pooling systematic reviews of systematic reviews: a bayesian panoramic meta-analysis

Research Article

Received 4 May 2010, Accepted 1 June 2011 Published online 3 October 2011 in Wiley Online Library

(wileyonlinelibrary.com) DOI: 10.1002/sim.4372

Pooling systematic reviews of systematicreviews: a Bayesian panoramicmeta-analysisKarla Hemming,a*† Russell James Bowaterb andRichard J. Lilforda

Systematic reviews and meta-analyses usually synthesise evidence from studies reporting outcomes from par-ticular interventions in specific diseases. For example, a meta-analysis of prophylactic antibiotics (intervention)in elective arterial reconstruction (disease) for rates of wound infection (outcome). However, because systematicreviews and meta-analyses are so widespread, a body of evidence often exists around specific intervention effectson particular outcomes over a range of diseases. So for example, a multitude of independent meta-analyses haveevaluated rates of wound infection with and without the use of prophylactic antibiotics over multiple surgerytypes. A systematic review of systematic reviews is a means of synthesising evidence for the same interven-tion over multiple disease types. We propose a panoramic meta-analysis as a means of pooling effect estimatesover systematic reviews of systematic reviews. We explore several methods ranging from a simple two-stepapproach, to a meta-regression or mixed effects approach, where variation between diseases are modelled asfixed covariate effects and between-study variation by random effects, and to a three-level hierarchical model inwhich exchangeability is assumed, which allows both a between-disease component of variance and a between-study (within disease) component of variance. In the surgery example, we pool 18 meta-analyses (each includingbetween 4 and 26 studies) of prophylactic antibiotics reporting rates of wound infection from 18 different surgerysites to obtain a single pooled estimate of effect and estimates of between-disease, within-disease and within-studyvariability. Copyright © 2011 John Wiley & Sons, Ltd.

Keywords: meta-analysis; random effects models; systematic reviews; panoramic meta-analysis

1. Introduction

Meta-analysis pools estimates of effects across related studies [1, 2]. For example, a meta-analysis ofRCTs of prophylactic antibiotics in elective caesarean sections would pool trial estimates of treatmentefficacy (i.e. relative risks of wound infection). In a fixed effects approach, it is assumed that there existsa single or common treatment effect, such that if all studies were infinitely large, all would obtain thesame results [1]. This assumption of no statistical heterogeneity is often a priori unlikely, and so randomeffects models assume instead that individual studies are estimating different treatment effects, but thesedifferent treatment effects are distributed around some central value [3].

The drive towards evidence-based medicine has resulted in a huge body of systematic reviews andmeta-analyses. For example, the Cochrane database contains more than 10 systematic reviews on theefficacy of a range of antiepileptic drugs on seizure frequencies in refractory epilepsy, and more than20 systematic reviews have been published on the efficacy of prophylactic antibiotics on rates ofpost-operative wound infection [4]. When considering the efficacy of antiepileptic drugs on seizure fre-quency both because of the diversity of the antiepileptic drugs (ranging from gamma-aminobutyric acidinhibitors to barbiturates) and because of the propensity for different types of epilepsy to respond dif-ferently to different drugs, the question is not so much on should antiepileptic drugs be used (outcomes

aUnit of Public Health, Epidemiology and Biostatistics, University of Birmingham, Birmingham, UKbDepartment of Mathematics, Universidad Autónoma Metropolitana,Unidad Iztapalapa, Mexico City, Mexico*Correspondence to: Karla Hemming, Unit of Public Health, Epidemiology and Biostatistics, University of Birmingham,Birmingham, UK.

†E-mail: [email protected]

Copyright © 2011 John Wiley & Sons, Ltd. Statist. Med. 2012, 31 201–216

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K. HEMMING, R. J. BOWATER AND R. J. LILFORD

are so debilitating that the answer is almost certainly yes, except in very mild cases) but rather on whichantiepileptic drug performs best in a particular type of epilepsy. Recent developments in meta-analysesof multiple treatment comparisons in theory now allow investigation of such issues [5, 6].

However, the primary question of interest in the surgery example is somewhat different. Here, interestis in the question ‘should prophylactic antibiotics be used as a preventative measure to reduce post oper-ative wound infection or not?’ The question of which antibiotic should be used is of lesser interest, oftenbeing decided by biological reasoning, although trials do sometimes compare efficacy of differing antibi-otics, and so this may be of primary interest occasionally. So, although not being specifically focusedon the type of antibiotic, these reviews focus on the type of disease: individual reviews are publishedwith evidence synthesised from different disease (or surgery) types, evaluating the same or very simi-lar intervention. So for example, systematic reviews of the effects of prophylactic antibiotics on ratesof post-operative wound infection exist independently for a multitude of surgery types ranging fromcomplicated appendicitis, abdominal hysterectomy, to hernia repair, to name but a few [4]. Similarly, amultitude of systematic reviews and meta-analyses exist on the efficacy of adjuvant chemotherapy over amultitude of different cancers: within each particular cancer type, the question of interest being whetheradjuvant therapy improves outcomes (submitted for publication); the efficacy of cognitive behaviourtherapy for different psychological disorders [7]; and drug adverse outcomes across therapeutic areas.

