Simplifying Disease Staging Models into a Single Anatomical Axis - A Case Study of Aortic Coarctation In-utero

Statistical shape modelling and classification methods are used to study characteristic disease phenotypes, to derive novel shape biomarkers, and to extract insights into disease mechanisms. Linear classification models are commonly chosen due to their ability to provide a single score, as well as easy-to-interpret characteristic shapes. In disease staging models, a multi-class problem is generally set. Then, one would expect that the set of linear models comparing any pair of classes will lead to the same unique anatomical axis capturing characteristic shapes for each group in the disease spectrum, and a unique mechanistic interpretation. In this work, we aim to explore the validity of this assumption and assess the confidence in simplifying both mechanistic interpretations and clinical classification performance into a single axis in disease staging models. To do so, we used a statistical shape model of fetal great arteries in cases with suspected coarctation of the aorta. Data included control, false positive and confirmed coarctation cases, representative of three categories of developmental impairment from the disease spectrum. Principal component analysis combined with a fisher linear discriminant analysis was used to explore phenotypes associated with each group and classification performance. A combination of classification overfitting, a co-linearity index between axes, and the three-dimensional extreme phenotypes provided useful information for simplification into a single anatomical axis. Careful consideration should be taken in disease progression studies where either overfitting or co-linearity are compromised, as the simplification with a single anatomical axis might lead to the inference of misleading mechanisms associated with disease.