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Ora Paltiel, October 28, 2014. Meta-Analysis: The Art and Science of Combining Information. DEFINITIONS. The statistical analysis of a large collection of results from individual studies for the purpose of integrating the findings

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  • The statistical analysis of a large collection of results from individual studies for the purpose of integrating the findings
  • A quantitative review and synthesis of results of related but independent studies
  • “overview”
  • “data pooling”
  • “data synthesis”
  • systematic review
“Meta “
  • Webster’s dictionary:

a) occurring later than or in succession to

b) situated behind or beyond

c) change, transformation

Examples: metaphysics,


over 2 million medical articles are published each year

The findings of new studies not only “ differ from previously established truths but disagree with one another, often violently”

-Morton Hunt, How Science Takes Stock, P.1

The Problem

Over 2 million medical articles are published each year.
the goal of meta analysis making order of scientific chaos
The Goal of Meta-Analysis:“Making Order of Scientific Chaos”
  • Began as a tool in Social Sciences

21 citations in 1986

431 citations in 1991

more than 45000 today

In Medicine – at first only RCTs

Now – thousands of meta-analyses of observational studies


is a group of over 15,000 volunteers in

more than 90 countries who review the

effects of health care interventions tested

in biomedicalrandomized controlled trials

  • reviews have also studied the results of

non-randomizedobservational studies.

  • The results of thesesystematic reviewspublished as "Cochrane Reviews" in theCochrane Library
  • Founded in 1993 under the leadership of Iain Chalmers.
  • developed in response to Archie Cochrane's call for up-to-date, systematic reviews of all relevant randomized controlled trials of health care.
cochrane collaboration
Cochrane collaboration

Goal : to help people make well informed decisions about health care by preparing, maintaining and ensuring the accessibility of systematic reviews of the effects of health care interventions.

The principles of the Cochrane Collaboration are:

  • collaboration
  • building on the enthusiasm of individuals
  • avoiding duplication
  • minimizing bias
  • keeping up to date
  • striving for relevance
  • promoting access
  • ensuring quality
  • continuity
  • enabling wide participation
major goals of meta analysis
Major goals of Meta-Analysis
  • Objective summaries
  • Increase powerto detect true effects
  • Estimate effect size
  • Resolve uncertainty
  • Explore heterogeneity and reasons for itIf the studies produced dissimilar results, How did they differ? Why? Study design, quality, populations, subtle intervention differences etc
  • Tool for conducting evidence-based medicine and for setting policy
how to do a meta analysis
How to do a Meta-Analysis

1. Define research question, including intervention, population, and outcome to be assessed

2. Define eligibility criteria (types of study, design)

3. Identify all studies (published or un) which deal with the specified problem

4. Evaluate each article for inclusion or exclusion, on the basis of predefined criteria

5. Summarize, numerically, the results of these studies

6. Interpret these findings, with emphasis on explaining differences as well as summarizing the data

literature review
Literature review
  • A comprehensive, systematic literature review should be conducted
  • Sources: citation indexes, abstract databases, clinical trials registers, references ,
  • Issues: language, “grey literature”, conference abstracts, unpublished findings
  • Meta-analysis is research, which should be reproducible, methods incl key words must be able to be replicated

Problem of publication bias



Horvath et al BMJ 2010;340:c1395

information assembled
Information Assembled
  • The report ( author, year)
  • The study (population)
  • The patients (demographic and clinical characteristics)
  • The design
  • The treatment
  • The effect size ( estimate , SE)

Methods, reliability and validity of recording information need to be documented


Thirty three trials of streptokinase vs. conventional treatment for Acute Myocardial Infarction

  • “Head-Counting - Statistical”: Count the number of significant results in each direction Result: 6 favor treatment, 0 favor placebo, 27 nonsignificant
  • “Head-Counting”: Count the direction of the results in the studiesResult: 24 favor treatment, 9 favor placebo
streptokinase summary
Streptokinase - Summary
  • Streptokinase reduces mortality by about 22%
  • Efficacy proven by 2 large RCTs in 1986 and 1988
  • Meta-analysis proved efficacy in 1971
  • 6380 lives could have been saved in large RCTs alone
what can we learn from the forest plot
What can we learn from the Forest Plot?

