A primer on network metaanalysis for dental research.  
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In the last decade, a new statistical methodology, namely, network metaanalysis, has been developed to address limitations in traditional pairwise metaanalysis. Network metaanalysis incorporates all available evidence into a general statistical framework for comparisons of all available treatments. A further development in the network metaanalysis is to use a Bayesian statistical approach, which provides a more flexible modelling framework to take into account heterogeneity in the evidence and complexity in the data structure. The aim of this paper is therefore to provide a nontechnical introduction to network metaanalysis for dental research community and raise the awareness of it. An example was used to demonstrate how to conduct a network metaanalysis and the differences between it and traditional metaanalysis. The statistical theory behind network metaanalysis is nevertheless complex, so we strongly encourage close collaboration between dental researchers and experienced statisticians when planning and conducting a network metaanalysis. The use of more sophisticated statistical approaches such as network metaanalysis will improve the efficiency in comparing the effectiveness between multiple treatments across a set of trials. 
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YuKang Tu; Clovis Mariano Faggion 
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Type: Journal Article Date: 20120621 
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Title: ISRN dentistry Volume: 2012 ISSN: 2090438X ISO Abbreviation: ISRN Dent Publication Date: 2012 
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Created Date: 20120824 Completed Date: 20120824 Revised Date: 20130402 
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Nlm Unique ID: 101560640 Medline TA: ISRN Dent Country: Egypt 
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Languages: eng Pagination: 276520 Citation Subset:  
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Department of Oral Biology, Leeds Dental Institute, Leeds LS2 9JT, UK. 
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Journal Information Journal ID (nlmta): ISRN Dent Journal ID (isoabbrev): ISRN Dent Journal ID (publisherid): ISRN.DENTISTRY ISSN: 20904371 ISSN: 2090438X Publisher: International Scholarly Research Network 
Article Information Download PDF Copyright © 2012 Y.K. Tu and C. M. Faggion Jr. openaccess: Received Day: 22 Month: 4 Year: 2012 Accepted Day: 8 Month: 5 Year: 2012 collection publication date: Year: 2012 Electronic publication date: Day: 21 Month: 6 Year: 2012 Volume: 2012Elocation ID: 276520 ID: 3418651 PubMed Id: 22919506 DOI: 10.5402/2012/276520 
A Primer on Network MetaAnalysis for Dental Research  
YuKang Tu^{1}^{2}*  
Clovis Mariano Faggion, Jr.^{3}  
^{1}Department of Oral Biology, Leeds Dental Institute, Leeds LS2 9JT, UK 

^{2}Division of Biostatistics, Leeds Institute of Genetics, Health and Therapeutics, University of Leeds, Leeds LS2 9JT, UK 

^{3}Department of Oral Sciences, Faculty of Dentistry, University of Otago, P.O. Box 647, Dunedin 9054, New Zealand 

Correspondence: *YuKang Tu: y.k.tu@leeds.ac.uk [other] Academic Editors: M. Del Fabbro, G. Perinetti, J. Walters, and P. Ylöstalo 
With the rise of evidencebased medicine movement in the last two decades, systematic reviews and metaanalyses have been widely used for synthesis of evidence on beneficial and/or harmful effects of different treatments. Results from those reviews and metaanalyses provide important information for drawing clinical guidelines and making health policy recommendations. For most clinical conditions, several interventions (which may be drugs, medical devices, surgeries, or a combination of them) are usually available, but most systematic reviews of randomised controlled trials (RCTs) tend to limit their scopes by only evaluating two active treatments or comparing one treatment to a control. Even if a systematic review evaluates multiple treatments, traditional metaanalysis can only perform pairwise comparisons.
There are several limitations to this approach [^{1}–^{4}]. For instance, suppose there are three new and more expensive treatments A, B, and C and a standard treatment D, six pairwise metaanalyses (AB, BC, A–C, A–D, B–D, and CD) may be undertaken to compare the differences for pairs of the four treatments. None or few of included RCTs in the paper would have compared all four treatments, and most RCTs compared only 2 or 3 of them. Consequently, those pairwise metaanalyses use different sets of RCTs for each comparison, and the evidence base is therefore different across all comparisons. A possible consequence is that results from multiple pairwise metaanalyses may not be consistent: for example, in three pairwise comparisons, treatment A is shown to be better than treatment B, and B better than treatment C; but A is inferior to C. Secondly, some headtohead trials may not have been conducted yet (especially between the new treatments), so it is not possible to undertake traditional pairwise metaanalysis for these comparisons. Thirdly, because the number of studies available for pairwise comparisons is few, each metaanalysis may not have sufficient power to detect any genuine difference between treatments, yielding inconclusive results and providing no useful guidance on decision making.
