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suggest limiting searches[9][10][11] while other studies advocate exhaustive searches[12][13][14][15][16][17] including unpublished studies[18][19].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

Comparing rates of dichotomous outcomes

Studies are usually statistically combined by a method such as the DerSimonian and Laird.[27] 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.[28][29] An alternative is to use a continuity correction.[30] Rather than using a constant continuity correction, less bias may occur by correcting with either[31]

  • "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:[28]

  • 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.[32][33]

Subgroup analysis

There are two types of interactions:[34]

  • 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.[35]

If the subgrouping does not account for all heterogeneity, interaction can be tested with meta-regression to avoid false-positive results.[35][36] Metagression is detailed in a section below.

Software

Software available for meta-analysis includes:[37]

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[39]

Measuring consistency of study results

Consistency can be statistically tested using either the Cochran's Q or I2.[40][41] The I2 is the "percentage of total variation across studies that is due to heterogeneity rather than chance."[40] 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[42][43].

The following has been proposed for interpreting I2:[40]

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

or according to the Handbook of the Cochrane Collaboration:[44]

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

Statistical methods exist for assessing the importance of subgroups.[45]

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[46] and have shown the delay in adoption of evidence by experts[47].

Cumulative meta-analyses may be prone to false positive results due to repeated tests of statistical significance.[48]

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."[49]

Individual patient data meta-analysis (IPD meta-analysis) may have more long lasting results than other meta-analyses.[50]

Meta-regression

Meta-regression allows simultaneous comparison of multiple sources of heterogeneity.[51][52][53][54]

Meta-regression can also analyze subgroups.[35]A permutation test may reduce the chance of a false positive subgroup analysis.[36]

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[55] of the R programming language as described by Everitt and Hothorn[56][57].

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[58] and Bayesian hierarchical models[59] pool studies in order to compare to treatments that have not been directly compared.[60] Network meta-analyses are commonly not well performed[61]and can have misleading conclusions.[62][63][64] Network meta-analyses have been conducted by the Cochrane Collaboration.[65][66]

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.[67][68] The traditional summary receiver operating characteristic curve (SROC curve) should be replaced by either the hierarchical summary receiver operating characteristic curve(HSROC curve).[68][69] or bivariate random-effects model.[70] Discussions of HSROC and bivariate random-effects meta-analysis are available.[71][70] An example of a meta-analysis using bivariate mixed-effects binomial regression model is available.[72] Examples of using the HSROC and diagnostic odds ratio are available.[73]

Factors associated with higher quality meta-analyses

Meta-analyses by the Cochrane Collaboration tend to be of higher quality.[74]

Individual data meta-analyses, in which the records from individual patients are pooled together into one dataset, tend to have more stable conclusions.[50]

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.[75]

Publication bias

Publication bias against negative studies may threaten the validity of meta-analyses that are positive and all the studies included within the meta-analysis are small.[76][77]

In performing a meta-analysis, a file drawer[78]or a funnel plot analysis[77][79] 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.[80] This may be due a bias against reporting negative results.[81]

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.[82][83] Strategies have been developed for updating meta-analyses.[84]

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.
  9. ↑ Stevinson C, Lawlor DA (2004). "Searching multiple databases for systematic reviews: added value or diminishing returns?". Complement Ther Med 12 (4): 228-32. DOI:10.1016/j.ctim.2004.09.003. PMID 15649836. Research Blogging.
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