Bayesian hierarchical models for network meta-analysis incorporating nonignorable missingness

Abstract

Network meta-analysis expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatments, synthesizing both direct and indirect information and thus strengthening inference. Since most of trials only compare two treatments, a typical data set in a network meta-analysis managed as a trial-by-treatment matrix is extremely sparse, like an incomplete block structure with significant missing data. Zhang et al. proposed an arm-based method accounting for correlations among different treatments within the same trial and assuming that absent arms are missing at random. However, in randomized controlled trials, nonignorable missingness or missingness not at random may occur due to deliberate choices of treatments at the design stage. In addition, those undertaking a network metaanalysis may selectively choose treatments to include in the analysis, which may also lead to missingness not at random. In this paper, we extend our previous work to incorporate missingness not at random using selection models. The proposed method is then applied to two network meta-analyses and evaluated through extensive simulation studies. We also provide comprehensive comparisons of a commonly used contrast-based method and the arm-based method via simulations in a technical appendix under missing completely at random and missing at random.

The Impact of Excluding Trials from Network Meta-Analyses – An Empirical Study

“…The AB approach focuses on absolute risks for each treatment arm, while the CB approach focuses on relative effects (e.g., ORs under binary case). Existing literature [1–4, 31, 32] has explored and discussed the model assumptions and model fit of the two approaches, and two recent discussion papers have further provided detailed comparisons on their strengths and limitations; see [33, 34]. …”

“…For the AB approach proposed by Zhang et al [1, 4], it specifies y ik ~ Bin ( n ik , p ik ), k ∈ S i , i = 1,…, I , and Φ −1 (p ik ) = μ k + σv ik , ( v i 1 ,…, v ik ) T ~ MVN (0, R K ). Here μ k is the fixed treatment effect for the k th treatment, σ is the standard deviation for the random effects v ik , and R K is an exchangeable correlation matrix.…”

“…Network meta-analysis (NMA) expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatment options [1–4] by collectively synthesizing direct evidence within trials and indirect evidence across trials. In the simplest case, one may be interested in comparing two treatments A and B.…”

“…We investigate both the AB [1, 4] and CB [3] (a more general version than in [2]) NMA approaches by reanalyzing 20 published NMAs with binary outcomes. The impact on treatment rankings and inconsistency between direct and indirect evidence are also assessed based on the AB approach.…”

CORR Insights®: Can We Estimate Short- and Intermediate-term Survival in Patients Undergoing Surgery for Metastatic Bone Disease?

“…Their model is based on Bayesian belief network analysis, a form of artificial intelligence that can account for missing data based on probabilities [8,17]. The Bayesian predictive model can manage big data, which is becoming more central to the medical field [6].…”