The contrast-based model (CBM) is the most popular network meta-analysis (NMA) method, although alternative approaches, e.g., the baseline model (BM), have been proposed but seldom used. This article aims to illuminate the difference between the CBM and BM and explores when they produce different results. These models differ in key assumptions: The CBM assumes treatment contrasts are exchangeable across trials and models the reference (baseline) treatment’s outcome levels as fixed effects, while the BM further assumes that the baseline treatment’s outcome levels are exchangeable across trials and treats them as random effects. We show algebraically and graphically that the difference between the CBM and BM is analogous to the difference between the two analyses in a statistical conundrum called Lord’s Paradox, in which the t-test and analysis of covariance (ANCOVA) yield conflicting conclusions about the group difference in weight gain. We show that this conflict arises because the t-test compares the observed weight change, whereas ANCOVA compares an adjusted weight change. In NMA, analogously, the CBM compares observed treatment contrasts, while the BM compares adjusted treatment contrasts. We demonstrate how the difference in modeling baseline effects can cause the CBM and BM to give different results. The analogy of Lord’s Paradox provides insights into the different assumptions of the CBM and BM regarding the relationship between baseline effects and treatment contrasts. When these two models produce substantially different results, it may indicate a violation of the transitivity assumption. Therefore, we should be cautious in interpreting the results from either model.

For network meta-analysis (NMA), we usually assume that the treatment arms are independent within each included trial. This assumption is justified for parallel design trials and leads to a property we call consistency of variances for both multi-arm trials and NMA estimates. However, the assumption is violated for trials with correlated arms, for example, split-body trials. For multi-arm trials with correlated arms, the variance of a contrast is not the sum of the arm-based variances, but comes with a correlation term. This may lead to violations of variance consistency, and the inconsistency of variances may even propagate to the NMA estimates. We explain this using a geometric analogy where three-arm trials correspond to triangles and four-arm trials correspond to tetrahedrons. We also investigate which information has to be extracted for a multi-arm trial with correlated arms and provide an algorithm to analyze NMAs including such trials.

Network meta-analysis (NMA) is becoming increasingly important, especially in the field of medicine, as it allows for comparisons across multiple trials with different interventions. For time-to-event data, that is, survival data, traditional NMA based on the proportional hazards (PH) assumption simply synthesizes reported hazard ratios (HRs). Novel methods for NMA based on the non-PH assumption have been proposed and implemented using R software. However, these methods often involve complex methodologies and require advanced programming skills, creating a barrier for many researchers. Therefore, we developed an R Shiny tool, NMAsurv (https://psurvivala.shinyapps.io/NMAsurv/). NMAsurv allows users with little or zero background in R to conduct survival-data-based NMA effortlessly. The tool supports various functions such as drawing network plots, testing the PH assumption, and building NMA models. Users can input either reconstructed pseudo-individual participant data or aggregated data. NMAsurv offers a user-friendly interface for extracting parameter estimations from various NMA models, including fractional polynomial, piecewise exponential models, parametric survival models, Cox PH model, and generalized gamma model. Additionally, it enables users to effortlessly create survival and HR plots. All operations can be performed by an intuitive “point-and-click” interface. In this study, we introduce all the functionalities and features of NMAsurv and demonstrate its application using a real-world NMA example.

Network meta-analysis (NMA) enables simultaneous assessment of multiple treatments by combining both direct and indirect evidence. While NMAs are increasingly important in healthcare decision-making, challenges remain due to limited direct comparisons between treatments. This data sparsity complicates the accurate estimation of correlations among treatments in arm-based NMA (AB-NMA). To address these challenges, we introduce a novel sensitivity analysis tool tailored for AB-NMA. This study pioneers a tipping point analysis within a Bayesian framework, specifically targeting correlation parameters to assess their influence on the robustness of conclusions about relative treatment effects. The analysis explores changes in the conclusion based on whether the 95% credible interval includes the null value (referred to as the interval conclusion) and the magnitude of point estimates. Applying this approach to multiple NMA datasets, including 112 treatment pairs, we identified tipping points in 13 pairs (11.6%) for interval conclusion change and in 29 pairs (25.9%) for magnitude change with a threshold at 15%. These findings underscore potential commonality in tipping points and emphasize the importance of our proposed analysis, especially in networks with sparse direct comparisons or wide credible intervals for correlation estimates. A case study provides a visual illustration and interpretation of the tipping point analysis. We recommend integrating this tipping point analysis as a standard practice in AB-NMA.

