Sequential Methods for Random Effects MetaAnalysis

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Sequential Methods for Random Effects
Meta-Analysis
Medical and Pharmaceutical Statistics Research
Unit

• Julian Higgins
• MRC Biostatistics Unit, Cambridge, UK
• Mark Simmonds, Anne Whitehead
• MPS Research Unit, Reading, UK

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Cumulative Meta-Analysis

• Studies occur in time
• Unethical to continue with studies if evidence
  shows treatment to be effective or harmful
• We could conduct a meta-analysis at the end of
  each study
• No further studies when sufficient evidence
  obtained
• Repeated analyses Multiple looks Inflates
  Type I error
• Need 95 certainty that all confidence intervals
  contain truth

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A Formal Sequential Design

• Test for a significant effect with a
  predetermined significance level and power to
  detect a given effect
• Base analysis on score statistic Z and
  Information V
• Stop for benefit if or stop if
• H and Vmax depend on power, , and
• Equivalently stop if

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An Example
90 power, ? 0.05, to detect an effect ?R 0.5
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A Random Effects Sequential Design

• Incorporate heterogeneity in a sequential
  meta-analysis
• Plot new cumulative statistics at look j
• Use a DerSimonian-Laird estimate of heterogeneity
• Must recalculate these values at each look
  

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Problems

• Large heterogeneity may lead to path moving
  backwards
• Few trials poor heterogeneity estimate
• Underestimation of leads to overestimation of
  Z and V
• May stop with incorrect findings

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Bayesian Approach

• Take the likelihood
• Combine with an prior for
  
• Assume that ? is known
  
• Generate the posterior for
• Numerically integrate to obtain posterior mean
• Use this as an estimate of
• Can incorporate genuine prior information or use
  a suitable vague prior

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Approximate Bayesian Approach

• Assume
• Set
• Likelihood Inverse Gamma prior Inverse Gamma
  posterior
• Estimate heterogeneity by the mean of the
  posterior

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Eliciting the Inverse Gamma Prior

• The mean of the prior is
• gives a prior estimate of
  heterogeneity derived from trials
• has with the
  weight of one trial

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A Meta-Analysis of Peptic Ulcer Trials

• 23 trials comparing endoscopic haemostasis to
  control for treatment of peptic ulcers
• Log odds ratio for no bleeding
• Random effects meta analysis gives

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Cumulative Meta-Analysis

• A random effects cumulative meta-analysis
• No correction for multiple looks
• Significant result after 4 trials

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Results from Sequential Meta-Analyses
Perform a sequential meta-analysis with 90
power, ? 1, to detect ?R log 2 0.69
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Graphical Representation
Fixed effect Approx Bayes IG(1.5,0.08)
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Conclusions

• Cumulative meta-analysis has practical and
  ethical benefits
• Standard cumulative meta-analysis does not
  account for multiple looks and may lead to
  spurious findings
• Formal sequential methods should be preferred
• Simple fixed or random effects approaches suffer
  from poor coverage and potentially spurious
  findings
• The Bayesian approaches can reduce these problems
• The approximate Bayes method is simpler to
  implement
• Easy to program in standard software
• Careful choice of priors is needed