Network meta-analysis made simple: a composite likelihood approach

Network meta-analysis, also known as mixed treatments 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 network meta-analysis 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 paper 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 a network meta-analysis comparing interventions for primary open-angle glaucoma, and another comparing treatments for chronic prostatitis and chronic pelvic pain syndrome. Highlights What is already known? Network meta-analysis extends conventional pairwise meta-analysis by simultaneously synthesizing multiple interventions in a single integrated analysis. A significant challenge in network meta-analysis is the lack of reported within-study correlations among treatment comparisons in the published studies. What is new? We propose a new method for network meta-analysis that ensures vaild statistical inference without the need for knowledge of within-study correlations. The proposed method employs a composite likelihood and a sandwich-type robust variance estimator, offering a computationally efficient and scalable solution, particularly for network meta-analysis with a large number of treatments and studies. Potential impact for Research Synthesis Methods readers The proposed method can be easily applied to any univariate network meta-analysis project without requiring knowledge of within-study correlations among treatment comparisons.