The importance of network meta-analysis (NMA) methods for time-to-event (TTE) that do not rely on the proportional hazard (PH) assumption is increasingly recognized in oncology, where clinical trials evaluating new interventions versus standard comparators often violate this assumption. However, existing NMA methods that allow for time-varying treatment effects do not directly leverage individual events and censor times that can be reconstructed from Kaplan–Meier curves, which may be more accurate than discrete hazards. They are also challenging to implement given reparameterizations that rely on discrete hazards. Additionally, two-step methods require assumptions regarding within-study normality and variance. We propose a one-step fully Bayesian parametric individual patient data (IPD)-NMA model that fits TTE data with the exact likelihood and allows for time-varying treatment effects. We define fixed or random effects with the following distributions: Weibull, Gompertz, log-normal, log-logistic, gamma, or generalized gamma distributions. We apply the one-step model to a network of randomized controlled trials (RCTs) evaluating multiple interventions for advanced melanoma and compare results with those obtained with the two-step approach. Additionally, a simulation study was performed to compare the proposed one-step method to the two-step method. The one-step method allows for straightforward model selection among the “standard” distributions, now including gamma and generalized gamma, with treatment effects on either the scale alone or with multivariate treatment effects. Generalized gamma offers flexibility to model U-shaped hazards within a network of RCTs, with accessible interpretation of parameters that simplifies to exponential, Weibull, log-normal, or gamma in special cases.

Network meta-analysis allows the synthesis of relative effects from several treatments. Two broad approaches are available to synthesize the data: arm-synthesis and contrast-synthesis, with several models that can be fitted within each. Limited evaluations comparing these approaches are available. We re-analyzed 118 networks of interventions with binary outcomes using three contrast-synthesis models (CSM; one fitted in a frequentist framework and two in a Bayesian framework) and two arm-synthesis models (ASM; both fitted in a Bayesian framework). We compared the estimated log odds ratios, their standard errors, ranking measures and the between-trial heterogeneity using the different models and investigated if differences in the results were modified by network characteristics. In general, we observed good agreement with respect to the odds ratios, their standard errors and the ranking metrics between the two Bayesian CSMs. However, differences were observed when comparing the frequentist CSM and the ASMs to each other and to the Bayesian CSMs. The network characteristics that we investigated, which represented the connectedness of the networks and rareness of events, were associated with the differences observed between models, but no single factor was associated with the differences across all of the metrics. In conclusion, we found that different models used to synthesize evidence in a network meta-analysis (NMA) can yield different estimates of odds ratios and standard errors that can impact the final ranking of the treatment options compared.

The treatment recommendation based on a network meta-analysis (NMA) is usually the single treatment with the highest expected value (EV) on an evaluative function. We explore approaches that recommend multiple treatments and that penalise uncertainty, making them suitable for risk-averse decision-makers. We introduce loss-adjusted EV (LaEV) and compare it to GRADE and three probability-based rankings. We define properties of a valid ranking under uncertainty and other desirable properties of ranking systems. A two-stage process is proposed: the first identifies treatments superior to the reference treatment; the second identifies those that are also within a minimal clinically important difference (MCID) of the best treatment. Decision rules and ranking systems are compared on stylised examples and 10 NMAs used in NICE (National Institute of Health and Care Excellence) guidelines. Only LaEV reliably delivers valid rankings under uncertainty and has all the desirable properties. In 10 NMAs comparing between 5 and 41 treatments, an EV decision maker would recommend 4–14 treatments, and LaEV 0–3 (median 2) fewer. GRADE rules give rise to anomalies, and, like the probability-based rankings, the number of treatments recommended depends on arbitrary probability cutoffs. Among treatments that are superior to the reference, GRADE privileges the more uncertain ones, and in 3/10 cases, GRADE failed to recommend the treatment with the highest EV and LaEV. A two-stage approach based on MCID ensures that EV- and LaEV-based rules recommend a clinically appropriate number of treatments. For a risk-averse decision maker, LaEV is conservative, simple to implement, and has an independent theoretical foundation.