When the intervention is unequivocally dependent on the type of disease, independent trials arerequired to assess efficacy over the range of diseases, and ultimately, it will be necessary to synthe-sise evidence independently within the different disease types. For example, the Scottish IntercollegiateGuidelines Network recommended prophylactic antibiotics be used in those surgeries (i.e. disease types)for which systematic reviews have demonstrated conclusive evidence that the intervention is effectiveat reducing post-operative wound infection [8]. However, where the overwhelming evidence begins tosuggest that the intervention works across the range of diseases, it may be of medical interest to considerwhether the intervention should be considered efficacious over all disease types, unless demonstratedotherwise. Indeed in the surgery example, a subsequent systematic review of systematic reviews of pro-phylactic antibiotics, synthesising evidence over 21 surgery sites, concluded that because in each of the21 reviews there existed evidence to suggest that prophylactic antibiotics was efficacious, prophylacticantibiotics should be used in all surgery types until evidence to the contrary existed [4].

The concept of performing a systematic review of systematic reviews is a novel concept and possi-bly controversial. It might be argued that different disease types (or types of surgery as in the previousexample) are so biologically different that they should be treated independently and important decisions,such as whether an intervention should be recommended or is beneficial, should be dependent upon thedisease type. However, it is also very reasonable that although clinicians might require evidence fromwithin their speciality, they may also wish to consider the question of interest within the broader frame-work across all specialities and hence, implicitly at least, consider efficacy across diseases. Indeed, theUK body, the National Institute for Health and Clinical Excellence already summarised treatment effectsacross disease types and have for example considered the question of whether staples or sutures improvelocalised post-operative infection rates across a multitude of surgery types [9].

Although it is clearly the case that a particular intervention could not be expected to have a com-mon or single effect over different disease types (i.e. that a fixed effects meta-analysis would not beappropriate), it might be reasonable to explore heterogeneity between diseases and perhaps synthesiseevidence using random effects models in which not only treatment effects vary because of the individ-ual study but also because of the disease type. We therefore propose to extend the usual random effectsmeta-analysis model in which variation between treatment effects is composed both of a within-studyand between-study variation components (i.e. a two-level hierarchal model) to a random effects meta-analysis in which variation in treatment estimates is composed of a within-study component of variance,a between-study component of variance (within disease) and a between-disease component (i.e. a three-level hierarchal model). To relax the strong exchangeability assumption of such an approach, we alsoconsider a meta-regression analysis, which can also be viewed as a mixed effects approach in whichrandom effects model between-study variability, but fixed covariate effects model between-disease vari-ability. We call such pooling of effect estimates across different reviews a panoramic meta-analysis. Weuse Bayesian methods with uninformative priors throughout. As the models proposed are hierarchical,they could be fitted using frequentist methods, although because of the uninformative priors used, resultsshould not be very sensitive to either method.

We illustrate the approach using a previously undertaken systematic review of systematic reviews ofprophylactic antibiotics over different surgery types [4]. Previous analysis had consisted of a graphical

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display of review results. We augment this by analysing the data using the proposed panoramic meta-analysis model, attributing variances to within study, within disease and between disease, and by con-sidering the different surgery types as fixed covariate effects to obtain a pooled estimate of treatmentefficacy.

2. Meta-analysis synthesising evidence across studies within a particular disease:independent analysis

Bayesian approaches to random effects meta-analysis have been previously described and are outlinedin the succeeding text for completeness for both continuous and binary outcome data [3, 10]. Thesemeta-analyses essentially consist of two-level hierarchical models.

Where each trial (i D 1; : : : ; N ) reports a continuous outcome measure of treatment efficacy, wi withvariance �2i and ıi is the actual but unknown measure of treatment efficacy, then the combined treatmentefficacy measure using random effects modelling allowing for between-study variation is ı, such that

wi �N�ıi ; �

2i

�

ıi �NŒı; �2� (1)

where ı is the pooled treatment effect (for example, if wi are log odds ratios, then the pooled odds ratiois ORD exp.ı/), �2 is the between-study variance, and �2i is the within-study variance (for study i).

For trials reporting binary outcomes (1 for success and 0 for failure), we suppose there are niT obser-vations (i.e. patients) in study i randomised to the treatment arm and niC observations on the controlarm; and where riT and riC positive responses are observed on the treatment and control arms, respec-tively. Then, let �iT and �iC be the true risk of event in study i for the treatment and control armsrespectively, such that

riC � Bin.niC ; �iC /

riT � Bin.niT ; �iT / (2)

Then, the pooled estimate of treatment efficacy is ı, where

logit�iC D �ilogit�iT D �i C ıi

ıi �N.ı; �2/ (3)

Here, ı represents the pooled treatment effect on the logit scale, and again �2 is the between-studyvariation.

3. Panoramic meta-analysis: synthesising evidence across studies andacross diseases

Suppose a systematic review of systematic reviews identifies k D 1; : : : ; K systematic reviews, whereeach review k identifies i D 1; : : : ; Nk trials in which treatment and control are compared. For trialsreporting continuous outcomes, suppose trial i within systematic review k reports continuous out-come (again some measure of treatment efficacy) wik with variance �2

ik, where the actual but unknown

measure of treatment efficacy is ıik , such that

wik �N�ıik; �

2ik

�(4)

For trials reporting binary outcomes, with nikC and nikT observations on the treatment and control armsin systematic review k, study i , where rikC and rikT successes are observed; let �ikT and �ikC be thetrue risk of event in review k, study i under treatment and control arms respectively, such that

rikC � Bin.nikC ; �ikC / (5)

rikT � Bin.nikT ; �ikT / (6)


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We consider three approaches for pooling evidence across systematic reviews. The two-step analysisis an intuitive approach, which consists of a meta-analysis of the pooled estimates from each of the Ksystematic reviews and is outlined for the continuous case only. The three-level hierarchical approach isa natural extension to the random effects meta-analysis. Both the two-step analysis and the three-levelhierarchical model assume exchangeability of disease types. To relax this assumption, we consider amixed effects analysis in which random study variation is incorporated as random effects, but the effectof different diseases are modelled as fixed covariate effects. We also consider effects of review levelcovariates (in the example considered, this consists of whether the surgery type is classified as clean ornot clean).

