Bayesian Hierarchical Methods for Network Meta-Analysis

Abstract

In clinical practice, and at a wider societal level, treatment decisions in medicine need to consider all relevant evidence. Network meta-analysis (NMA) collectively analyzes many randomized controlled trials (RCTs) evaluating multiple interventions relevant to a treatment decision, expanding the scope of a conventional pairwise meta-analysis to simultaneously handle multiple treatment comparisons. NMA synthesizes both direct information, gained from direct comparison for example between treatments A and C, and indirect information obtained from A versus B and C versus B trials, and thus strengthens inference. Under current contrast-based (CB) 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, creating some unnecessary obstacles for patients to comprehensively understand and trade-off efficacy and safety measures. Many NMAs only report odds ratios (ORs) which are commonly misinterpreted as risk ratios (RRs) by many physicians, patients and their care givers. In order to overcome these obstacles of the CB methods, a novel Bayesian hierarchical arm-based (AB) model developed from a missing data perspective is proposed to illustrate how treatment-specific event proportions, risk differences (RD) and relative risks (RR) can be computed in NMAs. Since most of the trials in NMA only compare two of the treatments of interest, the typical data in a NMA managed as a trial-by-treatment matrix is extremely sparse, like an incomplete block structure with serious missing data problems. The previously proposed AB method assumes a missing at random (MAR) mechanism. However, in RCTs, nonignorable missingness or missingness not at random (MNAR) may occur due to deliberate choices at the design stage. In addition, those undertaking an NMA will often selectively choose treatments to include in the analysis, which will also lead to nonignorable missingness. We then extend the AB method to incorporate nonignorable missingness using \textit{selection models} method. Meta-analysts undertaking an NMA often selectively choose trials to include in the analysis. Thus inevitably, certain trials are more likely to be included in an NMA. In addition, it is difficult to include all existing trials that meet the inclusion criteria due to language barriers (i.e., some trials may be published using other languages) and other technical issues. If the omitted trials are quite different from the ones we include, then the estimates will be biased. We obtain empirical evidence on whether these selective inclusions of trials can make a difference in the results, such as treatment effect estimates in an NMA setting, using both the AB and CB methods. In the opposite direction of the fact that some trials which should have been included but are omitted, some trials may appear to deviate markedly from the others, and thus be inappropriate to be synthesized. we call these trials \textit{outlying trials} or \textit{trial-level outliers}. To the best of our knowledge, while the key NMA assumptions of inconsistency and heterogeneity have been well-studied, few previous authors have considered the issue of trial-level outliers, their detection, and guidance on whether or not to discard them from an NMA. We propose and evaluate Bayesian approaches to detect trial-level outliers in the NMA evidence structures.