Network meta-analysis (NMA), also known as mixed treatment comparison meta-analysis or multiple treatments meta-analysis, extends conventional pairwise meta-analysis by simultaneously synthesizing multiple interventions in a single integrated analysis. Despite the growing popularity of NMA within comparative effectiveness research, it comes with potential challenges. For example, within-study correlations among treatment comparisons are rarely reported in the published literature. Yet, these correlations are pivotal for valid statistical inference. As demonstrated in earlier studies, ignoring these correlations can inflate mean squared errors of the resulting point estimates and lead to inaccurate standard error estimates. This article introduces a composite likelihood-based approach that ensures accurate statistical inference without requiring knowledge of the within-study correlations. The proposed method is computationally robust and efficient, with substantially reduced computational time compared to the state-of-the-science methods implemented in R packages. The proposed method was evaluated through extensive simulations and applied to two important applications including an NMA comparing interventions for primary open-angle glaucoma, and another comparing treatments for chronic prostatitis and chronic pelvic pain syndrome.

Several methods have been proposed for the synthesis of continuous outcomes reported on different scales, including the Standardised Mean Difference (SMD) and the Ratio of Means (RoM). SMDs can be formed by dividing the study mean treatment effect either by a study-specific (Study-SMD) or a scale-specific (Scale-SMD) standard deviation (SD). We compared the performance of RoM to the different standardisation methods with and without meta-regression (MR) on baseline severity, in a Bayesian network meta-analysis (NMA) of 14 treatments for depression, reported on five different scales. There was substantial between-study variation in the SDs reported on the same scale. Based on the Deviance Information Criterion, RoM was preferred as having better model fit than the SMD models. Model fit for SMD models was not improved with meta-regression. Percentage shrinkage was used as a scale-independent measure with higher % shrinkage indicating lower heterogeneity. Heterogeneity was lowest for RoM (20.5% shrinkage), then Scale-SMD (18.2% shrinkage), and highest for Study-SMD (16.7% shrinkage). Model choice impacted which treatment was estimated to be most effective. However, all models picked out the same three highest-ranked treatments using the GRADE criteria. Alongside other indicators, higher shrinkage of RoM models suggests that treatments for depression act multiplicatively rather than additively. Further research is needed to determine whether these findings extend to Patient- and Clinician-Reported Outcomes used in other application areas. Where treatment effects are additive, we recommend using Scale-SMD for standardisation to avoid the additional heterogeneity introduced by Study-SMD.

Effect modification occurs when a covariate alters the relative effectiveness of treatment compared to control. It is widely understood that, when effect modification is present, treatment recommendations may vary by population and by subgroups within the population. Population-adjustment methods are increasingly used to adjust for differences in effect modifiers between study populations and to produce population-adjusted estimates in a relevant target population for decision-making. It is also widely understood that marginal and conditional estimands for non-collapsible effect measures, such as odds ratios or hazard ratios, do not in general coincide even without effect modification. However, the consequences of both non-collapsibility and effect modification together are little-discussed in the literature.

In this article, we set out the definitions of conditional and marginal estimands, illustrate their properties when effect modification is present, and discuss the implications for decision-making. In particular, we show that effect modification can result in conflicting treatment rankings between conditional and marginal estimates. This is because conditional and marginal estimands correspond to different decision questions that are no longer aligned when effect modification is present. For time-to-event outcomes, the presence of covariates implies that marginal hazard ratios are time-varying, and effect modification can cause marginal hazard curves to cross. We conclude with practical recommendations for decision-making in the presence of effect modification, based on pragmatic comparisons of both conditional and marginal estimates in the decision target population. Currently, multilevel network meta-regression is the only population-adjustment method capable of producing both conditional and marginal estimates, in any decision target population.

