Re-analysis of the Cochrane Library data and heterogeneity challenges

Background
Methods
Results
So what?
A re-analysis of the Cochrane Library data
the dangers of unobserved heterogeneity in meta-analyses
Evan Kontopantelis12 David Springate13 David
Reeves13
1NIHR School for Primary Care Research
2Centre for Health Informatics, Institute of Population Health
3Centre for Biostatistics, Institute of Population Health
ISCB35, 25 Aug 2014
Kontopantelis A re-analysis of the Cochrane Library data

Background
Methods
Results
So what?
Outline
1 Background
2 Methods
Data
Analyses
3 Results
Method performance
Cochrane data
4 So what?
Summary

Background
Methods
Results
So what?
Meta-analysis
Synthesising existing evidence to answer clinical questions
Relatively young and dymanic ﬁeld of research
Activity reﬂects the importance of MA and potential to
provide conclusive answers
Individual Patient Data meta-analysis is the best option,
but considerable cost and access to patient data required
When original data unavailable, evidence combined in a
two stage process
retrieving the relevant summary effect statistics
using MA model to calculate the overall effect estimate ˆµ

Background
Methods
Results
So what?
Heterogeneity estimate
or between-study variance estimate ˆτ2
Model selection depends on the heterogeneity estimate
If present usually a random-effects approach is selected
But a ﬁxed-effects model may be chosen for theoretical or
practical reasons
Different approaches for combining study results
Inverse variance
Mantel-Haenszel
Peto

Background
Methods
Results
So what?
Meta-analysis methods
Inverse variance: fixed- or random-effects & continuous or
dichotomous outcome
DerSimonian-Laird, moment based estimator
Also: ML, REML, PL, Biggerstaff-Tweedie,
Follmann-Proschan, Sidik-Jonkman
Mantel-Haenszel: fixed-effect & dichotomous outcome
odds ratio, risk ratio or risk difference
different weighting scheme
low events numbers or small studies
Peto: fixed-effect & dichotomous outcome
Peto odds ratio
small intervention effects or very rare events
if ˆτ2 > 0 only modelled through inverse variance weighting

Background
Methods
Results
So what?
Random-effects (RE) models
Accurate ˆτ2 important performance driver
Large ˆτ2 leads to wider CIs
Zero ˆτ2 reduces all methods to ﬁxed-effect
Three main approaches to estimating:
DerSimonian-Laird (ˆτ2
DL)
Maximum Likelihood (ˆτ2
ML)
Restricted Maximum Likelihood (ˆτ2
REML)
Many methods use one of these but vary in estimating µ
In practice, ˆτ2
DL computed and heterogeneity quantiﬁed and
reported using Cochran’s Q, I2 or H2

Background
Methods
Results
So what?
Random or fixed?
two ‘schools’ of thought
Fixed-effect (FE)
‘what is the average result of trials conducted to date’?
assumption-free
Random-effects (RE)
‘what is the true treatment effect’?
various assumptions
normally distributed trial effects
varying treatment effect across populations although findings
limited since based on observed studies only
more conservative; findings potentially more generalisable
Researchers reassured when ˆτ2 = 0
FE often used when low heterogeneity detected

Background
Methods
Results
So what?
Not always a simple choice between FE and RE
Start
(sort of)
Outcome(s)
continuous
Inverse Variance weighting methods (IV)
Yes
Fixed-effect by
conviction
Fixed-effect IV
model
Yes
No
Detected
heterogeneity
No Random-effects IV model
DL VC ML
REMLPL
Yes
Outcome(s)
dichotomous
No
Maentel-Haenszel methods (MH)
Fixed-effect by
conviction
Fixed-effect MH true
model
Yes
Detected
heterogeneity
No
Combining dichotomous
and continuous outcomes
Transform
dichotomous
outsomes to SMD
Feeling
adventurous?
Yes
Yes!
No!
Rare events
Very rare
events?
Estimate
heterogeneity (τ2
)
No
No
Random-effects MH-IV
hybrid model
Yes
Peto methods (P)
Fixed-effect Peto
true model
Yes
No
Outcome(s)
time-to-event
No
Fixed-effect Peto O-E
true model
Yes
Bayesian?
No
τ2
est
BP
MVa
MVb
Yes
Random-effects
IV model
DL
τ2
estimation
DL DL2 DLb VC
VC2ML REML PL
Non-zero
prior
Yes
τ2
est
B0
No