3.1. Two-step analysis

The two-step analysis is a natural approach to the synthesis of evidence over reviews as it follows froma very practical point of view to the way in which a conventional meta-analysis is tackled: obtain esti-mates of treatment efficacy and measures of precision from primary sources (in a regular meta-analysis,the primary sources are the trials; in the panoramic meta-analysis, the primary sources are the reviews)and then synthesise via a random effects model. The two-step analysis therefore consists of performingKC 1 conventional (but Bayesian) meta-analyses. In the first step, each of theK systematic reviews areanalyzed independently (as outlined in Section 2) to obtain a pooled treatment effect parameter (withvariance) for each of the K reviews, each estimated via a random effects meta-analysis (hence, K meta-analyses). In the second step, these K-pooled estimates (with variances) from each of the systematicreviews are combined into an overall (over all reviews) pooled estimate again using a random effectsapproach (hence, an additional meta-analysis resulting in a total of K C 1 meta-analyses).

3.1.1. Step 1. In step 1, the study estimates are pooled independently within reviews. So, essentiallyeach of theK systematic reviews are analysed independently using random effects models. Fixing k, weagain let wik denote the treatment estimate from study i with associated variance �2

ik, where ıik is the

actual but unknown measure of treatment effect, such that

wik �N�ıik; �

2ik

�(7)

Using a random effects approach and pooling across the studies within review k, allowing for bothbetween-study and within-study variations, such that

ıik �N�ık; �

2k

�(8)

where ık is the pooled (within-review k) treatment effect and �2k

is the between-study variance for

review k. Suppose further that these models have been fitted and Oık obtained as estimates for the pooledtreatment effect for review k, along with an estimate of variance of the estimate, which we call var. Oık/.

3.1.2. Step 2. In the second step, the pooled estimates of treatment effects (over studies but withinreviews) from the first step are pooled over reviews using a random effects meta-analysis. So, taking theK-pooled treatment effect estimates as Oık with associated variance var. Oık/, these are pooled across thereviews:

Oık �Nhık; var

�Oık

�i

ık �NŒı; �2� (9)

where ık is the unobserved but actual treatment effect within review k; ı is the pooled (over studies andreviews) treatment effect; and �2 is the between review variance.

Whereas the two-step approach is very intuitive, this model (like the three-level hierarchical model inthe following text) makes strong exchangeability assumptions. Exchangeability assumptions are inherentin any conventional random effects meta-analysis, assuming treatment effects are centred around a singlecommon value for all studies; in the panoramic meta-analysis, the assumption becomes even stronger,assuming treatment effects centred around a single common value across all studies and all reviews.

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3.2. Three-level hierarchical model

The three-level hierarchical model is an extension to the conventional two-level hierarchical meta-analysis model in which variations in efficacy are attributable to within-study, between-study (within-review) and between-review variances. Although being a natural extension of the conventional meta-analysis approach, this model does assume exchangeability across reviews, which will not always beappropriate.

For trials reporting continuous outcomes, a pooled estimate of treatment efficacy, allowing for bothbetween-study and within-study variations, is ı, where


2k

�

ık �NŒı; �2� (10)

where ıik is the observed treatment effect in trial i within review k; ık is the pooled treatment effectwithin review k; �2

kis the between-study variance within review k; ı is the pooled (over studies and

reviews) treatment effect; and �2 is the between-review variance.For trials reporting binary outcomes, a pooled estimate of treatment effect, allowing for both

between-review and within-review variations, is ı, where

logit�ikC D �iklogit�ikT D �ik C ıik (11)


2k

�

ık �N.ı; �2/ (12)

where again ı represents the pooled treatment effect over reviews and studies (on the logit scale), ık isthe pooled treatment effect with review k, �2

kthe between-study variation within review k and �2 is the

between review variation.

3.3. The meta-regression approach: mixed effects

In the meta-regression approach, the data are modelled as a two-level hierarchical model, allowingfor between-study variation (within review) and for variation between disease types by way of fixedcovariate effect (hence, a mixed effects model) per review using an extension of the conventional meta-regression model. In this way, it is assumed that within reviews, the individual studies are estimatingdifferent treatment effects, which are distributed around some central value, but these central values dif-fer for each of the reviews with a separate parameter estimating each of these central values. Althoughthis method relaxes the exchangeability of the three-level hierarchical approach (mentioned earlier) byallowing for partial exchangeability only (for within-review variation), the model does not provide for apooled (over all reviews) estimate of treatment efficacy and also results in an increase in the number ofparameters to be estimated.

Following the notation used earlier, for trials reporting continuous outcomes, a pooled estimate oftreatment efficacy for review k, allowing for between-study (within review) variation, is ık , where


2k

�

ık D ˛k´k C ˇxk (13)

where ´k is a dummy covariate representing review (k D 1; : : : ; K � 1). Review level covariatescan be included, and here, xk is a binary covariate representing whether the surgery type is clean(k D 1; : : : ; K). That is, within reviews, the treatment effects are pooled using a random effectsmeta-analysis, but across reviews, variation is modelled via fixed effects.

For trials reporting binary outcomes, a pooled estimate of treatment effect for review k, allowing forboth between-review and within-review variation is ık , where

logit �ikC D �iklogit �ikT D �ik C ıik (14)


205



2k

�

ık D ˛k´k C ˇxk (15)

where again ´k is a dummy covariate representing review (k D 1; : : : ; K�1) and xk is a binary covariaterepresenting whether the surgery type is clean (1) or not clean (0) (k D 1; : : : ; K). Again, within reviews,the treatment effects are pooled using a random effects meta-analysis, but across reviews, variation ismodeled via fixed efects.

