the time the meta-analysis has been published.[87][88] Strategies have been developed for updating meta-analyses.[89]

References

  1. ↑ National Library of Medicine. Meta-analysis. Retrieved on 2007-12-06.
  2. ↑ 2.0 2.1 Moher D, Liberati A, Tetzlaff J, Altman DG (July 2009). "Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement". Ann. Intern. Med.. PMID 19622511. [e] Cite error: Invalid <ref> tag; name "pmid19622511" defined multiple times with different content
  3. ↑ 3.0 3.1 LeLorier J, Grégoire G, Benhaddad A, Lapierre J, Derderian F (August 1997). "Discrepancies between meta-analyses and subsequent large randomized, controlled trials". N. Engl. J. Med. 337 (8): 536–42. PMID 9262498. [e] Cite error: Invalid <ref> tag; name "pmid9262498" defined multiple times with different content
  4. ↑ Villar J, Carroli G, Belizán JM (March 1995). "Predictive ability of meta-analyses of randomised controlled trials". Lancet 345 (8952): 772–6. PMID 7891492. [e]
  5. ↑ Cappelleri JC, Ioannidis JP, Schmid CH, et al (1996). "Large trials vs meta-analysis of smaller trials: how do their results compare?". JAMA 276 (16): 1332–8. PMID 8861993. [e]
  6. ↑ Ioannidis JP, Cappelleri JC, Lau J (April 1998). "Issues in comparisons between meta-analyses and large trials". JAMA 279 (14): 1089–93. PMID 9546568. [e]
  7. ↑ 7.0 7.1 The Cochrane Collaboration. Cochrane Handbook
  8. ↑ Royle P, Milne R (2003). "Literature searching for randomized controlled trials used in Cochrane reviews: rapid versus exhaustive searches.". Int J Technol Assess Health Care 19 (4): 591-603. PMID 15095765.
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