Design and Analysis of Clinical Study 12. Meta-analysis

1
Design and Analysis of Clinical Study 12.
Meta-analysis

• Dr. Tuan V. Nguyen
• Garvan Institute of Medical Research
• Sydney, Australia

2
Overview

• What is meta-analysis
• Two types of data
• Statistical procedures

3
Why Meta-analysis/Systematic Reviews?

• . . . the mass of new information makes it
  difficult for practicing physicians to follow the
  literature in all areas that might be relevant to
  their practices. New methods to synthesize and
  present information from widely dispersed
  publications are needed . . . .Jerome
  Kassirer. Clinical trials and meta-analysis
  what do they do for us? N Engl J Med 1992
  327273-4.

4
Why Need Meta-analysis? Information Explosion

• 10-fold Increase in Number of Professional
  Journals
• Psychology Journals 91 (1951) --gt 1,175 (1992)
• Math Science Journals 91 (1953) --gt 920 (1992)
  
• Biomedical Journals 2,300 (1940)--gt 23,000
  (1993)

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Problem Conflicting Information

• Not only is there more information, but . . .
• Not all information is of equal quality
• Information does not necessarily evidence
• There is often conflicting information reports
  Traditional narrative reviews can be very
  impressionistic

6
Problems With Traditional Literature Reviews
Addressed in Meta-analysis

• Selective inclusion of studies, often based on
  the reviewer's own impressionistic view of the
  quality of the study
• Differential subjective weighting of studies in
  the interpretation of a set of findings
• Misleading interpretations of study findings
• Failure to examine characteristics of the studies
  as potential explanations for disparate or
  inconsistent results across studies
• Failure to examine moderating variables in the
  relationship under examination

7
Rationale for Systematic Reviews

• provide summaries of what we know, and do not
  know, that are as free from bias as possible.
  (Chalmers et al 1999)
• research that uses explicit transparent
  methods to synthesise relevant studies, allowing
  others to comment on, criticise or attempt to
  replicate the conclusions reached. Systematic
  reviews follow same set of procedures as any
  individual study, are often reported in the
  same way. . . . (Petrsino et al 1999)

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4 Basic Questions That a SR/MA Tries to Answer

• Are the results of the different studies similar?
  
• To the extent that they are similar, what is the
  best overall estimate of effect?
• How precise and robust is this estimate?
• Can dissimilarities be explained?
• Lau J, Ioannidis JPA, Schmid CH. Quantitative
  Synthesis in Systematic Reviews. Annals of
  Internal Medicine 1997 127820-826.

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What is a Systematic Review?

• Assemble the most complete dataset feasible, with
  involvement of investigators
• Analyse results of eligible studies. Use
  statistical synthesis of data (meta-analysis) if
  appropriate possible
• Perform sensitivity analyses, if appropriate
  possible (including subgroup analyses)
• Prepare a structured report of the review,
  stating aims, describing materials methods,
  reporting results

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Cochrane Library

• Cochrane Library CD ( WWW)
• Cochrane Database of Systematic Reviews (CDSR)
• Database of Abstracts of Reviews of Effectiveness
  (DARE)
• Cochrane Central Register of Controlled Trials
  (CENTRAL)
• Cochrane Review Methodology Database
• Health Technology Assessment DB (HTA)
• NHS Economic/Evaluation Database (NHS EED)

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Search Strategy References Databases

• Studies were identified from
• Cochrane Airways Group's Special Register of
  Controlled Trials comprised of references from
• MEDLINE (1966-2000)
• EMBASE (1980-2000)
• CINAHL (1982-2000)
• hand searched airways-related journals
• PsychINFO
• Reference lists from relevant review articles
  that were identified (ancestry approach

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Search Strategy - Terms

• Congestive Heart Failure OR Heart Failure AND
• clinical trial OR beta blocker
• placebo OR trial OR random OR double-blind OR
  double blind OR single-blind OR single blind OR
  controlled study OR comparative study.

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Identification of Trials

• Potentially relevant studies from literature
  search and hand searches
• Excluded on basis of abstract, e.g., not
  randomised or controlled clinical trials Articles
  selected for full text review
• Excluded after full text review
• Eligible trials

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Main Outcome Measures

• Mortality / death

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Beta-blocker and Congestive Heart Failure
Study (i) Beta-blocker Beta-blocker Placebo Placebo
Study (i) N1 Deaths (d1) N2 Deaths (d2)
1 25 5 25 6
2 9 1 16 2
3 194 23 189 21
4 25 1 25 2
5 105 4 34 2
6 320 53 321 67
7 33 3 16 2
8 261 12 84 13
9 133 6 145 11
10 232 2 134 5
11 1327 156 1320 228
12 1990 145 2001 217
13 214 8 212 17
T?ng c?ng 4879 420 4516 612
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Model of Meta-analysis