Background
Methods
Results
So what?
Cochrane Database for Systematic Reviews
Richest resource of meta-analyses in the world
Fifty-four active groups responsible for organising, advising
on and publishing systematic reviews
Authors obliged to use RevMan and submit the data and
analyses ﬁle along with the review, contributing to the
creation of a vast data resource
RevMan offers quite a few ﬁxed-effect choices but only the
DerSimonian-Laird random-effects method has been
implemented to quantify and account for heterogeneity

Background
Methods
Results
So what?
Data
Analyses
‘Real’ Data
Python code to crawl Wiley website for RevMan files
Downloaded 3,845 relevant RevMan files (of 3,984
available in Aug 2012) and imported in Stata
Each file a systematic review
Within each file, various research questions might have
been posed
investigated across various relevant outcomes?
variability in intervention or outcome?

Background
Methods
Results
So what?
Data
Analyses
‘Real’ Data
Cochrane
database
CD000006
Group: Pregnancy and
Childbirth
Review name:
Absorbable suture
materials for primary
repair of episiotomy and
second degree tears
Meta-analysis 1
Synthetic sutures
versus catgut
Meta-analysis 2
Fast-absorbing synthetic versus
standard absorbable synthetic material
Meta-analysis 3
Glycerol impregnated catgut (softgut)
versus chromic catgut
Meta-analysis 4
Monofilament versus standard
polyglycolic sutures
Outcome 1.1
Short-term pain: pain at day 3 or less
(women experiencing any pain)
Subgroup 1.1.1
Standard synthetic; k=9
Subgroup 1.1.2
Fast absorbing; k=1
Outcome 1.9
Dyspareunia - at 3 months
postpartum
Subgroup 1.9.1
Standard synthetic; k=5
Subgroup 1.9.2
Fast absorbing; k=1
Main 1.9.0
k=6
Main 1.1.0
k=10
Outcome 2.1
Short-term pain: at 3 days or less
Main 2.1.0
k=3
Outcome 2.11
Maternal satisfaction: satisfied with
repair at 12 months
Main 2.11.0
k=1
Outcome 3.1
Short-term pain: pain at 3 days or
less
Main 3.1.0
k=1
Outcome 3.8
Dyspareunia at 6 - 12 months
Main 3.8.0
k=1
Outcome 4.1
Short-term pain: mean pain scores at
3 days
Main 4.1.0
k=1
Outcome 4.4
Wound problems at 8 - 12 weeks:
women seeking professional help for
problem with perineal repair
Main 4.4.0
k=1

Background
Methods
Results
So what?
Data
Analyses
Simulated Data
Generated effect size Yi and within study variance
estimates ˆσ2
i for each simulated meta-analysis study
Distribution for ˆσ2
i based on the χ2
1 distribution
For Yi (where Yi = θi + ei)
assumed ei ∼ N(0, ˆσ2
i )
various distributional scenarios for θi : normal, moderate
and extreme skew-normal, uniform, bimodal
three τ2
values to capture low (I2
= 15.1%), medium
(I2
= 34.9%) and large (I2
= 64.1%) heterogeneity
For each distributional assumption and τ2 value, 10,000
meta-analysis cases simulated

Background
Methods
Results
So what?
Data
Analyses
The questions
Investigate the potential bias when assuming ˆτ2 = 0
Compare the performance of τ2
estimators in various
scenarios
Present the distribution of ˆτ2
derived from all
meta-analyses in the Cochrane Library
Present details on the number of meta-analysed studies,
model selection and zero ˆτ2
Assess the sensitivity of results and conclusions using
alternative models

