Design and Analysis of Clinical Study 12. Meta-analysis

Dr. Tuan V. Nguyen

Garvan Institute of Medical Research

Sydney, Australia

Overview

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

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; 327:273-4.

Why Need Meta-analysis? Information Explosion

• 10-fold Increase in Number of Professional Journals

• Psychology Journals: 91 (1951) --> 1,175 (1992)

• • Math Science Journals:

91 (1953) --> 920 (1992)

• Biomedical Journals: 2,300 (1940)--> 23,000 (1993)

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”

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

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)

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; 127:820-826.

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

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)

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

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.

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

Main Outcome Measures

• Mortality / death

Beta-blocker and Congestive Heart Failure

Study(i)

Beta-blocker Placebo

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

Tổng cộng 4879 420 4516 612

Model of Meta-analysis

• For each study– Relative risk

– Variance and standard error of logRR

1 1 1 2 2 2

1 1 1 1log iSE RR

d N d d N d

1

2i

pRR

p

1 1 1 2 2 2

1 1 1 1var log iRR

d N d d N d

log 1.96 loge RR SE RR

– 95% confidence interval of RR

– Weight

1

var logii

WRR

Model of Meta-analysis

• For all studies

– Overall relative risk

loglog

i i

i

W RRRR

W

– Variance and standard error

1var log

i

RRW

1log

i

SE RRW

– 95% confidence interval

log 1.96 logRR SE RR

Meta-analysis: an example

Study p1 p2 RRi logRRi Var[logRR] Wi Wi×log[RRi]

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 0.1730.681 -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

Meta-analysis: an example

95% CI of logRR = -0.38 ± 1.96×0.06 = -0.498, -0.265

95% of RR: exp(-0.498) = 0.61 to exp(-0.265) = 0.77

log108.42

log 0.38284.24

i i

i

W RRwRR

W

1 1log 0.0035

284.24i

Var wRRW

1log 0.0035 0.06

i

SE wRRW

Meta-analysis using R

library(meta) n1 <- c(25.9.194.25.105.320.33.261.133.232.1327.1990.214)

d1 <- c(5.1.23.1.4.53.3.12.6.2.156.145.8)n2 <- c(25.16.189.25.34.321.16.84.145.134.1320.2001.212)

d2 <- c(6.2.21.2.2.67.2.13.11.5.228.217.17)

bb <- data.frame(n1.d1.n2.d2)

res <- metabin(d1.n1.d2.n2.data=bb.sm=”RR”.meth=”I”)

res

plot(res. lwd=3)

Meta-analysis using R

> res RR 95%-CI %W(fixed) %W(random)1 0.8333 [0.2918; 2.3799] 1.26 1.262 0.8889 [0.0930; 8.4951] 0.27 0.273 1.0670 [0.6116; 1.8617] 4.47 4.474 0.5000 [0.0484; 5.1677] 0.25 0.255 0.6476 [0.1240; 3.3814] 0.51 0.516 0.7935 [0.5731; 1.0986] 13.08 13.087 0.7273 [0.1346; 3.9282] 0.49 0.498 0.2971 [0.1410; 0.6258] 2.49 2.499 0.5947 [0.2262; 1.5632] 1.48 1.4810 0.2310 [0.0454; 1.1744] 0.52 0.5211 0.6806 [0.5635; 0.8221] 38.81 38.8112 0.6719 [0.5496; 0.8214] 34.31 34.3113 0.4662 [0.2056; 1.0570] 2.07 2.07Number of trials combined: 13 RR 95%-CI z p.valueFixed effects model 0.6821 [0.6064; 0.7672] -6.3741 < 0.0001Random effects model 0.6821 [0.6064; 0.7672] -6.3741 < 0.0001Quantifying heterogeneity:tau^2 = 0; H = 1 [1; 1.45]; I^2 = 0% [0%; 52.6%]Test of heterogeneity: Q d.f. p.value 11 12 0.5292

Forest Plot

0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00Relative Risk

1

2

3

4

5

6

7

8

9

10

11

12

13

An Inverted Funnel Plot to Detect Publication Bias

An Inverted Funnel Plot to Detect Publication Bias

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

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)

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

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

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 1994;140;290-6.

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

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 & > 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

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; 127:820-826.