Generalized Fused Lasso for Treatment Pooling in Network Meta-Analysis

This work develops a generalized fused lasso (GFL) approach to fitting contrast-based network meta-analysis (NMA) models. The GFL method penalizes all pairwise differences between treatment effects, resulting in the pooling of treatments that are not sufficiently different. This approach offers an intriguing avenue for potentially mitigating biases in treatment rankings and reducing sparsity in networks. To fit contrast-based NMA models within the GFL framework, we formulate the models as generalized least squares problems, where the precision matrix depends on the standard error in the data, the estimated between-study heterogeneity and the correlation between contrasts in multi-arm studies. By utilizing a Cholesky decomposition of the precision matrix, we linearly transform the data vector and design matrix to frame NMA within the GFL framework. We demonstrate how to construct the GFL penalty such that every pairwise difference is penalized similarly. The model is straightforward to implement in R via the "genlasso" package, and runs instantaneously, contrary to other regularization approaches that are Bayesian. A two-step GFL-NMA approach is recommended to obtain measures of uncertainty associated with the (pooled) relative treatment effects. Two simulation studies confirm the GFL approach's ability to pool treatments that have the same (or similar) effects while also revealing when incorrect pooling may occur, and its potential benefits against alternative methods. The novel GFL-NMA method is successfully applied to a real-world dataset on diabetes where the standard NMA model was not favored compared to the best-fitting GFL-NMA model with AICc selection of the tuning parameter ( $\Delta AICc>13)$ .