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Diagnostics for prev[1]
Density
prev[1]
(a)
(b)
(c)
Iteration
0000
Diagnostics for sp[1]
Density
sp[1]
(a)
(c)
Iteration
0000
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Running mean
0246810
0.2
0.4
0.6 1. 00.8
prev[1]
0.2 0.4 0.6 0.8 1. 0
8000060000 10000 1200014000
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 4000 60002000 80000
Iteration
1
(b)
Running mean
0e+00 2e+05 4e+05
0.20.0 0.4 0.6 0.8 1. 0
0.20.0
0.4
Figure10.8.a MCMC diagnostics plots for parameters from the bivariate latent class meta- analysis model
0.6 1. 00.8
sp[1]
8000060000 10000 1200014000
0.0 0.2 0.4 0.6 0.8 1. 0
0 4000 60002000 80000
Iteration
1
Box 10.8.a Comparison of results from Bayesian bivariate latent class and standard bivariate meta- analysis models
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Bivariate latent class meta- analysis model Standard bivariate meta- analysis model
Iterations = 31010:331000
Thinning interval = 10
Number of chains = 5
Sample size per chain = 30000
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-
Summary_Se 0.6465190 0.051066 1.319e- 04 8.234e- 04
Summary_Se2 0.7000913 0.052723 1.361e- 04 8.537e- 04
Summary_Sp 0.9942673 0.003753 9.690e- 06 9.778e- 05
Summary_Sp2 0.9914815 0.004494 1.160e- 05 1.053e- 04
Predicted_Se 0.6397513 0.111522 2.879e- 04 7.782e- 04
Predicted_Sp 0.9930580 0.008756 2.261e- 05 1.129e- 04
rho 0.0530568 0.571872 1.477e- 03 7.836e- 03
tau.sq[1] 0.2191830 0.135772 3.506e- 04 1.329e- 03
tau.sq[2] 0.3822149 0.385743 9.960e- 04 4.324e- 03
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
Summary_S 5.496e- 01 6.119e- 01 0.645373 0.6799865 0.750382
Summaryan_S2 5.975e- 01 6.650e- 01 0.699523 0.7345158 0.806461
Summary_C 9.850e- 01 9.923e- 01 0.995022 0.9970767 0.999236
Summary_C2
Predicted_Se 4.060e- 01 5.679e- 01 0.644651 0.7171661 0.844417
Predicted_Sp 9.748e- 01 9.913e- 01 0.995149 0.9974802 0.999469
rho - 9.374e- 01 - 4.321e- 01 0.080262 0.5518103 0.951745
tau.sq[1] 7.387e- 02 1.312e- 01 0.184130 0.2650333 0.575089
tau.sq[2] 8.752e- 02 1.764e- 01 0.273575 0.4494636 1.325901
9.811e- 01 9.888e- 01 0.992067 0.9948021 0.998417
series SE
Iterations = 6001:16000
Thinning interval = 1
Number of chains = 3
Sample size per chain = 10000
1.
Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time- series SE
Summary_Se 0.7143 0.048716 2.813e- 04 9.707e- 04
Summary_Sp 0.9812 0.004695 2.710e- 05 1.045e- 04
Predicted_Se 0.6862 0.175487 1.013e- 03 1.219e- 03
Predicted_Sp 0.9713 0.035431 2.046e- 04 2.314e- 04
rho 0.2989 0.263569 1.522e- 03 7.750e- 03
tau.sq[1] 0.8680 0.463325 2.675e- 03 1.495e- 02
tau.sq[2] 0.9229 0.439277 2.536e- 03 1.285e- 02
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
Summary_Se 0.6154 0.6830 0.7157 0.7470 0.8076
Summary_Sp 0.9711 0.9783 0.9815 0.9844 0.9894
Predicted_Se 0.2766 0.5801 0.7136 0.8203 0.9454
Predicted_Sp
rho - 0.2517 0.1221 0.3144 0.4925 0.7631
tau.sq[1] 0.2828 0.5468 0.7657 1.0756 2.0372
tau.sq[2] 0.3354 0.6122 0.8350 1.1386 2.0107
0.8832 0.9658 0.9813 0.9899 0.9976
10 Undertaking meta- analysis
Specificity
Sensitivity
Specificity
0
Latent class meta-analysis Standard bivariate meta-analysis
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0.6 0.8 1.0
0.2 0.4
0.0
1. 0 0.8 0.6
Figure10.8.b Comparison of credible and prediction regions from bivariate latent class and standard
bivariate meta- analysis models
0.4 0.2 0.0
0.6 0.8 1.0
Sensitivity
0.2 0.4
0.0
1. 00.8 0.6
0.40.2 0.
