Non-Gaussian Normative Modelling With Hierarchical Bayesian Regression

Abstract

AbstractNormative modelling is an emerging technique for parsing heterogeneity in clinical cohorts. This can be implemented in practice using hierarchical Bayesian regression, which provides an elegant probabilistic solution to handle site variation in a federated learning framework. However, applications of this method to date have employed a Gaussian assumption, which may be restrictive in some applications. We have extended the hierarchical Bayesian regression framework to flexibly model non-Gaussian data with heteroskdastic skewness and kurtosis. To this end, we employ a flexible distribution from the sinh-arcsinh (SHASH) family, and introduce a novel reparameterisation that is more suitable for Markov chain Monte Carlo sampling than existing variants. Using a large neuroimaging dataset collected at 82 different sites, we show that the results achieved with this extension are better than a warped Bayesian linear regression baseline model on most datasets. We also demonstrate that the attained flexibility is essential for accurately modelling highly nonlinear relationships between aging and imaging derived phenotypes, which shows that the extension is important for pushing the field of normative modelling forward. All methods described here are available in the open-sourcepcntoolkit.HighlightsWe extended the Hierarchical Bayesian Regression framework for normative modellingOur extension allows modelling data with heteroskedastic skewness and kurtosisWe developed a reparameterization of the SHASH distribution, suitable for samplingWe provide the first implementation of the SHASH distribution in a fully Bayesian frameworkResults show that the extension outperforms current methods on various measures