3.4. Implementation

We obtained posterior summaries for all model parameters using MCMC simulations, using WINBUGS1.4.3 software and following their guidance on model parameterisation [11]. Chains were run for 200,000iterations, after disregarding an initial 100,000 burn-in iterations, at which point visual inspection ofchains and the Brooks convergence statistic [12] suggested that chains had converged. All continuousparameters have been given vague priors N.0; 1002/. For variance parameters, it is recommended to usenoninformative uniform priors on standard deviation parameters, which have generally been shown towork well in hierarchical models, except for the case in which the number of groups (i.e. Nk or K) aresmall, in which case the variances tended to be overestimated [13]. Within WINBUGS, a convenientproper approximation to such an improper prior is the uniform U.0; 10/. In the example considered, aswithin many meta-analyses, the number of trials included within some reviews are small (less than 5),and some sensitivity was observed for the variance parameters (although not the main effect parameters).For all our analyses (i.e. all analyses except those extracted from primary reports), all estimates quotedare medians along with 95% credible intervals (CrI). In addition, for pooled estimates over all surgerytypes, 95% prediction intervals for a new surgery type are also given.

4. Example: synthesising evidence on efficacy of prophylactic antibiotics acrosssurgery types

A recent systematic review of systematic reviews of antibiotic prophylaxis to reduce post-surgery woundinfection identified 21 reviews (Table I) reporting pooled estimates of treatment efficacy over 21 differentsurgery types. Full details of this systematic review of systematic reviews can be found in the relevantcitation [4]. Briefly, this systematic review consisted of a search of Medline and the Cochrane databaseof systematic reviews for reviews published in English between 1990 and 2006. The included reviewshad to involve a type of surgery defined as an incision to the skin using the Medical Subject Headingsdefinition, and trials had to report the outcome of wound infection. Intervention groups had to havereceived a course of antibiotic prophylaxis and the control group no antibiotics. The original analysis ofthis data consisted of a variation of a forest plot in which instead of plotting trial treatment effects andcorresponding confidence intervals, the plot consisted of pooled treatment effect estimates for each ofthe 21 systematic reviews, along with estimates of confidence bands. Because almost all of the confi-dence bands excluded one, the authors concluded that prophylactic antibiotics was most likely effectivein all surgery types and recommended its routine use across all surgery types, not only those includedwithin the review. No formal synthesis of evidence was carried out. We synthesise the evidence acrossthe reviews using the proposed panoramic meta-analysis and consider the effect of the intervention forthose surgeries considered to be ‘clean’ and those considered to be ‘nonclean’ or ‘dirty’.

We initially performed an independent synthesis of evidence within surgery types using the modeloutlined in Section 2, where all trials identified within each of the surgery types are synthesised inde-pendently of other surgery types. We term this an independent analysis, and although it results in pooledestimates of treatment efficacy for each of the individual surgery types (along with estimates of between-study variation within surgery type), it does not result in a pooled estimate of treatment efficacy overall surgery types. These independent analyses are comparable with those performed within the pri-mary systematic reviews, except for differences because of computational details (i.e. treatment of zerocells), treatment effect parameter reported and modelled (i.e. relative risk or odds ratio) and Bayesian orfrequentist analysis. Using the two-step approach, we synthesised these treatment effect estimates, essen-tially by pooling the effect estimates using a conventional (but Bayesian) random effects meta-analysis,to obtain a pooled estimate of treatment efficacy over all surgery types. More formally, we then analysedthese data using the proposed three-level hierarchal model (Section 3) again to obtain a pooled estimateof efficacy of prophylactic antibiotics over all surgery types. We term this a panoramic analysis, and it

206



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results in a pooled (over all surgery types) estimate of treatment efficacy, along with estimates of within-surgery (i.e. between-study variation within surgery type) and between-surgery variations. Finally, forfurther comparison, we consider the mixed effects analysis using the meta-regression approach in whichvariation between studies is incorporated as a fixed covariate effect.

We screened each of the 21 identified reviews and abstracted data on the number of trials includedin the reviews and the reported estimated pooled relative risk and standard error (Table I). In addition,we abstracted data for every trial within each review on the number of individuals randomised to thetreatment and control arms, respectively, and the number of wound infections on each arm. All but three(review numbers 4,15 and 16) of the 21 reviews reported the individual trial level outcome data withinthe primary reviews. The analysis presented here contains a subanalysis of 18 of the 21 reviews identi-fied and so should be considered for illustrative purposes (for a full clinical recommendation, it would benecessary to obtain trial data for all reviews). For all analyses, we added one to the number of respondersfor all studies in which zero responders were observed.

Table II shows the results from the independent analyses, and these results essentially consist of inde-pendent Bayesian random effects meta-analyses fitted to the binary trial data for each of the 18 surgerytypes. These inferences are roughly comparable with those reported by each of the systematic reviews(Table I). All of the original relative risk estimates (reported in the primary reviews) were based on fre-quentist analyses, and the Bayesian estimates of odds ratios reported here have wider confidence bands.All estimated odds ratios (from the Bayesian independent analyses, Table II) are below 1. In addition,the majority (10 of 18) of upper 95% CrI were also below 1, indicating that treatment with prophylacticantibiotics is preferable to no treatment in the majority of surgery types. All 18 independent reviewsshow evidence of statistical heterogeneity, as indicated by estimates of between-study variability (�2

k).

The two-step approach, combining the estimates obtained from the independent analyses into a pooledestimate, estimates the pooled effect to be 0.34 95% CrI: (0.24,0.48) with a between-review variance ofof 0.01, with 95% CrI: (0.0,0.18).