The box shows that the latent class meta- analysis model resulted in a lower estimate
of the sensitivity of the index test (Summary_S = 0.645373) than the standard bivariate
meta- analysis (Summary_Se = 0.7157). The summary specificity of the index test was
slightly higher in the latent class meta- analysis model (Summary_C = 0.995022 versus
Summary_Sp = 0.9815). Of course, the standard bivariate meta- analysis does not provide any estimates for the sensitivity and specificity of the reference standard, which
are assumed to be 100%. Under the latent class meta- analysis model, the posterior
median estimates of the summary sensitivity and specificity of the reference standard
were Summary_S2 = 0.699523 and Summary_C2 = 0.992067, respectively. An important
consequence of adjusting for the imperfect nature of the reference standard is that the
apparent heterogeneity in the accuracy of the index test is reduced. We can see this
reflected in the parameters tau.sq[1] and tau.sq[2], which are much higher in the standard bivariate meta- analysis, and also in the standard deviations of the predicted sensitivity and specificity in a future study. Furthermore, the correlation parameter (rho) is
practically zero in the latent class meta-
analysis, removing the apparent positive correlation suggested by the standard bivariate meta- analysis. This is confirmed by a comparison of the credible and prediction regions on the SROC plot (Figure10.8.b).
10.8.4 Sensitivity analyses
Sensitivity analyses are particularly important for latent class models, as the number of
unknown parameters is very large and the model can encounter identifiability problems (i.e. where there are multiple solutions). In such situations, informative prior distributions may be necessary over some parameters, e.g. the sensitivity and specificity
of the reference standard. In this situation it would be important to carry out sensitivity
analyses to see whether the results are robust to the form of the prior distribution. As
with any bivariate meta- analysis, it is important to examine the impact of changing the
form of the vague prior distributions over the parameters capturing the between- study
320
10.10 Chapter information
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variability, as the results are known to be sensitive to this choice, particularly when the
number of studies is small.
10.9 Concluding remarks
Prior to 2008, only one user- written program (metandi) was available for fitting the
bivariate model for meta- analysis of test accuracy. Since then considerable progress
has been made and there is now a plethora of user- written programs for fitting bivariate
or HSROC models for meta- analysis of test accuracy. Using software packages frequently used for frequentist analyses and different published systematic reviews, this
chapter has illustrated how to fit standard bivariate and HSROC models. The chapter
also illustrated analyses within a Bayesian framework for the standard models as well
as when there is an imperfect reference standard. Many tests are measured on a continuum and so a threshold is needed for defining test positivity. Studies may report one
or more thresholds, and this chapter has also shown how to perform metaallows for multiple thresholds from the included studies.
When performing hierarchical meta- regression for investigating heterogeneity and
test comparisons, it is often assumed that the variances of the respective model parameters are identical across subgroups or tests (i.e. equal variances). A similar assumption
is commonly made about between- study variances for treatment effects in multiple
treatment comparisons (network meta- analysis). While this assumption has the advantage of simplifying estimation of the models and may be appropriate for treatment
effects, it is not generalizable, as shown by examples in this chapter and empirically by
Takwoingi (2016). The complexity of models and/or the number of tests or subgroups in
relation to the number of studies available pose a challenge. Therefore, the chapter
also addressed how to facilitate convergence, and how to simplify hierarchical models
if appropriate.
This chapter has provided several examples and guidance on fitting meta- analysis models, but the expertise of a statistician or methodologist familiar with these methods may
still be required. Commercial software packages like Stata and SAS require purchase of
a user licence and this may limit software options available to some meta- analysts. SAS
has a free package (SAS on demand for academics; www.sas.com/en_gb/software/ondemand- for- academics.html) for academic, non- commercial use. Additional resources
such as tutorials and user guides that provide step- by- step guidance for both novice and
experienced meta- analysts of test accuracy are available on the Cochrane Screening and
Diagnostic Tests Methods Group website (methods.cochrane.org/sdt). The resources also
include other programs and macros not covered in this chapter.
analysis that
10.10 Chapter information
Authors: Yemisi Takwoingi (Institute of Applied Health Research, University of
Birmingham, UK), Nandini Dendukuri (McGill University, Montreal, Canada), Ian Schiller
(Centre for Outcomes Research, McGill University Health Centre – Research Institute,
Canada), Gerta Rücker (Institute of Medical Biometry and Statistics, University of Freiburg,
Germany), Hayley E. Jones (Population Health Sciences, University of Bristol, UK),
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10 Undertaking meta- analysis
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Christopher Partlett (Nottingham Clinical Trials Unit, University of Nottingham, UK), Petra
Macaskill (Sydney School of Public Health, University of Sydney, Australia).
Sources of support: Yemisi Takwoingi is funded by a UK National Institute for Health
Research (NIHR) Postdoctoral Fellowship. Yemisi Takwoingi is supported by the NIHR
Birmingham Biomedical Research Centre at the University Hospitals Birmingham NHS
Foundation Trust and the University of Birmingham. The views expressed are those of
the authors and not necessarily those of the NHS, the NIHR or the Department of Health
and Social Care. Ian Schiller was supported by a grant from the Canadian Institutes of
Health Research (PJT- 156039). Gerta Rücker was supported by the German Research
Foundation (DFG), grant RU 1747/1- 2. Hayley E. Jones was supported by an MRC- NIHR
New Investigator Research Grant (MR/T044594/1). No other authors declare sources of
support for writing this chapter.