In the last decade, a new statistical methodology, namely, network metaanalysis, has been developed to address those limitations [^{5}–^{7}]. Network metaanalysis incorporates all available evidence into a general statistical framework for comparisons of all available treatments. Thus, network metaanalysis may play an important role in the improvement of the decision making process by optimizing the use of the existing data. A further development in the network metaanalysis is to use a Bayesian statistical approach, which provides a more flexible modelling framework to take into account of heterogeneity in the evidence and complexity in the data structure [^{1}–^{4}].
Although systematic reviews with network metaanalysis for evidence synthesis has been published in mainstream medical journals [^{8}–^{12}], many dental researchers are still not aware of this new methodology, and, to the best of our knowledge, only a few network metaanalyses have appeared in dental journals [^{13}–^{16}]. The aim of this paper is therefore to provide a nontechnical introduction to network metaanalysis for dental research community and raise the awareness of it. In the next sections, we first explained the rationale and assumptions behind the network metaanalysis; then, we described the statistical model for the network metaanalysis and used an example from periodontology for illustration. In the final section, we discussed a few practical issues to be considered when conducting a network metaanalysis.
The basic rationale behind network metaanalysis is simple: suppose we have three treatments A, B, and C. Results from RCTs comparing A and B provide direct evidence on the difference in the treatment effects between A and B. In contrast, results from RCTs comparing A–C and those comparing BC provide indirect evidence on the difference between A and B. The three treatments A, B, and C therefore form a network for treatment effect comparisons (Figure 1). Let us use d_{AB}, d_{AC}, and d_{BC} to denote the differences in the treatment effects for AB, A–C, and BC comparisons, respectively. The difference in treatment effects between A and B from indirect comparisons is therefore d_{AC} − d_{BC} = d_{AB}^{Ind}. If d_{AB} is similar to d_{AB}^{Ind}, the direct and indirect evidence is consistent; otherwise, there is inconsistency in the evidence, that is, results from direct and indirect evidence are not the same.
There are several assumptions for the network metaanalysis to yield meaningful results [^{1}–^{4}]. The first assumption is homogeneity for standard metaanalysis, that is, all A–C trials are “comparable” and all BC trials are “comparable.” This is a universal assumption for all metaanalysis, although some heterogeneity increases the generalizability of results. However, whilst evidence may be homogeneous within a set of trials for certain pairwise comparisons, but it may not be so across sets of trials within the network. This leads us to the similarity assumption for the network metaanalysis, that is, the included trials are clinically and methodologically similar in term of key factors that modify the response to a treatment, such as patients' characteristics, study settings, lengths of followup, and outcome measurements. In other words, potential confounders for treatment effect comparisons are similarly distributed across included studies. When these two assumptions are questionable, results from direct and indirect evidence may be inconsistent, and consistency is the third assumption that will be discussed in the next section.
It has been suggested that results from the network metaanalysis may be less trustworthy than results from multiple pairwise comparisons, because indirect evidence is less reliable than direct evidence and more prone to biases [^{17}, ^{18}]. Whilst we agree that interpretation of results from the network metaanalysis always needs to be cautious because of potential biases, network metaanalysis is no more prone to biases that traditional metaanalysis, for instance, heterogeneity is also common in traditional metaanalysis. This is because the distinction between direct and indirect evidence is not meaningful in multiple treatments comparisons, as direct evidence for one comparison becomes indirect for some other comparisons [^{1}, ^{2}]. For example, trials including A and C are direct evidence for A–C comparisons, and trials including A and B are evidence for AB comparisons, but they are also indirect evidence for BC comparison. So the argument that results from mixed treatment comparison are less reliable than those from direct comparisons is untenable. We do agree that because the scope of a network metaanalysis is much broader than a traditional pairwise metaanalysis and a greater number of studies is included in the analysis, more resources and efforts are required to minimize potential errors and biases in the literature search, quality assessment, data analysis, and final interpretation of results [^{19}, ^{20}].
