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Design and Analysis of Clinical Study 12. Meta-analysis

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Title: 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)

5
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)

8
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.

9
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

10
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)

11
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

12
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.

13
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

14
Main Outcome Measures
  • Mortality / death

15
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
16
Model of Meta-analysis
  • For each study
  • Relative risk
  • Variance and standard error of logRR
  • 95 confidence interval of RR
  • Weight

17
Model of Meta-analysis
  • For all studies
  • Overall relative risk
  • Variance and standard error
  • 95 confidence interval

18
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
19
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)

21
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

22
Forest Plot
23
An Inverted Funnel Plot to Detect Publication Bias
24
An Inverted Funnel Plot to Detect Publication Bias
25
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

26
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)

27
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

28
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

29
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.

30
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

32
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.
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