Network meta-analysis of randomized clinical trials: Reporting the proper summaries

Abstract

Background In the absence of sufficient data directly comparing two or more treatments, indirect comparisons using network meta-analyses (NMA) across trials can potentially provide useful information to guide the use of treatments. Under current contrast-based methods for NMA of binary outcomes, which do not model the “baseline” risks and focus on modeling the relative treatment effects, the patient-centered measures including the overall treatment-specific event rates and risk differences are not provided, which may create some unnecessary obstacles for patients to comprehensively understand and trade-off efficacy and safety measures. Many NMAs only report odds ratios which are commonly misinterpreted as risk ratios by many physicians, patients and their care givers. Purpose We aim to develop network meta-analysis to accurately estimate the overall treatment-specific event rates. Methods A novel Bayesian hierarchical model, developed from a missing data perspective, that borrows information across multiple treatment arms, is used to illustrate how treatment-specific event proportions, risk differences (RD) and relative risks (RR) can be computed in NMAs. We first compare our approach to alternative methods using two hypothetical NMAs assuming either a fixe RR or a fixed RD, and then use two published NMAs on new-generation anti-depressants and antimanic drugs to illustrate the improved reporting of NMAs possible with this new approach. Results In the hypothetical NMAs, our approach outperforms current contrast-based NMA methods in terms of bias. In the NMAs on new-generation anti-depressants and on antimanic drugs, the outcomes were common with proportions ranging from 0.21 to 0.62. As expected, the RR estimates differ from ORs. In addition, differences in the magnitude of relative treatment effects and the statistical significance of several pairwise comparisons from previous report could lead to different treatment recommendations. Limitations First, to facilitate the estimation of overall treatment-specific event proportions, we assume that each study hypothetically compares all treatments, with unstudied arms being missing at random conditional on the observed arms. However, it is plausible that investigators may have selected treatment arms on purpose based on the results of previous trials, which may lead to “nonignorable missingness” and potentially bias our event rate estimation. Second, we have not considered methods to identify and account for potential inconsistency in our missing data network meta-analysis framework. Both methods await further development. Conclusions The proposed NMA method can accurately estimate treatment-specific event rates or proportions, RDs, and RRs, and is recommended in practice. Application of this approach can lead to different conclusions, as illustrated here, from current NMA models that only estimate ORs.

Detecting outlying trials in network meta‐analysis

“…Among other authors, Zhang et al [6] have proposed an arm-based NMA model for binary data. Here we modify their model to adapt to the Gaussian diabetes data as follows: $$y_{ik}~Ntrue({\mathrm{\Delta }}_{ik},\frac{{\sigma }^2}{n_{ik}}true)$$ $$S{d}_{ik}^2~\text{italicGamma}true(\frac{n_{ik}-1}{2},\frac{n_{ik}-1}{2{\sigma }^2}true)$$ $$\text{and}{\mathrm{\Delta }}_{ik}={\mu }_k+\gamma {\nu }_{ik},$$ where the observations y ik (most often thought of as group means ${ȳ}_{ik}=\frac{1}{n_{ik}}\sum _{j=1}^{n_{ik}}{y}_{ikj}$) represent the mean response change of HbA1c over n ik patients assigned to the k th treatment in the i th trial.…”

Comparing the effectiveness profile of pharmacological interventions used for orthodontic pain relief: an arm-based multilevel network meta-analysis of longitudinal data

“…This because in an arm-based NMA, it is assumed that each study hypothetically compares all interventions, many of which are missing by design and thus can be considered as missing at random (4). However, to compare an intervention effect against a single reference group, we used the 'Control' group as a comparator in our presentation of results of the NMA.…”

“…However, PMAs are limited in their Comparative Effectiveness Research (CER) based decision making value because such conventional meta-analysis approach does not utilize all the available evidence if direct comparisons are not provided by all studies included in the analysis (3,4). Network meta-analysis (NMA) has extended this concept of CER by providing estimates for comparative effectiveness of all competing interventions even when no head-head comparisons are available (3,4).…”

“…Network meta-analysis (NMA) has extended this concept of CER by providing estimates for comparative effectiveness of all competing interventions even when no head-head comparisons are available (3,4). Recently, Sandhu et al (5) conducted a NMA to examine the effectiveness of various intentions used for orthodontic pain relief.…”

Comparative effectiveness of pharmacologic and nonpharmacologic interventions for orthodontic pain relief at peak pain intensity: A Bayesian network meta-analysis

“…9,10 The network metaanalysis, also called mixed treatment comparison, has extended this concept of comparative effectiveness research by providing estimates for comparative effectiveness of all competing treatments even when no head-tohead comparisons are available. [8][9][10] Synthesizing all available evidence (direct and indirect) also usually improves the precision of the estimates. Therefore, it is recommended that even when pairwise meta-analyses exist for any condition, the results obtained from network meta-analyses are more precise.…”