Using the panoramic analysis (Table II), allowing for both between-study and between-surgery typevariability, results in a pooled odds ratio of 0.37 95% CrI: (0.29,0.47). This result suggests that prophy-lactic treatment with antibiotics prior to surgery reduces the odds, on average, of post-operative infectionconsiderably over all surgery types. Once again, each of the 18 reviews showed evidence of statisticalheterogeneity, with estimates of between-study variance greater than zero. The estimate of variancebetween surgery types is less than that associated with between-study variance and lends support tothe notion of a pooled estimate over surgery types. It is of interest to note that all 18 estimated oddsratios from the panoramic analysis (i.e. that accounting for both between-study and between-surgeryvariability) had associated confidence bands less than one. This is in contrast to both the independentanalysis (Table II) and the results reported by the systematic reviews (Table I). This is a reflection ofthe natural sharing of data and borrowing of strength, which occurs in Bayesian analyses, but is also areflection of the strong effects of the exchangeability assumption. We further extended this panoramicanalysis by stratifying the analysis by clean and nonclean surgery types (Figure 1). This provides twoseparate pooled estimates of treatment efficacy over clean and nonclean surgery types. Consistent withclinical expectation, the effect of treatment in the clean surgery types (OR 0.42 (95% CrI: 0.31,0.55))suggests less evidence of effect compared with that with the nonclean surgery types (OR 0.31 (95% CrI:0.21,0.44))—Figure 1, results not tabulated.

We obtained predictive estimates (Table III) for both new studies (within reviews) and new reviews (orsurgery types) from both the independent and panoramic model fits. As expected, CrIs for the predictiveestimates are wider than those of the nonpredictive estimates. For the most part, the CrIs obtained underthe independent analysis were wider than those obtained under the panoramic analysis, again a featureof the exchangeability assumption.

The meta-regression analysis or mixed effects approach allows for between-study variation (withinsurgery types) and models between-surgery type variability through fixed covariate effects (for eachsurgery type) but does not provide a pooled estimate (over all surgery types) of treatment efficacy(Table IV). The estimated surgery effects (on the logit scale) range from �0:63 (95% CrI:�1:99,0.76)for colorectal surgery, a surgery type for which the estimated benefit from prophylaxis is above average,to 1.08 (95% CrI:�0:07,2.15) for elective laparoscopic cholecysectomy, a surgery type for which theestimated benefit from prophylaxis is below average. The pooled odds ratios (for each surgery type) aresimilar to those of the independent analysis, although showing some shrinkage towards the mean andsome shrinkage of CrIs (as a result of the assumption of partial exchangeability of the meta-regression).

208



Tabl

eII

.E

ffec

tof

prop

hyla

ctic

antib

iotic

sby

surg

ery

type

:poo

led

met

a-an

alys

isov

er18

surg

ery

type

s.

Inde

pend

enta

naly

sis

Pano

ram

ican

alys

is

Pool

edod

dsra

tioV

aria

nce

Pool

edod

dsra

tioV

aria

nce

Surg

ery

type

ORk

LC

rIU

CrI

�2 k

LC

rIU

CrI

ORk

LC

rIU

CrI

�2 k

LC

rIU

CrI

Art

eria

lrec

onst

ruct

ion

0.21

0.10

0.39

0.22

0.00

2.47

0.29

0.17

0.44

0.19

0.00

2.39

Pace

mak

erin

sert

ion

0.23

0.06

1.02

0.84

0.00

11.4

00.

340.

170.

590.

760.

008.

81T

une

thor

acos

tom

y0.

210.

040.

780.

320.

0010

.29

0.34

0.17

0.56

0.25

0.00

6.27

Cra

niot

omy

Intr

acra

nial

vent

ricu

lar

shun

t0.

500.

320.

750.

070.

000.

770.

450.

310.

640.

070.

000.

76To

talh

ipre

plac

emen

t0.

250.

070.

800.

220.

008.

550.

330.

180.

540.

160.

004.

69C

lose

dlo

ngbo

nefr

actu

re0.

590.

242.

230.

480.

006.

090.

440.

260.

760.

250.

004.

36H

ipfr

actu

rere

pair

0.48

0.25

0.82

0.27

0.00

2.32

0.44

0.28

0.65

0.26

0.00

2.05

Spin

alsu

rger

y0.

380.

131.

040.

180.

004.

430.

390.

220.

640.

140.

002.

99B

reas

tsur

gery

0.49

0.16

1.18

0.37

0.00

6.40

0.43

0.25

0.68

0.34

0.00

3.99

Ingu

inal

hern

iare

pair

(with

outm

esh)

0.66

0.15

1.85

0.40

0.00

10.4

60.

460.

240.

830.

590.

017.

74In

guin

alhe

rnia

repa

ir(w

ithm

esh)

0.44

0.11

1.46

0.75

0.00

10.2

60.

410.

230.

690.

550.

006.

32C

aesa

rean

sect

ion

(ele

ctiv

e)0.

650.

381.

030.

090.

001.

030.

510.

320.

800.

150.

001.

26C

aesa

rean

sect

ion

(non

elec

tive)

0.36

0.22

0.59

0.22

0.00

1.29

0.37

0.25

0.53

0.20

0.00

1.20

Abd

omin

alhy

ster

ecto

my

Bili

ary

trac

tsur

gery

Perc

utan

eous

endo

scop

icga

stro

stom

y0.

250.

110.

540.

230.

003.

640.

320.

190.

500.

230.

003.

01L

apar

osco

pic

chol

ecys

ecto

my

(ele

ctiv

e)0.

900.