Background
Methods
Results
So what?
Data
Analyses
Between-study variance estimators
frequentist, more or less
DerSimonian-Laird
one-step (ˆτ2
DL)
two-step (ˆτ2
DL2)
non-parametric bootstrap (ˆτ2
DLb)
minimum ˆτ2
DL = 0.01 assumed (ˆτ2
DLi )
Variance components
one-step (ˆτ2
VC)
two-step (ˆτ2
VC2)
Iterative
Maximum likelihood (ˆτ2
ML)
Restricted maximum likelihood (ˆτ2
REML)
Proﬁle likelihood (ˆτ2
PL)

Background
Methods
Results
So what?
Data
Analyses
Between-study variance estimators
Bayesian
Sidik and Jonkman model error variance
crude ratio estimates used as a-priori values (ˆτ2
MVa)
VC estimator used to inform a-priori values with minimum
value of 0.01 (ˆτ2
MVb)
Rukhin
prior between-study variance zero (ˆτ2
B0)
prior between-study variance non-zero and ﬁxed (ˆτ2
BP)

Background
Methods
Results
So what?
Method performance
Cochrane data
Which method?
Performance not affected much by effects’ distribution
Absolute bias
B0 (k ≤ 3) and ML
Coverage
MVa-BP (k ≤ 3) and DLb
Error-interval estimation and detecting
DLb
DLb seems best method overall, especially in detecting
heterogeneity
appears to be a big problem: DL failed to detect high τ2
for
over 50% of small meta-analyses
Bayesian methods did well for very small MAs

Background
Methods
Results
So what?
Method performance
Cochrane data
Meta-analyses numbers
Of the 3,845 ﬁles 2,801 had identiﬁed relevant studies and
contained any data
98,615 analyses extracted 57,397 of which meta-analyses
32,005 were overall meta-analyses
25,392 were subgroup meta-analyses
Estimation of an overall effect
Peto method in 4,340 (7.6%)
Mantel-Haenszel in 33,184 (57.8%)
Inverse variance in 19,873 (34.6%)
random-effects more prevalent in inverse variance methods
and larger meta-analyses
34% of meta-analyses on 2 studies (53% k ≤ 3)!

Background
Methods
Results
So what?
Method performance
Cochrane data
Meta-analyses by Cochrane group
22
Figures
Figure 1: All meta-analyses, including single-study and subgroup meta-analyses
0
2000
4000
6000
8000
10000
12000
14000
PregnancyandChildbirth
Schizophrenia
Neonatal
MenstrualDisordersandSubfertility
DepressionAnxietyandNeurosis
Airways
Hepato-Biliary
FertilityRegulation
Musculoskeletal
Stroke
AcuteRespiratoryInfections
Renal
DementiaandCognitiveImprovement
PainPalliativeandSupportiveCare
InfectiousDiseases
Heart
BoneJointandMuscleTrauma
MetabolicandEndocrineDisorders
GynaecologicalCancer
DevelopmentalPsychosocialandLearning…
ColorectalCancer
Hypertension
Anaesthesia
HaematologicalMalignancies
DrugsandAlcohol
Incontinence
InflammatoryBowelDiseaseandFunctional…
MovementDisorders
NeuromuscularDisease
OralHealth
PeripheralVascularDiseases
BreastCancer
TobaccoAddiction
CysticFibrosisandGeneticDisorders
Back
Skin
HIV/AIDS
Injuries
EyesandVision
Wounds
EarNoseandThroatDisorders
Epilepsy
UpperGastrointestinalandPancreaticDiseases
EffectivePracticeandOrganisationofCare
ProstaticDiseasesandUrologicCancers
MultipleSclerosisandRareDiseasesofthe…
MultipleSclerosis
ConsumersandCommunication
LungCancer
SexuallyTransmittedDiseases
ChildhoodCancer
OccupationalSafetyandHealth
SexuallyTransmittedInfections
PublicHealth
Single Study Fixed-effect model (by choice or necessity) Random-effects model