Consistency in direct and indirect evidence is another assumption behind network metaanalysis. Suppose results from trials comparing A with B show A is on average better than B, and trials comparing B with C show B is on average better than C, and indirect comparisons will then show A is better than C. If trials comparing A with C also show A is on average better than C, the indirect and direct evidence is consistent. However, what if direct evidence shows C is better than A? Does this contradiction mean that evidence from indirect comparisons is unreliable and should be disregarded?
If this argument is true, it implies the direct comparisons for AB and BC cannot be trusted either. This can be applied to all pairwise comparisons in the network. Therefore, when there is inconsistency in the direct and indirect evidence, the issue is not whether indirect comparisons are less reliable but how this inconsistency may be explained. If trials involved in the indirect comparisons have a better quality and fewer biases, results from indirect evidence may be more reliable than those from direct evidence. Heterogeneity in study protocols (e.g., doses, followup time, etc.), patient populations (age, underlying medical conditions, clinical settings, etc.), and methods for the assessment of outcomes is likely to be the source for inconsistency, while random variations may also cause inconsistency. Therefore, it is imperative to check consistency in evidence when undertaking network metaanalysis, and we will explain later in this paper how to conduct a simple test for checking it. Interpretation of network metaanalysis should always take inconsistency into account as the interpretation of traditional metaanalysis should take heterogeneity into account [^{21}–^{23}]. Assessment of quality and characteristics of included trials should be undertaken for network metaanalysis; thus, heterogeneity in evidence can be explored when inconsistency occurs.
Different statistical approaches have been proposed in the literature for comparing multiple treatments [^{5}, ^{7}]. A fixed effects model assumes a common effect behind the observed effects, while a random effects model assumes that the “true” effect follows a distribution. In this section, we introduce the random effects model approach as suggested by Whitehead [^{24}]:
(1)
f(yijk)=u+si+tj+(st)ij, 
(2)
θij=u+si+tj+(st)ij, 
Statistical models for network metaanalysis become more complex, when some of the included studies have more than 2 treatment arms. This is because the differences in treatment effects within a study with multiple arms are not independent. Currently, a Bayesian approach to network metaanalysis developed by researchers in the Bristol and Leicester Universities is the most popular approach in the literature and used for the analysis of our example data in the next section [^{26}, ^{27}]. The differences between nonBayesian and Bayesian approaches are mainly computational (i.e., the statistical algorithms for obtaining the results) rather than conceptual (i.e., the basic statistical models are the same).
Bayesian network metaanalysis, also known as mixed treatments comparison, uses a Bayesian statistical framework for a synthesis of direct and indirect comparisons of different treatments [^{8}–^{12}, ^{14}, ^{16}]. In the Bayesian paradigm, prior beliefs about parameters in the models are specified and factored into the estimation. For example, the mean treatment effect may be specified as 0.5 mm and with a standard error of 2 mm. However, in most scenarios, a noninformative prior is usually specified, for example, the mean effect is zero with a extremely large standard error. Posterior distributions of model parameters are then derived from the prior information and observed data [^{28}]. In the Bayesian network metaanalysis, noninformative prior is usually used to minimise the impact of prior information on final results, as evidence for supporting a specific treatment effect is generally lacking. A flat prior distribution such as a uniform distribution or a normal distribution with a large variance can be specified for a study on the difference in the therapeutic effects between two treatments; consequently, the posterior distributions were almost entirely derived from the observed data. For example, we can specify that the prior distribution of log hazard ratio in implant survival between two treatments for periimplantitis follows a normal distribution with zero mean and variance of 10,000. Suppose the observed variance of the difference between periodontal treatments is usually around 3 and 5, within which our prior distribution will consequently look flat and is therefore noninformative. As the probability distribution within the range of possible values is the same, the posterior distribution for the difference in log hazard ratio is mainly determined by the observed data.