312.

550.

180.

004.

510.

500.

270.

950.

290.

005.

10C

olor

ecta

lsur

gery

0.14

0.04

0.48

0.23

0.00

11.8

00.

300.

130.

530.

660.

0013

.76

Sim

ple

appe

ndic

itis

0.35

0.25

0.47

0.15

0.00

0.68

0.36

0.26

0.46

0.13

0.00

0.64

Com

plic

ated

appe

ndic

itis

0.25

0.14

0.37

0.24

0.00

1.54

0.29

0.19

0.41

0.19

0.00

1.34

Pool

edes

timat

esTw

o-st

epap

proa

chT

hree

-lev

elm

odel

0.34

0.24

0.48

0.01

0.00

0.18

0.37

0.29

0.47

0.09

0.00

0.38

Not

e:O

Rk

isth

em

edia

npo

oled

estim

ated

odds

ratio

for

revi

ewk

.L

CrI

isth

e95

%lo

wer

CrI

.U

CrI

isth

e95

%up

per

CrI

.�2 k

isth

ees

timat

edm

edia

nbe

twee

n-st

udy

vari

atio

n(w

ithin

surg

ery

typek

).�2

isth

ees

timat

edm

edia

nbe

twee

n-su

rger

yty

pes

vari

atio

n.


209


0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00

Odds RatioFavours controlFavours treatment

Clean surgery typesArterial reconstruction

Pacemaker insertion

Tube thoracostomy

Craniotomy

Intracranial ventricular shunts

Total hip replacement

Closed long bone fractures

Hip fracture repair

Spinal surgery

Breast surgery

Inguinal hernia repair (without mesh)

Inguinal hernia repair (with mesh)

Caesarean section (elective)

Pooled clean surgeries

Non−clean surgery typesCaesarean section (non−elective)

Abdominal hysterectomy

Biliary tract surgery

Percutaneous endoscopic gastrostomy

Laparoscopic cholecysectomy (elective)

Colorectal surgery

Simple appendicitis

Complicated appendicitis

Pooled non−clean surgeries

Pooled all surgeries

Predictive estimate (new surgery type)

Figure 1. For each study, the independently estimated (i.e. independent of other surgical types) posterior medianwith 95% credible interval (solid line) and the posterior median with 95% credible interval from the noninde-pendent analysis (i.e. from the panoramic analysis large dotted line) and from the stratified analysis by clean ornonclean surgery (small dotted line). Also presented from the panoramic analysis and stratified analysis are thepooled (over all surgeries and over all clean and nonclean surgeries) median estimated with 95% credible interval

and with corresponding predictive interval (for a new surgical type).

5. Discussion

We have proposed a method for pooling study estimates across trials, which are all evaluating the same(or very similar) outcomes under the same (or similar) intervention but do so for different disease types.We have termed this a panoramic meta-analysis. In this setting, it is almost certain that the effect oftreatment will not be constant over the different diseases. It might be the case that the treatment effects,which will vary depending on the disease and study, will be distributed around some common value. Thistype of heterogeneity lends itself to the three-level hierarchical model in which variation between studyestimates is composed of variation between studies (but within disease types) and variation betweendisease. However, although being a natural extension of the standard two-level hierarchal meta-analysis,this approach also makes the possibly untenable exchangeability assumption. As an alternative, we havetherefore proposed a mixed effect analysis, which still allows for some exchangeability, but because the

210



Table III. Predictive estimates: new studies and new surgery types.

Independent analysis Panoramic analysis

New studies ORk LCrI UCrI ORk LCrI UCrIArterial reconstruction 0.21 0.04 0.97 0.28 0.07 1.33Pacemaker insertion 0.23 0.01 7.20 0.32 0.02 5.60Tune thoracostomy 0.20 0.01 3.10 0.32 0.04 2.72CraniotomyIntracranial ventricular shunt 0.50 0.19 1.23 0.45 0.17 1.06Total hip replacement 0.25 0.02 2.57 0.32 0.06 1.97Closed long bone fracture 0.55 0.07 8.59 0.42 0.07 2.80Hip fracture repair 0.49 0.09 2.19 0.44 0.09 1.75Spinal surgery 0.38 0.05 2.68 0.37 0.08 1.70Breast surgery 0.50 0.04 4.11 0.43 0.06 2.32Inguinal hernia repair (without mesh) 0.68 0.03 7.86 0.48 0.03 4.60Inguinal hernia repair (with mesh) 0.45 0.02 8.02 0.40 0.04 3.82Caesarean section (elective) 0.66 0.21 1.73 0.53 0.14 1.46Caesarean section (nonelective) 0.35 0.10 1.35 0.36 0.11 1.27Abdominal hysterectomyBiliary tract surgeryPercutaneous endoscopic gastrostomy 0.25 0.04 1.53 0.31 0.06 1.68Laparoscopic cholecysectomy (elective) 0.91 0.12 6.28 0.49 0.06 3.21Colorectal surgery 0.14 0.01 1.88 0.25 0.02 7.14Simple appendicitis 0.35 0.12 0.88 0.36 0.14 0.87Complicated appendicitis 0.25 0.06 0.89 0.29 0.08 0.99

Pooled:New surgery type 0.37 0.17 0.78

Note:ORk is the median pooled estimated odds ratio for review k.LCrI is the 95% lower credible interval.UCrI is the 95% upper credible interval.

effect of disease type is included as a fixed covariate effect in a meta-regression type approach, it doesnot assume that the different disease types are exchangeable, yet allows comparison between surgerytypes.

