MetaAnalysis

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Meta-Analysis
Part 1
Reza Yousefi Nooraie
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(No Transcript)
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How do we summarize medical information?

• Traditional Approach
• Expert Opinion
• Narrative review articles
• Consensus statements (group expert opinion)
• New Approach (Systematic reviews)
• Explicit quantitative synthesis of ALL the
  evidence

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Definition - Meta-analysis

• Meta-analysis is a statistical analysis of a
  collection of studies
• Meta-analysis methods focus on contrasting and
  comparing results from different studies in
  anticipation of identifying consistent patterns
  and sources of disagreements among these results
• Primary objective
• Synthetic goal (estimation of summary) vs
• Analytic goal (estimation of differences)

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Definition - Meta-analysis

• Primary objective
• Synthetic goal (estimation of summary)
• Analytic goal (estimation of differences)

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• Systematic Review
• the application of scientific strategies that
  limit bias to the systematic assembly, critical
  appraisal and synthesis of all relevant studies
  on a specific topic
• Meta-Analysis
• a systematic review that employs statistical
  methods to combine and summarize the results of
  several studies

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Systematic Review VS Meta-Analysis
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Steps of a Systematic Review

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

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When can you do a meta-analysis?

• When more than one study has estimated an effect
• When there are no differences in study
  characteristics that are likely to substantially
  affect the outcome
• When the outcomes has been measured in similar
  ways
• When all data are available (beware when only
  some are available)

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Meta-analysisMethods
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Meta-analysis is typically a two-stage process

• A summary statistic for each study
• A summary (pooled) treatment effect estimate as a
  weighted average of the treatment effects
  estimated in the individual studies.

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Averaging studies

• A simple average would give each study equal
  weight
• This is wrong
• Some studies are more likely to give an answer
  closer to the true effect than others

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Weighting

• The weights are chosen to reflect the amount of
  information that each trial contains.

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Weighting

• Give more weight to the more informative studies.
  Weight by
• Size (sample size (n))
• Event rate
• Homogeneity (inverse of the variance)
• Quality
• Other factors

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weighted average
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Inverse variance method

• The weight given to each study is chosen to be
  the inverse of the variance of the effect
  estimate

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Inverse variance method

• Larger studies
• which have smaller standard errors
• more weight than
• smaller studies
• which have larger standard errors.

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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Forest plot
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Continuous (measured)
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Why log OR?
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Why log OR?
LogOR
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Dichotomous data

• Inverse Variance
• Mantel-Haenszel
• Peto
• DerSimonian and Laird

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Mantel-Haenszel methods

• data must be in form of 2 x 2 table for
  Mantel-Haenszel
• odds ratio, rate ratio, risk ratio
• Most commonly used method for meta-analysis
• (has optimal statistical properties)

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Mantel-Haenszel methods

• When event rates are low or trial size is small,
  the estimates of the standard errors of the
  effect estimates in the inverse variance methods
  may be poor.
• Mantel-Haenszel methods use a different weighting
  scheme that depends upon which effect measure is
  being used.
• They have been shown to have better statistical
  properties when there are few events.
• In other situations the two methods give similar
  estimates.

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Mantel-Haenszel Method
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Mantel-Haenszel Method

• ORmh ? (weighti x ORi) / ? weighti
• ORi (ai x di) / (bi x ci)
• weighti 1 / variancei
• For OR variancei Ni / (bi x ci)
• For RR variancei Ni / ((aibi ) x ci)
• For RD variancei Ni / n1i x n2i

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Mantel-Haenszel Method

• 95 CI e ln(ORmh) /- 1.96 x sqrt(var ORmh)
• var ORmh (?F / 2 x ?R2) ?G / (2 x ?R x ?S)
  (?H/(2 x ?S2)
• where
• F ai x di x (ai di)/ni2
• G ai x di x (bici) (bi x ci x (ai di))
  / ni2
• H (bi x ci x (bici)) / ni2
• R (ai x di) / ni
• S (bi x ci) / ni

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(Sir Richard) Peto Method

• very similar to Mantel-Haenszel method (same 2x2
  requirement)
• computationally somewhat simpler, especially to
  calculate the confidence interval
• may provide biased results under some
  circumstances in which Mantel-Haenszel would not
• Best applied to RCTs and not observational
  studies
• Petos method can only be used to pool odds
  ratios.

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Peto odds ratio method

• The approximation works well when
• treatment effects are small (odds ratios are
  close to one)
• events are not particularly common
• the trials have similar numbers in experimental
  and control groups

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Peto odds ratio method

• In other situations it has been shown to give
  biased answers.
• As these criteria are not always fulfilled,
  Petos method is not recommended as a default
  approach for meta-analysis.

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Peto Odds Ratio
Mantel-Haenszel Odds Ratio
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Relative Risk
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Risk Difference
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Which measure for dichotomous outcomes?

• Relative or Absolute measures?
• Which one?
• Which test?

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The selection of a summary statistic for use in
meta-analysis depends on

• A summary statistic that gives values that are
  similar for all the trials and subdivisions of
  the population
• The summary statistic must have the mathematical
  properties required for performing a valid
  meta-analysis.
• The summary statistic should be easily understood
  and applied by those using the review.
• No single measure is uniformly best

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Consistency

• Relative effect measures are, on average, more
  consistent than absolute measures.
• On average there is little difference between the
  odds ratio and risk ratio in this regard .
• When the trial aims to reduce the incidence of an
  adverse outcome there is empirical evidence that
  risk ratios of the adverse outcome are more
  consistent than risk ratios of the non-event
• Selecting an effect measure on the basis of what
  is the most consistent in a particular situation
  is not a generally recommended strategy

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Mathematical properties

• The most important mathematical criterion is the
  availability of a reliable variance estimate
• The number needed to treat does not have a simple
  variance estimator and cannot easily be used
  directly in meta-analysis,

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Ease of interpretation

• The odds ratio is the hardest summary statistic
  to understand and to apply in practice
• There are many published examples where authors
  have misinterpreted odds ratios from
  meta-analyses as if they were risk ratios.
• Odds ratios will lead to frequent overestimation
  of the benefits and harms of treatments
• Absolute measures of effect are more easily
  interpreted, although they are less likely to be
  generalisable.

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Outcome
Discrete (event)
Continuous (measured)
Mean Standardized Difference Mean
Difference (MD) (SMD)
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Continuous data

• Weighted mean difference
• When the same outcome has been measured in the
  same way in each trial
• Result is in natural units
• Standardised mean difference
• When the same outcome has been measured in the
  different ways in each trial
• Result needs to be converted into natural units

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Mean Difference (MD)

• Each study used the same scale or variable
• meansummary ?(weighti x meani) / ?weighti
• meani meantx - meancontrol
• weighti 1 / variancei 1 / SDi2
• (use pooled variance)
• 95 CI means /- (1.96 x (variances)0.5)
• variances 1 / ?weighti

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Mean Difference (MD)
number mean standard deviation Experimental ne
se Control nc sc
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Standardized Mean Difference (SMD)

• Each study used a similar but different scale
• dsummary ?(weighti x di) / ?weighti
• dsummary summary estimate of the difference in
  effect sizes
• di effect size (meantx - meancontrol) /
  SDpooled
• weighti 1 / variancei (2 x Ni) / (8 di2)
• (use pooled variance)
• 95 CI ds /- (1.96 x (variances)0.5)
• variances 1 / ?weighti

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Standardized Mean Difference (SMD)
number mean standard deviation Experimental ne
se Control nc sc
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Weighted Mean Difference
Standardized Mean Difference