Declarations of interest: Yemisi Takwoingi, Nandini Dendukuri and Petra Macaskill are
members of Cochrane’s Diagnostic Test Accuracy Editorial Team. Yemisi Takwoingi and
Petra Macaskill are co-
convenors of the Cochrane Screening and Diagnostic Tests
Methods Group. Yemisi Takwoingi created the MetaDAS SAS macro and wrote the Stata
tutorial for fitting the bivariate model. Yemisi Takwoingi and Christopher Partlett coauthored the R tutorial for fitting the bivariate model. Gerta Rücker is the first author of
the R package diagmeta. Hayley E. Jones led development of the multiple thresholds
model described in Section10.7.2. The authors declare no other potential conflicts of
interest relevant to the topic of this chapter.
Acknowledgements: The authors would like to thank Sarah Berhane, Kurinchi
Gurusamy, Alex Sutton and Bada Yang for useful comments.
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Presenting findings
Jonathan J. Deeks, Patrick M. Bossuyt, Mariska M. Leeflang and Yemisi Takwoingi
KEY POINTS
Results of the search, characteristics of the included studies and methodological
•
quality assessment should be summarized to provide the reader with an overview of
the evidence.
For each objective, the review should present the relevant evidence and the findings,
•
such as results from individual studies and from metato be drawn about the accuracy of the index test(s).
When summarizing findings from a comparison of two tests, review authors should
•
focus on describing the
uncertainty in the estimates and the degree of heterogeneity.
Review authors should express the degree of statistical uncertainty associated with
•
summary estimates of test accuracy and consider the betweenWhen investigations of sources of heterogeneity were made, the results should be
•
cautiously interpreted.
Presenting summary estimates of sensitivity, specificity and predictive values as
•
frequencies has been shown to helpful for readers and is strongly encouraged.
Tables, forest plots and/or summary receiver operating characteristic (SROC) plots are
•
valuable tools for presenting findings in reviews with and without meta-
magnitude and direction of the difference between tests, the
analyses to enable conclusions
study variability.
analysis.
11.1 Introduction
The potential to inform readers of a systematic review not only depends on the
quality of the search and other steps of the systematic review process, but also on
thereview authors’ ability to present the key findings of the review in a valid and
informative way.
This chapter should be cited as: Deeks JJ, Bossuyt PM, Leeflang MM, Takwoingi Y. Chapter11: Presenting findings. In: Deeks JJ, Bossuyt PM, Leeflang MM, Takwoingi Y, editors. Cochrane Handbook for Systematic Reviews
of Diagnostic Test Accuracy. 1st edition. Chichester (UK): John Wiley & Sons, 2023: 327–348.
Cochrane Handbook for Systematic Reviews of Diagnostic Test Accuracy, First Edition. Edited by
Jonathan J. Deeks, Patrick M. Bossuyt, Mariska M. Leeflang and Yemisi Takwoingi.
© 2023 The Cochrane Collaboration. Published 2023 by John Wiley & Sons Ltd.
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This chapter focuses on the contents of the results section of a review. It describes
what is expected in such a report and how to report the findings to ensure that they are
adequately presented in an accessible manner to readers.
Reporting the results of a review requires judicious use of text, tables and figures to
produce a full description of the included evidence and the associated analyses. The
results section of the review will summarize the following.
●
The results of the search.
●
Key characteristics and the methodological quality of the included studies.
●
Key findings about test accuracy.
●
Findings for secondary objectives, including investigations of heterogeneity.
●
Findings for any additional analyses, such as sensitivity analyses.
Unlike Cochrane Reviews of interventions, Cochrane Reviews of diagnostic test accuracy allow more flexibility in how the findings can be presented. These reviews invite
authors to construct tables and select figures to report results as they think most appropriate. Review authors need to thoughtfully consider what evidence to include in the
results section of the main report and the supporting material that should be presented
in appendices.
11.2 Results ofthe search
This section will typically report the number of records that were screened for inclusion,
the number of titles that were retained, the number of full- text reports screened for
eligibility, the number of studies excluded and the number of studies eventually
included. The search and selection process will be clarified by including a PRISMA- style
flow diagram, summarizing the numbers of studies initially retrieved, excluded and
included in the review and eventual meta- analyses. For further information, see
Chapter6, Section6.4.2.
If additional efforts beyond searching bibliographic databases to identify studies
were stated as part of the search methods (such as screening reference lists, citing articles, conference proceedings or trial registries) review authors should also report the
outcome of these searches.
11.3 Description ofincluded studies
In reviews with a very small number of studies, the description of included studies can
be structured as a summary of each study. For larger reviews this will not be possible,
and the description can be phrased in terms of the overall composition of studies
included in the review.
Describing the evidence base requires summarizing key characteristics across the
included studies. This may include sample sizes and number of participants with the
target condition, key characteristics of the participants (typically summarizing both
demographic and clinical characteristics), the numbers of studies evaluating each
index test, variations in the testing processes, reference standards used and study
designs.
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