Vitamin D deficiency in infants is widely prevalent. Most paediatric professional associations recommend routine vitamin D prophylaxis for infants. However, the optimal dose and duration of supplementation are still debated. We aimed to compare the efficacy and safety of different vitamin D supplementation regimens in term and late preterm neonates. For this systematic review and network meta-analysis, we searched MEDLINE, the Cochrane Central Register of Controlled Trials and Embase. Randomised and quasi-randomised clinical trials that evaluated any enteral vitamin D supplementation regimen initiated within 6 weeks of life were included. Two researchers independently extracted data on study characteristics and outcomes and assessed quality of included studies. A network meta-analysis with a Bayesian random-effects model was used for data synthesis. Certainty of evidence (CoE) was assessed using GRADE. Primary outcomes were mean serum vitamin D concentrations and the proportion of infants with vitamin D insufficiency (VDI). We included twenty-nine trials that evaluated fourteen different regimens of vitamin D supplementation. While all dosage regimens of ≥400 IU/d increased the mean 25(OH)D levels compared with no treatment, supplementation of ≤250 IU/d and 1400 IU/week did not. The CoE varied from very low to high. Low CoE indicated that 1600 IU/d, compared with lower dosages, reduced the proportion of infants with VDI. However, our results indicated that any dosage of ≥800 IU/d increased the risk of hypervitaminosis D and hypercalcaemia. Data on major clinical outcomes were sparse. Vitamin D supplementation of 400–600 IU/d may be the most effective and safest in infants.

We employed a Bayesian network meta-analysis for comparison of the efficacy and tolerability of US Food and Drug Administration (FDA)-approved atypical antipsychotics (AAPs) for the treatment of bipolar patients with depressive episodes. Sixteen randomized controlled trials with 7234 patients treated by one of the five AAPs (cariprazine, lumateperone, lurasidone, olanzapine, and quetiapine) were included. For the response rate (defined as an improvement of ≥50% from baseline on the Montgomery-Åsberg Depression Rating Scale [MADRS]), all AAPs were more efficacious than placebo. For the remission rate (defined as the endpoint of MADRS ≤12 or ≤ 10), cariprazine, lurasidone, olanzapine, and quetiapine had higher remission rates than placebo. In terms of tolerability, olanzapine was unexpectedly associated with lower odds of all-cause discontinuation in comparison with placebo, whereas quetiapine was associated with higher odds of discontinuation due to adverse events than placebo. Compared with placebo, lumateperone, olanzapine, and quetiapine showed higher odds of somnolence. Lumateperone had a lower rate of ≥ weight gain of 7% than placebo and other treatments. Olanzapine was associated with a significant increase from baseline in total cholesterol and triglycerides than placebo. These findings inform individualized prescriptions of AAPs for treating bipolar depression in clinical practice.

We aim to assess the relationship between validated smoking cessation pharmacotherapies and electronic cigarettes (e-cigarettes) and insomnia and parasomnia using a systematic review and a network meta-analysis. A systematic search was performed until August 2022 in the following databases: PUBMED, COCHRANE, CLINICALTRIAL. Randomized controlled studies against placebo or validated therapeutic smoking cessation methods and e-cigarettes in adult smokers without unstable or psychiatric comorbidity were included. The primary outcome was the presence of “insomnia” and “parasomnia.” A total of 1261 studies were selected. Thirty-seven studies were included in the quantitative analysis (34 for insomnia and 23 for parasomnia). The reported interventions were varenicline (23 studies), nicotine replacement therapy (NRT, 10 studies), bupropion (15 studies). No studies on e-cigarettes were included. Bayesian analyses found that insomnia and parasomnia are more frequent with smoking cessation therapies than placebo except for bupropion. Insomnia was less frequent with nicotine substitutes but more frequent with bupropion than the over pharmacotherapies. Parasomnia are less frequent with bupropion but more frequent with varenicline than the over pharmacotherapies. Validated smoking cessation pharmacotherapies can induce sleep disturbances with different degrees of frequency. Our network meta-analysis shows a more favorable profile of nicotine substitutes for insomnia and bupropion for parasomnia. It seems essential to systematize the assessment of sleep disturbances in the initiation of smoking cessation treatment. This could help professionals to personalize the choice of treatment according to sleep parameters of each patient. Considering co-addictions, broadening the populations studied and standardizing the measurement are additional avenues for future research.