Background
Methods
Results
So what?
Method performance
Cochrane data
Meta-analyses by method choice
Figure 2: Model selection by number of available studies (and % of random-effects meta-analyses)*
*note that in many cases fixed-effect models were used when heterogeneity was detected
Figure 3: Comparison of zero between-study variance estimates rates in the Cochrane library data and in simulations,
21%
27%
31%
37%
41%
51%
15%
19%
22%
22%
27%
30%
0
2000
4000
6000
8000
10000
12000
2 3 4 5 6-9 10+
Number of Studies in meta-analysis
Peto (FE) Inverse Variance (FE) Inverse Variance (RE) Mantel-Haenszel (FE) Mantel-Haenszel (RE)

Background
Methods
Results
So what?
Method performance
Cochrane data
Comparing Cochrane data with simulated
To assess the validity of a homogeneity assumption we
compared the percentage of zero ˆτ2
DL, in real and
simulated data
Calculated ˆτ2
DL for all Cochrane meta-analyses
Percentage of zero ˆτ2
DL was lower in the real data than in
the low and moderate heterogeneity simulated data
Suggests that mean true between-study variance is higher
than generally assumed but fails to be detected; especially
for small meta-analyses

Background
Methods
Results
So what?
Method performance
Cochrane data
Comparing Cochrane data with simulated
*note that in many case fixed-effect models were used when heterogeneity was detected
Figure 3: Comparison of zero between-study variance estimates rates in the Cochrane library data and in simulations,
using the DerSimonian-Laird method*
*Normal distribution of the effects assumed in the simulations (more extreme distributions produced similar
results).
Peto (FE) Inverse Variance (FE) Inverse Variance (RE) Mantel-Haenszel (FE) Mantel-Haenszel (RE)
0
10
20
30
40
50
60
70
80
90
100
2 3 4 5 10 20
%ofzeroτ^2estimateswithDerSimonian-Laird
Number of studies in meta-analyis
Observed
true I^2=15%
true I^2=35%
true I^2=64%

Background
Methods
Results
So what?
Method performance
Cochrane data
Reanalysing the Cochrane data
We applied all methods to all 57,397 meta-analyses to
assess ˆτ2 distributions and the sensitivity of the results
and conclusions
For simplicity discuss differences between standard
methods and DLb; not a perfect method but one that
performed well overall
As in simulations, DLb identiﬁes more heterogeneous
meta-analyses; ˆτ2
DL = 0 for 50.5% & ˆτ2
DLb = 0 for 31.2%
Distributions of ˆτ2 agree with the hypothesised χ2
1

Background
Methods
Results
So what?
Method performance
Cochrane data
Changes in results and conclusions
e.g. inverse variance analyses
RevMan DerSimonian-Laird
Random-effects method says
heterogeneity is present
Analysis with bootstrap DL rarely
changes conclusions (although
higher heterogeneity estimates
and found in around 20% more
meta-analysis
Conclusions change for:
0.9% of analyses
No
Estimated heterogeneity
‘ignored’ by authors and a
fixed-effect model is chosen
Yes
Analysis with bootstrap DL rarely
changes conclusions
2.4% of analyses
No
Analysis with bootstrap DL makes
a difference in 1 in 5 analyses (as
would analysis with standard DL
but to a smaller extent)
19.1% of analyses
Yes

Background
Methods
Results
So what?
Summary
Findings
Methods often fail to detect τ2 in small MA
Even when ˆτ2 > 0, often ignored
Mean true heterogeneity higher than assumed or
estimated; but standard method fails to detect it
Non-parametric DerSimonian-Laird bootstrap seems best
method overall, especially in detecting heterogeneity
Bayesian estimators MVa (Sidik-Jonkman) and BP
(Ruhkin) performed very well when k ≤ 3
19-21% of statistical conclusions change, when ˆτ2
DL > 0
but ignored

Background
Methods
Results
So what?
Summary
Conclusions
Detecting and accurately estimating ˆτ2 in a small MA is
very difﬁcult; yet for 53% of Cochrane MAs, k ≤ 3
ˆτ2 = 0 assumed to lead to a more reliable meta-analysis
and high ˆτ2 is alarming and potentially prohibitive
Estimates of zero heterogeneity should also be a concern
since heterogeneity is likely present but undetected
Bootstrapped DL leads to a small improvement but
problem largely remains, especially for very small MAs
Caution against ignoring heterogeneity when detected
For full generalisability, random-effects essential?

