STATISTICAL METHODS FOR ARM-BASED BAYESIAN NETWORK META-ANALYSIS

Abstract

Network meta-analysis (NMA) is a recently developed tool to combine and contrast direct and indirect evidence in systematic reviews of multiple treatments. Compared to traditional pairwise meta-analysis, it can improve statistical efficiency and reduce certain biases. Unlike the contrast-based NMA approach, which focuses on estimating relative effects such as odds ratios, the arm-based (AB) NMA approach can estimate absolute effects (such as the overall treatment-specific event rates), which are arguably more useful in medicine and public health, as well as relative effects. In AB-NMA, treatment-specific variances are needed to estimate treatment-specific overall effects, while accurate estimation of correlation coefficients is critical to allow borrowing information across treatments. However, partially due to the lack of information, the estimation of correlation coefficients and variances can be biased and unstable if we use the conjugate priors (e.g., the inverse-Wishart (IW) distribution) for the covariance matrix. To address the first challenge of accurately estimating correlation coefficients, several separation strategies (i.e., separate priors on variances and correlations) can be considered. To study the IW prior's impact on AB-NMA and compare it with separation strategies, we did simulation studies under different missing-treatment mechanisms. A separation strategy with appropriate priors for the correlation matrix (e.g., equal correlations) performs better than the IW prior and is thus recommended as the default vague prior in the AB approach. To address the second challenge of variance estimation, we can either assume the variances of different treatments share a common distribution with unknown hyper-parameters (variance shrinkage) or in AB-NMA, borrow information from single arm studies (variance extrapolation). We did simulation studies to evaluate the performance of the proposed approaches and to illustrate the importance of variance shrinkage or variance extrapolation when the number of clinical studies involving each treatment is relatively small. The above results are further illustrated by multiple case studies.