Both the systematic review and the statistical technique of meta-analysis are relatively new devel-opments [14], and even the pooling of effect estimates by means of a meta-analysis is viewed ascontroversial by some. Clearly, these issues will still be of importance in a systematic review of sys-tematic reviews and any subsequent panoramic meta-analysis. In addition, more issues or controversieswill also arise. Many of these will be fundamental in nature, relating to whether effect estimates shouldbe pooled over clinical areas that might be quite heterogeneous, and as in a conventional meta-analysis, itwill not always be reasonable to combine study effect estimates into a single pooled estimate [15]. Otherissues will be more specific in nature, for example, relating to how disease types are assessed for clini-cal relevance. We suggest that a systematic review of systematic reviews should broadly follow existingreview guidelines and should include a systematic search with identification and screening of studies forinclusion, removal of duplicates, clear eligibility criteria and duplicate method of data abstraction [16].However, specific issues to be considered in a panoramic meta-analysis are whether only systematicreviews are to be included or whether reviews for source trials will be conducted in those therapeuticareas for which no current systematic review exists; whether publication date criteria will apply to sys-tematic reviews or to individual studies and validity assessment of the systematic review (as opposedto that of an RCT); and very importantly, how to determine which clinical areas to include within thereview. Limitations include issues of aggregation bias [17], small study bias [18], selective reporting ofpositive outcomes [19], missing data [20–22], normality assumptions and identification of patients mostlikely to benefit [23], and identifiability of parameters with small numbers of studies or participants, toname but a few.

Fundamental to the proposed three-level hierarchical model is the assumption of exchangeability. Theconcept of exchangeability invoked here is similar to that in a conventional meta-analysis, although


211


Table IV. Effect of prophylactic antibiotics by surgery type: mixed effects model over 18 surgery types.

Surgery effect Pooled odds ratio Variance

Surgery type ˛k LCrI UCrI ORk LCrI UCrI �2k

LCrI UCrI

Arterial reconstruction �0:23 �1:08 0.55 0.20 0.10 0.37 0.46 0.02 1.52Pacemaker insertion �0:19 �1:54 1.13 0.21 0.06 0.73 0.75 0.04 2.93Tune thoracostomy �0:31 �1:91 1.08 0.19 0.04 0.68 0.54 0.03 3.02CraniotomyIntracranial ventricular shunt 0.61 0.01 1.24 0.47 0.31 0.71 0.25 0.01 0.84Total hip replacement �0:05 �1:40 1.11 0.24 0.07 0.71 0.46 0.02 2.78Closed long bone fracture 0.67 �0:29 1.84 0.50 0.22 1.47 0.54 0.03 2.04Hip fracture repair 0.60 �0:19 1.31 0.47 0.25 0.79 0.51 0.04 1.47Spinal surgery 0.31 �0:88 1.37 0.35 0.12 0.90 0.41 0.02 2.04Breast surgery 0.62 �0:64 1.63 0.48 0.15 1.16 0.61 0.06 2.56Inguinal hernia repair (without mesh) 0.88 �0:75 2.01 0.63 0.14 1.71 0.65 0.03 3.27Inguinal hernia repair (with mesh) 0.48 �1:00 1.69 0.42 0.11 1.25 0.81 0.05 3.02Caesarean section (elective) 0.86 0.15 1.52 0.61 0.35 0.95 0.30 0.01 1.00Caesarean section (nonelective) 0.25 �0:38 0.92 0.33 0.21 0.53 0.43 0.03 1.05Abdominal hysterectomyBiliary tract surgeryPercutaneous endoscopic gastrostomy �0:02 �0:98 0.86 0.25 0.11 0.53 0.48 0.02 1.92Laparoscopic cholecysectomy (elective) 1.08 �0:07 2.15 0.75 0.27 1.98 0.40 0.02 1.99Colorectal surgery �0:63 �1:99 0.67 0.14 0.04 0.47 0.46 0.02 3.28Simple appendicitis 0.28 0:26 0.84 0.34 0.24 0.45 0.38 0.03 0.81Complicated appendicitis 0.26 0.16 0.39 0.46 0.03 1.19

Note:ORk is the median pooled estimated odds ratio for review k.LCrIis the 95% lower CrI.UCrIis the 95% upper CrI.�2k is the estimated median between-study variation (within surgery type k).˛k estimate of median surgery effect on logit scale; with complicated appendicitis as the baseline group.

because we are combining results across different clinical areas, the assumption becomes more ques-tionable. This assumption of exchangeability, although allowing the sharing of data, means that theunderlying intervention effects are identical between different diseases and might lead to biased esti-mates in either direction [24]. As with a conventional meta-analysis where the effects across surgerytypes were thought to be different and unrelated, a panoramic meta-analysis would be ruled out [15].Assessments of exchangeability are dependent on the data at hand. In the example considered here, therewas considerable variation between surgery types with risks of the outcome of interest ranging fromabout 4% to 40%; yet at the same time, estimates of between-disease variation (for odds ratios) wereless than estimates of between-study variation. The result of the assumption of exchangeability is to pullmedian estimates for each of the surgery types towards the overall pooled estimate and shrink CrI, andthis feature was most notable in those reviews thats were smaller (i.e. estimated with smaller precision),for example, laparoscopic cholecysectomy and closed long bone fraction. This feature, of more effectivetreatments looking less effective and vice versa, is particularly striking in the stratified analysis, whereeach of the clean surgeries looks less effective in comparison with the none stratified analysis, and thedirty surgeries all look more effective. The meta-regression approach, although not providing a pooledestimate of treatment efficacy, models the variation between surgery types by fixed effects in a meta-regression type approach and so does not need to assume exchangeability. This mixed effects approach,although leading to less precise estimates (compared with the three-level model), assumes only partialexchangeability and allows for incorporation of review level covariates.