Appendix Thank you!
A Re-Analysis of the Cochrane Library Data: The Dangers
of Unobserved Heterogeneity in Meta-Analyses
Evangelos Kontopantelis1,2,3
*, David A. Springate1,2
, David Reeves1,2
1 Centre for Primary Care, NIHR School for Primary Care Research, Institute of Population Health, University of Manchester, Manchester, United Kingdom, 2 Centre for
Biostatistics, Institute of Population Health, University of Manchester, Manchester, United Kingdom, 3 Centre for Health Informatics, Institute of Population Health,
University of Manchester, Manchester, United Kingdom
Abstract
Background: Heterogeneity has a key role in meta-analysis methods and can greatly affect conclusions. However, true levels
of heterogeneity are unknown and often researchers assume homogeneity. We aim to: a) investigate the prevalence of
unobserved heterogeneity and the validity of the assumption of homogeneity; b) assess the performance of various meta-
analysis methods; c) apply the findings to published meta-analyses.
Methods and Findings: We accessed 57,397 meta-analyses, available in the Cochrane Library in August 2012. Using
simulated data we assessed the performance of various meta-analysis methods in different scenarios. The prevalence of a
zero heterogeneity estimate in the simulated scenarios was compared with that in the Cochrane data, to estimate the
degree of unobserved heterogeneity in the latter. We re-analysed all meta-analyses using all methods and assessed the
sensitivity of the statistical conclusions. Levels of unobserved heterogeneity in the Cochrane data appeared to be high,
especially for small meta-analyses. A bootstrapped version of the DerSimonian-Laird approach performed best in both
detecting heterogeneity and in returning more accurate overall effect estimates. Re-analysing all meta-analyses with this
new method we found that in cases where heterogeneity had originally been detected but ignored, 17–20% of the
statistical conclusions changed. Rates were much lower where the original analysis did not detect heterogeneity or took it
into account, between 1% and 3%.
Conclusions: When evidence for heterogeneity is lacking, standard practice is to assume homogeneity and apply a simpler
fixed-effect meta-analysis. We find that assuming homogeneity often results in a misleading analysis, since heterogeneity is
very likely present but undetected. Our new method represents a small improvement but the problem largely remains,
especially for very small meta-analyses. One solution is to test the sensitivity of the meta-analysis conclusions to assumed
moderate and large degrees of heterogeneity. Equally, whenever heterogeneity is detected, it should not be ignored.
Citation: Kontopantelis E, Springate DA, Reeves D (2013) A Re-Analysis of the Cochrane Library Data: The Dangers of Unobserved Heterogeneity in Meta-
Analyses. PLoS ONE 8(7): e69930. doi:10.1371/journal.pone.0069930
Editor: Tim Friede, University Medical Center Go¨ttingen, Germany
Received February 20, 2013; Accepted June 13, 2013; Published July 26, 2013
Copyright: ß 2013 Kontopantelis et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: EK was partly supported by a National Institute for Health Research (NIHR) School for Primary Care Research fellowship in primary health care. The
funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. No additional external funding received for
this study.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: e.kontopantelis@manchester.ac.uk
Introduction
Meta-analysis (MA), the methodologies of synthesising existing
evidence to answer a clinical or other research question, is a
relatively young and dynamic area of research. The furore of
methodological activity reflects the clinical importance of meta-
analysis and its potential to provide conclusive answers, rather
When the original data are unavailable, researchers have to
combine the evidence in a two stage process, retrieving the
relevant summary effects statistics from publications and using a
suitable meta-analysis model to calculate an overall effect estimate
^mm. Model selection depends on the estimated heterogeneity, or
between-study variance, and its presence usually leads to the
This project was supported by the School for Primary Care Research
which is funded by the National Institute for Health Research (NIHR).
The views expressed are those of the author(s) and not necessarily
those of the NHS, the NIHR or the Department of Health.
Communication of this work has been supported by the MRC funded
HeRC, a member of the Farr Institute for Health Informatics
Comments, suggestions: e.kontopantelis@manchester.ac.uk

Re-analysis of the Cochrane Library data and heterogeneity challenges

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