Re-analysis of the Cochrane Library data and heterogeneity challenges

BackgroundMethodsResults

So what?

A re-analysis of the Cochrane Library datathe dangers of unobserved heterogeneity in meta-analyses

Evan Kontopantelis12 David Springate13 DavidReeves13

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


So what?

Outline

1 Background

2 MethodsDataAnalyses

3 ResultsMethod performanceCochrane data

4 So what?Summary



So what?

Meta-analysis

Synthesising existing evidence to answer clinical questionsRelatively young and dymanic field of researchActivity reflects the importance of MA and potential toprovide conclusive answersIndividual Patient Data meta-analysis is the best option,but considerable cost and access to patient data requiredWhen original data unavailable, evidence combined in atwo stage process

retrieving the relevant summary effect statisticsusing MA model to calculate the overall effect estimate µ



So what?

Heterogeneity estimateor between-study variance estimate τ 2

Model selection depends on the heterogeneity estimateIf present usually a random-effects approach is selectedBut a fixed-effects model may be chosen for theoretical orpractical reasonsDifferent approaches for combining study results

Inverse varianceMantel-HaenszelPeto



So what?

Meta-analysis methods

Inverse variance: fixed- or random-effects & continuous ordichotomous outcome

DerSimonian-Laird, moment based estimatorAlso: ML, REML, PL, Biggerstaff-Tweedie,Follmann-Proschan, Sidik-Jonkman

Mantel-Haenszel: fixed-effect & dichotomous outcomeodds ratio, risk ratio or risk differencedifferent weighting schemelow events numbers or small studies

Peto: fixed-effect & dichotomous outcomePeto odds ratiosmall intervention effects or very rare events

if τ2 > 0 only modelled through inverse variance weighting



So what?

Random-effects (RE) models

Accurate τ2 important performance driverLarge τ2 leads to wider CIsZero τ2 reduces all methods to fixed-effectThree main approaches to estimating:

DerSimonian-Laird (τ2DL)

Maximum Likelihood (τ2ML)

Restricted Maximum Likelihood (τ2REML)

Many methods use one of these but vary in estimating µIn practice, τ2

DL computed and heterogeneity quantified andreported using Cochran’s Q, I2 or H2



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 effectsvarying treatment effect across populations although findingslimited since based on observed studies only

more conservative; findings potentially more generalisable

Researchers reassured when τ2 = 0FE often used when low heterogeneity detected



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) dichotomousNo

Maentel-Haenszel methods (MH)

Fixed-effect by conviction

Fixed-effect MH true model

YesDetected

heterogeneity

NoCombining 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

YesNo

Outcome(s) time-to-eventNo

Fixed-effect Peto O-E true model

Yes

Bayesian?

No

τ2 est

BP

MVaMVb

Yes

Random-effects IV model

DL

τ2 estimation

DL DL2 DLb VC

VC2ML REML PL

Non-zero prior

Yes

τ2 est

B0

No



So what?

Cochrane Database for Systematic Reviews

Richest resource of meta-analyses in the worldFifty-four active groups responsible for organising, advisingon and publishing systematic reviewsAuthors obliged to use RevMan and submit the data andanalyses file along with the review, contributing to thecreation of a vast data resourceRevMan offers quite a few fixed-effect choices but only theDerSimonian-Laird random-effects method has beenimplemented to quantify and account for heterogeneity



So what?

DataAnalyses

‘Real’ DataCochrane Database for Systematic Reviews

Python code to crawl Wiley website for RevMan filesDownloaded 3,845 relevant RevMan files (of 3,984available in Aug 2012) and imported in StataEach file a systematic reviewWithin each file, various research questions might havebeen posed

investigated across various relevant outcomes?variability in intervention or outcome?



So what?

DataAnalyses

‘Real’ DataCochrane Database for Systematic Reviews

Cochrane database

CD000006

Group: Pregnancy and Childbirth

Review name: Absorbable suture

materials for primary repair of episiotomy and

second degree tears

Meta-analysis 1Synthetic sutures

versus catgut

Meta-analysis 2Fast-absorbing synthetic versus

standard absorbable synthetic material

Meta-analysis 3Glycerol impregnated catgut (softgut)

versus chromic catgut

Meta-analysis 4Monofilament versus standard

polyglycolic sutures

Outcome 1.1Short-term pain: pain at day 3 or less

(women experiencing any pain)