In Bayesian analysis, posterior distributions are usually quite complex, so software packages use simulationsbased algorithms known as Markov Chain Monte Carlo method to derive the approximate posterior probability distributions. Markov Chain Monte Carlo method starts with a set of initial values and then runs an iteration process to obtain the approximate posterior distribution. Samples are then taken from these posterior distributions for calculating each parameter in the model. Because Bayesian approach is a simulationsbased methodology, it also has several other advantages. For instance, it can estimate predicted treatment effects based on the observed data, and it can provide ranking for treatments, which is especially useful when the differences between treatments are small. The statistical software for Bayesian approach is also more flexible than standard software in adapting to each unique situation where, for example, some studies have more than two treatment arms and where studies have different designs, such as parallelgroup and splitmouth design.
The downside to Bayesian approach is that the statistical theory and estimation method for Bayesian network metaanalysis are mathematically advanced, and the software for Bayesian analysis, such as WinBUGS, has a steep learning curve. The website of the department of communitybased medicine in Bristol University (https://www.bris.ac.uk/cobm/research/mpes/mtc.html/) contains many WinBUGS code examples for network metaanalysis, and researchers can modify those codes for their analysis.
In this section, we used an example to illustrate how to undertake a network metaanalysis. We recently conducted a systematic review for the effectiveness of guided tissue regeneration (GTR), enamel matrix derivatives (EMD), and their combination therapies on the treatment of periodontal infrabony lesions [^{16}]. In this tutorial, we used a subgroup of RCTs that compared GTR with nonresorbable or resorbable membranes to flap operation and that compared GTR with different types of membranes. The literature search strategy and quality assessment of included studies can be found in our previous publication. The outcome variable for our illustration is change in clinical attachment level (CAL), and we found 18 RCTs that compared at least two of the three treatments (flap operation, GTR with nonresorbable membranes, and GTR with resorbable membranes) [^{29}–^{46}]. One study [^{46}] was then excluded, because it did not report the standard errors for the treatment effects for different GTR treatment groups. One study [^{35}] had two GTR treatment groups with nonresorbable membranes, and results from the two groups were combined into one. Of the 17 studies, only one study [^{36}] compared all three treatment groups. Table 1 provided a summary for the 17 studies included in the final network metaanalysis.
Traditional pairwise comparisons only use the direct evidence, and they should be undertaken in order to evaluate the consistency in direct and indirect comparisons. We used statistical software Stata (Version 12, StataCorp, College Station, TX, USA) for the analysis, and results were shown in Figure 2. Six studies compared GTR with nonresorbable membrane (GTRN) to flap operation, and results from random effects metaanalysis showed GTRN achieved 1.99 mm (95% confidence intervals (CI): 1.02 to 2.95) greater CAL gain than flap operation. Twelve studies compared GTR with resorbable membranes (GTRR) to flap operation, and results from random effects metaanalysis showed GTRR achieved 1 mm (95% confidence intervals (CI): 0.61 to 1.39) greater CAL gain than flap operation. Both metaanalyses showed substantial heterogeneity: the CochraneQ test is statistically significant (P < 0.001), and the Isquared was 76% and 85%, respectively. Funnel plot and Egger test suggested there might be small study bias in the comparison between GTRR and flap operation (Figure 3). Only one study compares the two GTR treatments, and its results showed that GTRN achieved 0.6 mm (95%CI: −0.44 to 1.64) greater CAL gain than GTRR.
Bayesian network metaanalysis was then undertaken using the software WinBUGS (MRC Biostatistics Unit, Cambridge, England). WinBUGS codes used in our analysis were a modification of codes available on the website of the department of communitybased medicine in Bristol University to accommodate continuous outcomes and studies with splitmouth design. Noninformative priors were used throughout the analyses. Markov Chain Monte Carlo method with 50,000 burnin and further 50,000 simulations and with three chains of different initial values (i.e., 150,000 simulations in total) was used to obtain medians and 95% credible intervals (i.e., the 2.5 and 97.5 percentiles of simulation results), which may be interpreted as the likely range of the estimated parameter by excluding the extreme values. Results from the Bayesian network metaanalysis using the 17 studies were similar to those from the traditional pairwise comparison: GTRN and GTRR achieved 1.88 mm (95% credible intervals (CrI): 1.15 to 2.63) and 0.99 mm (95% CrI: 0.48 to 1.52) greater CAL gain than flap operation, respectively; GTRN achieved 0.88 mm (95% CrI: 0.09 to 1.78) greater CAL gain than GTRR. Figure 4 provided comparisons between results from the Bayesian and traditional metaanalysis.
