A Bayesian approach to volumetric analysis in rare neurodegenerative disorders

Identifying regional brain atrophy is critical for understanding neurodegenerative disorders. Traditionally, group comparisons rely on frequentist statistics, utilising $p$-values and point estimates that offer limited characterization of uncertainty. Bayesian methods provide an alternative by estimating effect sizes and credible intervals while incorporating prior knowledge and uncertainty. This study evaluated the feasibility of Bayesian hierarchical modelling to assess regional brain atrophy in Progressive Supranuclear Palsy (PSP) and Corticobasal Syndrome (CBS) compared to healthy controls. Participants meeting diagnostic criteria for CBS or PSP, together with healthy controls, were recruited from the Cambridge Centre for Parkinson-plus. Grey matter volume, cortical thickness, and subcortical volumes were derived using FreeSurfer for 210 cortical and 36 subcortical regions defined by the Human Brainnetome Atlas. Participants with PSP were classified into Richardson syndrome (PSP-RS), corticobasal syndrome variant (PSP-CBS), frontal variant (PSP-F), and other presentations (PSP-Other). Bayesian hierarchical ANOVA models with appropriate priors were used to estimate group differences. Regions of practical equivalence (ROPE) were calculated to assess evidence of meaningful group effects. A total of 428 people were included (113 PSP-RS, 30 PSP-CBS, 23 PSP-Other, 19 PSP-F, 81 CBS, and 162 healthy controls). For grey matter volume, there was evidence of whole brain volume loss compared to controls for all disease groups except PSP-Other, which showed evidence of no difference. For cortical thickness, there was evidence of global cortical thinning in CBS compared to controls, but for no other group. For subcortical volume all groups showed evidence of volume loss compared to controls. Patterns of regional atrophy were identified in keeping with previous literature, with the largest effect observed in the left pre-motor thalamus (30\% reduction in CBS). There was greater loss of subcortical volume in PSP-RS compared to other PSP subgroups. Bayesian hierarchical modelling provides a feasible framework for quantifying regional brain atrophy, with interpretable effect size estimates and uncertainty measures. This approach complements conventional statistical methods, particularly in the assessment of rare neurodegenerative and neuropsychiatric disorders.