Subgroup 1.1.1Standard synthetic; k=9

Subgroup 1.1.2Fast absorbing; k=1

Outcome 1.9Dyspareunia - at 3 months

postpartumSubgroup 1.9.1

Standard synthetic; k=5

Subgroup 1.9.2Fast absorbing; k=1

Main 1.9.0k=6

Main 1.1.0k=10

Outcome 2.1Short-term pain: at 3 days or less

Main 2.1.0k=3

Outcome 2.11Maternal satisfaction: satisfied with

repair at 12 months

Main 2.11.0k=1

Outcome 3.1Short-term pain: pain at 3 days or

less

Main 3.1.0k=1

Outcome 3.8Dyspareunia at 6 - 12 months

Main 3.8.0k=1

Outcome 4.1Short-term pain: mean pain scores at

3 days

Main 4.1.0k=1

Outcome 4.4Wound problems at 8 - 12 weeks:

women seeking professional help for problem with perineal repair

Main 4.4.0k=1



So what?

DataAnalyses

Simulated Data

Generated effect size Yi and within study varianceestimates σ2

i for each simulated meta-analysis studyDistribution for σ2

i based on the χ21 distribution

For Yi (where Yi = θi + ei )assumed ei ∼ N(0, σ2

i )various distributional scenarios for θi : normal, moderateand extreme skew-normal, uniform, bimodalthree 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, 10,000meta-analysis cases simulated



So what?

DataAnalyses

The questions

Investigate the potential bias when assuming τ2 = 0Compare the performance of τ2 estimators in variousscenariosPresent the distribution of τ2 derived from allmeta-analyses in the Cochrane LibraryPresent details on the number of meta-analysed studies,model selection and zero τ2

Assess the sensitivity of results and conclusions usingalternative models



So what?

DataAnalyses

Between-study variance estimatorsfrequentist, more or less

DerSimonian-Lairdone-step (τ2

DL)two-step (τ2

DL2)non-parametric bootstrap (τ2

DLb)minimum τ2

DL = 0.01 assumed (τ2DLi )

Variance componentsone-step (τ2

VC)two-step (τ2

VC2)Iterative

Maximum likelihood (τ2ML)

Restricted maximum likelihood (τ2REML)

Profile likelihood (τ2PL)



So what?

DataAnalyses

Between-study variance estimatorsBayesian

Sidik and Jonkman model error variancecrude ratio estimates used as a-priori values (τ2

MVa)VC estimator used to inform a-priori values with minimumvalue of 0.01 (τ2

MVb)Rukhin

prior between-study variance zero (τ2B0)

prior between-study variance non-zero and fixed (τ2BP)



So what?

Method performanceCochrane data

Which method?

Performance not affected much by effects’ distributionAbsolute bias

B0 (k ≤ 3) and MLCoverage

MVa-BP (k ≤ 3) and DLbError-interval estimation and detecting

DLbDLb seems best method overall, especially in detectingheterogeneity

appears to be a big problem: DL failed to detect high τ2 forover 50% of small meta-analyses

Bayesian methods did well for very small MAs



So what?


Meta-analyses numbers

Of the 3,845 files 2,801 had identified relevant studies andcontained any data98,615 analyses extracted 57,397 of which meta-analyses

32,005 were overall meta-analyses25,392 were subgroup meta-analyses

Estimation of an overall effectPeto 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 methodsand larger meta-analyses

34% of meta-analyses on 2 studies (53% k ≤ 3)!



So what?


Meta-analyses by Cochrane group

22

Figures Figure 1: All meta-analyses, including single-study and subgroup meta-analyses

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Single Study Fixed-effect model (by choice or necessity) Random-effects model



So what?


Meta-analyses by method choice

23

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, using the DerSimonian-Laird method*

*Normal distribution of the effects assumed in the simulations (more extreme distributions produced similar results).

21%

27%

31% 37%

41% 51%

15%

19%

22%

22%

27% 30%

0

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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)

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Number of studies in meta-analyis

Observed

true τ^2=0.01

true τ^2=0.03

true τ^2=0.10



So what?


Comparing Cochrane data with simulated

To assess the validity of a homogeneity assumption wecompared the percentage of zero τ2

DL, in real andsimulated dataCalculated τ2

DL for all Cochrane meta-analysesPercentage of zero τ2

DL was lower in the real data than inthe low and moderate heterogeneity simulated dataSuggests that mean true between-study variance is higherthan generally assumed but fails to be detected; especiallyfor small meta-analyses



So what?


Comparing Cochrane data with simulated

23

Figure 2: Model selection by number of available studies (and % of random-effects meta-analyses)*

*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).

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)

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Number of studies in meta-analyis

Observed

true I^2=15%

true I^2=35%

true I^2=64%



So what?