Meta-analysis of gestational diabetes outcomes – 1. Maternal

Horvath et al BMJ 2010;340:c1395

statistical methods
Statistical Methods
  • We have a series of measures of association, one for each study
  • We wish to summarize these measures
  • This can be carried out using a weighted average of the estimates taken from each study.
classic meta analysis
Classic Meta-Analysis
  • Analyzes RR, OR, or absolute differences in percentages between groups.
  • Uses the the inverse of the variance of the estimate provided by each participating trial for the weights. This gives a minimum variance unbiased estimate of the effect.
  • Large trials carry more weight than small trials.
inference fixed v random effects
Inference: fixed .v. random effects

If interest is centered on making inferences for the populations that have been sampled, and we assume that there is a single effect of treatment - then a fixed effects approach is used.

In this approach the only source of uncertainty is that resulting from sampling patients into the studies. Variation stems

from within-study variation study.

The population to which we wish to generalized the results consists of a set of studies having identical characteristics

random effects
  • In random-effects approach the existing studies are considered as a random sample from a population of studies
  • Random-effects approach is used when inferences are to be generalized to a population in which studies may differ in their effect and characteristics
  • Random effects approach integrate also the between-study variability
fixed vs random effects
Fixed vs. Random-effects
  • The use of random-effects will produce somewhat larger 95% CI
  • A good practice is to first perform a test of heterogeneity between studies. If no significant variation is found between studies - a fixed-effects approach can be used
  • There are a number of ways to model random-effects

Horvath et al BMJ 2010;340:c1395

sensitivity analyses excluding studies with predefined less desirable characteristics as follows
Sensitivity analysesexcluding studies with predefined less desirable characteristics, as follows:

Risk of bias

When the analysis was limited to two studies with a low risk of bias for random sequence generation and/or allocation concealment the add-on effect of acupuncture on patient-reported global assessment remained significant (RR 0.39, 95% CI 0.18–0.88, I2 = 0%).

Sample size

When four studies with ≥ 40 participants per group were pooled, there was no significant difference in the risk of symptoms persisting or worsening between the acupuncture and control groups (RR 0.50, 95% CI 0.24–1.05, I2 = 55%).

assessing quality
Assessing Quality

A systematic approach should be used in order to assess the quality of the studies and to determine inclusion/exclusion of studies

Explicit methods limit bias in identifying and rejecting studies

Scales such as Jaddad scale

domains to be assessed
Domains to be assessed
  • Methodological quality ( bias)
  • Precision in estimation
  • External validity
further exploring heterogeneity
Further Exploring Heterogeneity
  • In case of substantial heterogeneity between studies, exploring its causes can be performed by considering covariates on the study level that could ‘explain’ differences between studies.
  • Such analyses are called meta-regression
Publication bias. Some studies are not published, selective presentation in those published.Do a comprehensive search. Use a funnel plot
  • In times of increasing amount of information-a systematic approach to synthesizing information has many advantages.
  • A systematic approach enables exploring heterogeneity between studies
  • As any other type of research systematic review should be carried out methodically and cautiously
problems with meta analysis in real life
Problems with Meta-Analysis in Real Life
  • “Meta-analysis” often not done, or very few studies combined
  • Retrospective study
  • Publication Bias
  • Heterogeneity
  • Expect to see lots of meta-analyses
  • Good ones and bad ones
  • Scientific community will decide whether it is useful

Be skeptical of everything

robustness of results meta regression
Robustness of results-meta-regression

an investigation of how a categorical study characteristic is associated with the intervention effects in the meta-analysis. For example, studies in which allocation sequence concealment was adequate may yield different results from those in which it was inadequate. Here, allocation sequence concealment, adequate /inadequate, is a categorical characteristic at the study level. MR in principle allows the effects of multiple factors to be investigated simultaneously (although this is rarely possible due to inadequate numbers of studies) (Thompson 2002). Meta-regression should generally not be considered when there are fewer than ten studies in a meta-analysis.

Meta-regressions are similar in essence to simple regressions, in which an outcomevariable is predicted according to the values of one or more explanatory variables. In meta-regression, the outcome variable is the effect estimate (for example, a mean difference, a risk difference, a log odds ratio or a log risk ratio). The explanatory variables are characteristics of studies that might influence the size of intervention effect