Meta-analysis

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."

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.

Validity of meta-analysis
Studies on the validity of meta-analyses conflict. Some of the conflict may be due to the methods used to compare the meta-analyses.

Methods of meta-analysis
Guidelines are available for the conduct and reporting of meta-analyses.

Searching for studies
Meta-analyses vary in the extent of their searches for underlying studies. 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 Some studies suggest limiting searches  while other studies advocate exhaustive searches      including unpublished studies.

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

Selecting studies for inclusion
Conflict in selection of trials to be included in the meta-analysis can affect the conclusions of a meta-analysis.

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

Cochrane bias scale
The Cochrane Collaboration uses a six item tool.

Jadad score
The Jadad score may be used to assess quality and contains three items:
 * 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).

Measuring consistency of study results
Consistency can be statistically tested using either the Cochran's Q or I2. The I2 is the "percentage of total variation across studies that is due to heterogeneity rather than chance." 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.

The following has been proposed for interpreting I2:
 * Low heterogeneity is I2 = 25%
 * Moderate heterogeneity is I2 = 50%
 * High heterogeneity is I2 = 75%

or according to the Handbook of the Cochrane Collaboration:
 * 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.

Statistical methods exist for assessing the importance of subgroups.

Comparing rates of dichotomous outcomes
Studies are usually statistically combined by a method such as the DerSimonian and Laird. 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. An alternative is to use a continuity correction. Rather than using a constant continuity correction, less bias may occur by correcting with either
 * "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:
 * 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.

Subgroup analysis
There are two types of interactions:
 * 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.

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

Software
Software available for meta-analysis includes:
 * Review Manager (RevMan) by the Cochrane Collaboration
 * R programming language:
 * rmeta package with reference manual
 * metafor package
 * HSAUR2 interactive package with a chapter containing sample demonstrations, "Meta-Analysis: Nicotine Gum and Smoking Cessation and the Effcacy of BCG Vaccine in the Treatment of Tuberculosis" in "A Handbook of Statistical Analyses Using R".

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

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

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

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."

Standards exist for conduct and reporting.

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

Meta-regression
Meta-regression allows simultaneous comparison of multiple sources of heterogeneity.

Meta-regression can examine relationships between predictor and outcome variables including non-linear relationships.

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

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)."

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

Examples of meta-regression analysis are:

Network meta-analysis
A network meta-analysis and Bayesian hierarchical models pool studies in order to compare to treatments that have not been directly compared. Network meta-analyses are commonly not well performed and can have misleading conclusions. Network meta-analyses have been conducted by the Cochrane Collaboration.

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

Overview of reviews
A systematic review may review other systematic reviews. The reviews may address different treatments of the same disease or different diseases that can be treated with an intervention.

Factors associated with higher quality meta-analyses
Meta-analyses by the Cochrane Collaboration tend to be of higher quality.

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

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.

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

Small study effect and publication bias
The small study effect is the observation that small studies tend to report more positive results. This is especially a threat when the original studies in a meta-analysis are less than 50 patients in size.

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.

In performing a meta-analysis, a file drawer or a funnel plot analysis 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. This may be due a bias against reporting negative results.

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. Strategies have been developed for updating meta-analyses.