Reanalysing the Cochrane data

We applied all methods to all 57,397 meta-analyses toassess τ2 distributions and the sensitivity of the resultsand conclusionsFor simplicity discuss differences between standardmethods and DLb; not a perfect method but one thatperformed well overallAs in simulations, DLb identifies more heterogeneousmeta-analyses; τ2

DL = 0 for 50.5% & τ2DLb = 0 for 31.2%

Distributions of τ2 agree with the hypothesised χ21



So what?


Changes in results and conclusionse.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 chosenYes

Analysis with bootstrap DL rarely changes conclusions


No

Analysis with bootstrap DL makes a difference in 1 in 5 analyses (as would analysis with standard DL

but to a smaller extent)


Yes



So what?

Summary

Findings

Methods often fail to detect τ2 in small MAEven when τ2 > 0, often ignoredMean true heterogeneity higher than assumed orestimated; but standard method fails to detect itNon-parametric DerSimonian-Laird bootstrap seems bestmethod overall, especially in detecting heterogeneityBayesian estimators MVa (Sidik-Jonkman) and BP(Ruhkin) performed very well when k ≤ 319-21% of statistical conclusions change, when τ2

DL > 0but ignored



So what?

Summary

Conclusions

Detecting and accurately estimating τ2 in a small MA isvery difficult; yet for 53% of Cochrane MAs, k ≤ 3τ2 = 0 assumed to lead to a more reliable meta-analysisand high τ2 is alarming and potentially prohibitiveEstimates of zero heterogeneity should also be a concernsince heterogeneity is likely present but undetectedBootstrapped DL leads to a small improvement butproblem largely remains, especially for very small MAsCaution against ignoring heterogeneity when detectedFor full generalisability, random-effects essential?


Appendix Thank you!

A Re-Analysis of the Cochrane Library Data: The Dangersof Unobserved Heterogeneity in Meta-AnalysesEvangelos 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 levelsof heterogeneity are unknown and often researchers assume homogeneity. We aim to: a) investigate the prevalence ofunobserved 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. Usingsimulated data we assessed the performance of various meta-analysis methods in different scenarios. The prevalence of azero heterogeneity estimate in the simulated scenarios was compared with that in the Cochrane data, to estimate thedegree of unobserved heterogeneity in the latter. We re-analysed all meta-analyses using all methods and assessed thesensitivity 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 bothdetecting heterogeneity and in returning more accurate overall effect estimates. Re-analysing all meta-analyses with thisnew method we found that in cases where heterogeneity had originally been detected but ignored, 17–20% of thestatistical conclusions changed. Rates were much lower where the original analysis did not detect heterogeneity or took itinto account, between 1% and 3%.

Conclusions: When evidence for heterogeneity is lacking, standard practice is to assume homogeneity and apply a simplerfixed-effect meta-analysis. We find that assuming homogeneity often results in a misleading analysis, since heterogeneity isvery 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 assumedmoderate 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 Gottingen, Germany

Received February 20, 2013; Accepted June 13, 2013; Published July 26, 2013

Copyright: � 2013 Kontopantelis et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted 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. Thefunders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. No additional external funding received forthis study.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail: [email protected]

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

than incremental knowledge contributions, much more cheaply

than a new large Randomised Clinical Trial (RCT).

The best analysis approach is an Individual Patient Data (IPD)

meta-analysis, which requires access to patient level data and

considerably more effort (to obtain the datasets mainly). However,

with IPD data, clinical and methodological heterogeneity,

arguably the biggest concern for meta-analysts, can be addressed

through patient-level covariate controlling or subgroup analyses

when covariate data are not available across all studies.

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

adoption of a random-effects (RE) model. The alternative, the

fixed-effects model (FE), is used when meta-analysts, for theoretical

or practical reasons, decide not to adjust for heterogeneity, or have

assumed or estimated the between-study variability to be zero.

Different approaches exist for combining individual study results

into an overall estimate of effect under the fixed- or random-effects

assumptions: inverse variance, Mantel-Haenszel and Peto [1].

Inverse variance approaches are the most flexible and are

suitable for continuous or dichotomous data through a fixed-effect

or one of numerous random-effects methods. The DerSimonian

and Laird [2] method (DL), a moment-based estimator, is the

PLOS ONE | www.plosone.org 1 July 2013 | Volume 8 | Issue 7 | e69930

This project was supported by the School for Primary Care Researchwhich is funded by the National Institute for Health Research (NIHR).The views expressed are those of the author(s) and not necessarilythose of the NHS, the NIHR or the Department of Health.

Communication of this work has been supported by the MRC fundedHeRC, a member of the Farr Institute for Health Informatics

Comments, suggestions: [email protected]


Science

Re-analysis of the Cochrane Library data and heterogeneity challenges