We applied the proposed models to a systematic review of systematic reviews of RCTs of prophylac-tic antibiotics in different surgery types. Combining treatment effects over trials but within diseases, itwas observed that the relative risk of infection post-surgery was lower in all surgery types, except one,in the treatment groups (relative risk range 0.15 (sd 0.09) in the colorectal surgery review to 1.03 (sd0.59) in the laparoscopic cholecysectomy review), and significantly lower in the treatment arms in 10 ofthe 18 surgery types. A heuristic interpretation of these results would provide fairly convincing but notconclusive evidence that prophylactic antibiotics reduces post-surgery infection rates over all or most

212



surgery types. Pooling study estimates using the proposed three-level hierarchical model allows for bothbetween-study and between-disease variations but requires the strong assumption of exchangeabilityand gives a pooled treatment effect of 0.37 95% CrI: (0.29,0.46). This pooled estimate suggests that, ifthe surgery types are exchangeable in those trials included within the reviews, prophylactic antibiotics,on average, reduces post-surgery infection rates over all surgery types considered. The mixed effectsapproach, assuming only partial exchangeability (within surgery types), although not providing an over-all pooled estimate of treatment efficacy, does through the assumption of partial exchangeability, produceslightly more precise estimates of treatment efficacy compared with the independent analysis.

The Bayesian approach used here allows for full appreciation of parameter uncertainty [25] andstraightforward implementation using WINBUGS but does require detailed evaluation of model con-vergence and full prior specification [15]. Frequentist approaches could be considered, perhaps usinggeneralised estimating equations, as the models proposed are hierarchical models. A full Bayesianapproach would incorporate informative priors perhaps elicited from experts or would allow incorpo-ration of a sceptical prior [25]. In comparisons of frequentist and Bayesian (with uninformative priors)conventional meta-analyses, it was observed that parameter estimates, other than those for variances,were similar between the approaches, but the Bayesian CrIs were wider than the frequentist confidenceintervals [25]. Others have considered in detail sensitivity of meta-analysis models to prior specification[3,22]. Parameter estimates, other than those for variances, have not been found to be sensitive to choice,although variance parameters are more so, and so consequently so too are the CrIs for the main param-eters. We have therefore followed recommendations by others to minimise these sensitivities by usingthe improper uniform prior [13]. As with all meta-analysis techniques, the proposed model has severalimportant limitations, which cannot be immediately overcome.

Acknowledgements

The Engineering and Physical Sciences Research Council of the United Kingdom through the MATCH pro-gramme (grant GR/S29874/01) partly funded all authors. A National Institute of Health Research grant forCollaborations for Leadership in Applied Health Research and Care (CLAHRC) supported also K. H. andR. J. L. PROMEP (El Programa de Mejoramiento del Profesorado) of Mexico partially funded R. J. B. Theviews expressed in this publication are not necessarily those of the NIHR or the Department of Health.

WINBUGS code

# K is the number of systematic reviews#k=1..K indexes reviews#J is total number of trials (over all reviews)#j=1..J indexes trials (over all reviews)#review[j] indexes the systematic review that the jth trial belongs to

#####################################################################

#Independent Analysis of Each Review

model{for(j in 1:J){rC[j] dbin(pC[j],NC[j])rT[j] dbin(pT[j],NT[j])logit(pC[j])<-mu[j]logit(pT[j])<-mu[j]+delta[j]mu[j] dnorm(0.0,1.0E-4)delta[j] dnorm(d[review[j]],prec1[review[j]])}

for(k in 1:K){d[k] dnorm(0.0,1.0E-4)OR[k]<-exp(d[k])


213


tau[k] dunif(0,10)prec1[k]<-1/(tau[k]*tau[k])}}

######################################################################Combined Analysis pooled over surgery types

model{for(j in 1:J){rC[j] dbin(pC[j],NC[j])rT[j] dbin(pT[j],NT[j])logit(pC[j])<-mu[j]logit(pT[j])<-mu[j]+delta[j]mu[j] dnorm(0.0,1.0E-4)delta[j] dnorm(d[review[j]],prec1[review[j]])}

for(k in 1:K){d[k] dnorm(Pooled_d,prec2)OR[k]<-exp(d[k])tau[k] dunif(0,10)prec1[k]<-1/(tau[k]*tau[k])

}Pooled_d dnorm(0.0,1.0E-4)Pooled_OR<-exp(Pooled_d)gamma dunif(0,10)prec2<-1/(gamma*gamma)theta.new dnorm(d1, prec2)OR2.predict<-exp(theta.new)}

######################################################################Mixed Analysis pooled over surgery types

model{for(j in 1:J){rC[j] dbin(pC[j],NC[j])rT[j] dbin(pT[j],NT[j])logit(pC[j])<-mu[j]logit(pT[j])<-mu[j]+delta[j]mu[j] dnorm(0.0,1.0E-4)delta[j] dnorm(d,prec1[review[j]])}

for(k in 1:K){tau[k] dunif(0,10)prec1[k]<-1/(tau[k]*tau[k])

}d dnorm(0.0,0.0001)Pooled_OR<-exp(d)}

######################################################################Initial Values

214



list(sigma=c(0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1),sigma_gamma=0.1)

#Example of first few rows of datareview[ ] NC[ ] rC[ ] NT[ ] rT[ ]1 86 22 93 121 15 5 18 01 30 10 30 01 66 11 121 51 66 14 62 11 237 16 225 21 15 1 15 01 13 3 14 01 23 2 27 21 72 14 69 42 197 7 234 22 50 7 50 12 256 1 244 22 54 0 52 02 100 12 100 02 106 1 107 0

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