Figure 4 showed that the three treatments in our network formed a loop, and, for every loop, it was possible to evaluate the consistency between direct and indirect evidence. For example, results from the single trial comparing GTRN to GTRR are direct comparison, whilst results from the traditional pairwise metaanalysis of the 6 trials comparing GTRN to flap operation and those from the 12 trials comparing GTRR to flap operation provide indirect comparisons between GTRN and GTRR by using flap operation as the reference treatment [^{47}]. We denote the difference in CAL gain for comparing GTRN to flap operation as d_{NF}, the difference in CAL gain for comparing GTRR to flap operation as d_{RF}, and the difference in CAL gain for comparing GTRN to GTRR as d_{NR}. The indirect comparison between GTRN and GTRR is therefore d_{NF} − d_{RF} = 1.99 − 1 = 0.99 = d_{NR}^{Ind}. The inconsistency is the difference between d_{NR} and d_{NR}^{Ind}: δ = d_{NR} − d_{NR}^{Ind} = 0.99 − 0.6 = 0.39. A simple statistical test for evaluating the inconsistency is [^{47}]:
(3)
z=δσδ2, 
(4)
σδ2σdNF2+σdRF2+σdNR2=(0.493)2+(0.201)2+(0.532)2=0.566,z=δσδ2=0.390.566=0.390.752=0.52. 
Note that, for any loop, results of testing inconsistency remain the same, irrespective of the reference group chosen from the loop.
Because Markov Chain Monte Carlo method for estimation used by Bayesian analysis is a simulationbased approach, we can calculate the rank for each treatment according its performance in each simulation [^{48}]. In 98.3% of simulations, GTRN ranked the best amongst the three treatments, and, in 1.7% of simulations, GTRR ranked the best; this is consistent with results for point estimates and their credible intervals. Information about Ranking is especially useful when the number of treatments in the network metaanalysis is large and the differences in their treatment effects are small. Figure 5 shows the treatment rankings for all three treatments.
As shown in our example, the main difference between a network metaanalysis and multiple pairwise metaanalyses for comparisons of multiple treatments is that the former use both direct and indirect evidence whilst the latter only use the direct evidence. All metaanalyses require comprehensive literature search, careful evaluation of available studies, and attentions to potential biases and heterogeneity. In this section, we discussed a few practical issues that may arise in conducting a network metaanalysis in dental research and provided some recommendations on how to deal with those issues.
Decisions on which studies should be included in the network metaanalysis are not always straightforward when undertaking network metaanalysis, because indirect evidence can be very broad [^{49}, ^{50}]. In our example, we included RCTs that compared at least two of the three treatments, GTRN, GTRR, and flap operation with the latter as the reference group. However, in terms of indirect comparisons, studies that contained one of even none of the three treatments could also be included. For example, studies that compared GTRN to enamel matrix derivatives (EMD) or EMD to flap operation provided indirect evidence for comparing GTRN with flap operation. Consequently, almost all RCTs on the treatment of periodontal infrabony lesions might be included in the network metaanalysis, and a practical decision has to be made for the inclusion criteria. This is why we decided that only studies that compared at least two of the three treatments were included. If the definition for relevant studies is too broad, the number of included studies will be large and results from network metaanalysis may be difficult to interpret due to the excessive heterogeneity and inconsistency in the evidence. The definition for relevant studies needs to be based on clinical knowledge; for instance, treatments or drugs that are either no longer used or available may be excluded. However, for a group of treatments within a network metaanalysis, the literature search should be comprehensive so that all eligible studies are included.
When there are more than two treatments in a trial, the studyspecific treatment effects are unlikely to be independent; for example, suppose a trial has three treatment arms, GTRN, GTRR, and flap operation, and they are carried out by experienced periodontists. Consequently, treatment effects of both GTRN and GTRR compared to flap operation are likely to be greater than those in a trial where treatments are carried out by a periodontist in training. Special care has to be taken to avoid using the same control group more than once in estimating the differences in treatment effects between the test groups and the control group [^{25}]. In our example, one study has three treatment arms, and it was assumed that the correlation between the two treatment effects differences (i.e., flap operation versus GTRN, and flap operation versus GTRR) was 0.5 following the suggestion by Lu and Ades [^{27}]. The impact on the network metaanalysis of disregarding the correlations among treatment effects depends on the number of studies with more than two treatment arms and the strength of those correlations.