• For each study
• Relative risk
• Variance and standard error of logRR

• 95 confidence interval of RR

• Weight

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Model of Meta-analysis

• For all studies
• Overall relative risk

• Variance and standard error

• 95 confidence interval

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Meta-analysis an example
Study p1 p2 RRi logRRi VarlogRR Wi WilogRRi
1 0.200 0.240 0.833 -0.182 0.264 3.79 -0.69
2 0.111 0.125 0.889 -0.118 1.304 0.77 -0.09
3 0.119 0.111 1.067 0.065 0.079 12.61 0.82
4 0.040 0.080 0.500 -0.693 1.415 0.71 -0.49
5 0.038 0.059 0.648 -0.434 0.709 1.41 -0.61
6 0.166 0.209 0.794 -0.231 0.026 38.30 -8.86
7 0.091 0.125 0.727 -0.318 0.729 1.37 -0.44
8 0.046 0.155 0.297 -1.214 0.142 7.03 -8.54
9 0.045 0.076 0.595 -0.520 0.242 4.13 -2.15
10 0.009 0.037 0.231 -1.465 0.688 1.45 -2.13
11 0.118 0.173 0.681 -0.385 0.009 110.78 -42.63
12 0.073 0.108 0.672 -0.398 0.010 96.13 -38.23
13 0.037 0.080 0.466 -0.763 0.174 5.75 -4.39
284.24 -108.42
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Meta-analysis an example

• 95 CI of logRR -0.38 1.960.06
• -0.498, -0.265
• 95 of RR
• exp(-0.498) 0.61 to exp(-0.265) 0.77

20
Meta-analysis using R

• library(meta)
• n1 lt- c(25.9.194.25.105.320.33.261.133.232.1327.19
  90.214)
• d1 lt- c(5.1.23.1.4.53.3.12.6.2.156.145.8)
• n2 lt- c(25.16.189.25.34.321.16.84.145.134.1320.200
  1.212)
• d2 lt- c(6.2.21.2.2.67.2.13.11.5.228.217.17)
• bb lt- data.frame(n1.d1.n2.d2)
• res lt- metabin(d1.n1.d2.n2.databb.smRR.methI
  )
• res
• plot(res. lwd3)

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Meta-analysis using R

• gt res
• RR 95-CI W(fixed) W(random)
• 1 0.8333 0.2918 2.3799 1.26 1.26
• 2 0.8889 0.0930 8.4951 0.27 0.27
• 3 1.0670 0.6116 1.8617 4.47 4.47
• 4 0.5000 0.0484 5.1677 0.25 0.25
• 5 0.6476 0.1240 3.3814 0.51 0.51
• 6 0.7935 0.5731 1.0986 13.08 13.08
• 7 0.7273 0.1346 3.9282 0.49 0.49
• 8 0.2971 0.1410 0.6258 2.49 2.49
• 9 0.5947 0.2262 1.5632 1.48 1.48
• 10 0.2310 0.0454 1.1744 0.52 0.52
• 11 0.6806 0.5635 0.8221 38.81 38.81
• 12 0.6719 0.5496 0.8214 34.31 34.31
• 13 0.4662 0.2056 1.0570 2.07 2.07
• Number of trials combined 13
• RR 95-CI
  z p.value
• Fixed effects model 0.6821 0.6064 0.7672
  -6.3741 lt 0.0001
• Random effects model 0.6821 0.6064 0.7672
  -6.3741 lt 0.0001

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Forest Plot
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An Inverted Funnel Plot to Detect Publication Bias
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An Inverted Funnel Plot to Detect Publication Bias
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Heterogeneity

• Common, to be expected, not the exception
• Should do test for homogeneity, but . . .
  interpret heterogeneity cautiously in spirit of
  exploratory data analysis
• Exploring sources of heterogeneity can lead to
  insights about modification of apparent
  associations by various aspects of
• Study design
• Exposure measurements
• Study populations

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Heterogeneity

• Relations discovered in process of exploring
  heterogeneity may be useful in planning
  carrying out new studies
• Excluding outliers solely on basis of
  disagreement with other studies can lead to
  seriously biased summary estimates (avoid)
• Easier to interpret sources of heterogeneity when
  identified in advance of data analysis (not when
  suggested only by data)

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Fixed Random Effects

• Fixed effects models assume that an intervention
  has a single true effect
• Random effects models assume that an effect may
  vary across studies

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Random Effects

• Assumes sample of studies randomly drawn from
  population of studies
• This is NOT typically true because
• All trials are included
• Trials are systematically (e.g., conveniently)
  sampled and not randomly sampled

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Random Effects

• Primary value of M-A is in search for predictors
  of between-study heterogeneity
• Random-effects summary is last resort only when
  predictors or causes of between-study
  heterogeneity cannot be identified
• Random-effects can conceal fact that summary
  estimate or fitted model is poor summary of the
  data Sander Greenland.
• Am J Epidemiol 1994140290-6.

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Random Effects

• Sometimes needed, but more sensitive to
  publication bias than fixed-effects
• Random effects weights vary less across studies
  than fixed-effects weights
• W 1/v versus w 1/(v t2)
• Leads to reduced variation in weights
• Thus smaller studies given larger relative
  weights when random effects models used
• Thus influenced more strongly by any tendency NOT
  to publish small statistically insignificant
  studies ? biased estimate, spuriously strong
  associations

31
Random Effects

• Fixed effects weights vs. random effects weights
• W 1/v versus w 1/(v t2)
• Identical when there is little or no between
  study variation
• When differ, confidence intervals are larger for
  random-effects than fixed effects
• Smaller studies given larger relative weights in
  random effects models gt influence
• Conversely, influence of larger studies is less
• May result in type II (beta error), e.g., Finding
  no significant difference when one truly exists

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Methodologic Choices Their Implications in
Dealing With Heterogeneous Data in a Meta-analysis
Lau J, Ioannidis JPA, Schmid CH. Quantitative
Synthesis in Systematic Reviews. Annals of
Internal Medicine 1997 127820-826.