In our example, there is no significant inconsistency in direct and indirect evidence, and, consequently, the discrepancy between results from traditional pairwise and Bayesian network metaanalyses is small. If the inconsistency test is significant, the discrepancy is likely to be large, as results from the Bayesian analysis are a combination of direct and indirect evidence. Substantial discrepancies usually indicate the heterogeneity, and similarity assumptions as discussed in Section 2.1 may be questionable, and researchers need to investigate the sources of heterogeneity. For instance, suppose treatment effects are related to baseline disease severity; if patients in A versus placebo trials have more severe baseline disease than those in B versus placebo trials, indirect comparisons will show that A seems to have greater treatment effects than B, even if there is no difference between A and B. In other scenarios, direct evidence comparing A with B may have a dubious quality and suffer a greater bias; consequently, indirect evidence becomes more reliable [^{51}]. Heterogeneity is an issue that should be investigated in any metaanalysis (including both pairwise and network metaanalyses), and, when there is inconsistency in direct and indirect evidence, characteristics of studies involved in comparisons should be carefully evaluated; if feasible, a metaregression or subgroup analysis should be undertaken to explore the sources of heterogeneity [^{21}–^{23}].
The most common missing information encountered in conducting a metaanalysis in dental research is the standard errors for the mean treatment effects which are usually used as the weights for combining the treatment effects reported by different studies, when the outcomes are continuous variables such as CAL. For binary outcomes, such as success or survival, treatment effects and its confidence intervals are derived from the numbers of patients in different categories, for example, the numbers of patients with or without success in different treatment groups. When the outcome is a continuous variable, we need the mean and its standard error for metaanalysis. The most common scenario is that a study reported the mean treatment effects and their standard errors without reporting the difference in treatment effects and its confidence intervals. Table 2 shows results from a hypothetic study with two treatments to illustrate how to impute the missing standard errors.
The change in the outcome CAL for the test group is 4.3 mm with standard deviation 1.3 mm, and the change in the outcome CAL for the control group is 1.9 mm with standard deviation 1.1 mm. Suppose this study uses a parallelgroup design and has 10 patients in each group; the mean difference in treatment effects between the test and control groups is 4.3 − 1.9 = 2.4, and its standard error (σ_{D}) can be obtained by using the following formula [^{52}]:
(5)
σD=S(1nT+1nC), 
(6)
S=[(nT−1)sT2+(nC−1)sC2(nT+nC−2)], 
(7)
S=[9(1.3)2+9(1.1)218]=1.69+1.212=1.204,σD=1.204(110+110)=0.54. 
In a study with parallelgroup design, the two treatments effects are supposed to be independent, but, in a study with splitmouth design (e.g., two teeth of the same patient are randomly assigned to the test and control groups), the treatment effects are likely to be correlated [^{53}] and (6) is no longer suitable for obtaining the pooled standard deviation S. Instead, we use the following formula to obtain S:
(8)
σD=Sn=sT2+sC2−2rsTsCn, 
(9)
σD=Sn=(1.69+1.21−0.5∗1.3∗1.1)10=0.47. 
Imputing missing values can increase the number of included studies in a metaanalysis, and this is especially useful for a network metaanalysis when the number of treatments in comparisons is large but the number of studies is relatively few.
Network metaanalysis is an extension of pairwise comparisons of treatments to comparisons of all available treatments by incorporating both direct and indirect evidence. This new methodology has become widely adopted by metaanalysts in medical research and has been proven to be a very useful tool for evidence synthesis. The use of more sophisticated statistical approaches such as network metaanalysis can improve the efficiency in comparative effectiveness research and in the quality of decisions making. This tutorial aims to bring this new methodology to the attentions of dental researchers and to facilitate its adoption but also highlight several important issues in conducting and interpreting a network metaanalysis. Further information and technical details can be found in [^{3}, ^{4}, ^{25}–^{27}]. The statistical theory behind network metaanalysis is nevertheless complex, so we strongly encourage close collaboration between dental researchers and experienced statisticians when planning and conducting a network metaanalysis.
The authors declare that they have no conflict of interests.
The first author was funded by the United Kingdom government's Higher Education Funding Council for England (HEFCE).
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