Towards a more reliable assessment of aortic diameters using a Bayesian Z-score

The Z-score is a conceptually simple and widely adopted standard for assessing aortic dilatation from echocardiographic measurements. It is routinely used to monitor patient progression and schedule follow-up checks. However, several criticisms have been raised due to the intrinsic limitations of the typically homoscedastic and linear predictive models. In this paper, we reinterpret the Z-score as a quantitative measure of the aleatoric uncertainty affecting aortic diameters, after indexing by a limited number of predictive variables. This view reveals an additional, previously overlooked limitation: the presence of epistemic uncertainty, arising from limited or biased reference datasets. When epistemic uncertainty is high, the Z-score becomes unreliable, yet current tools fail to indicate this. We therefore adopt a Bayesian reformulation based on heteroscedastic Gaussian process regression, where diameters and their aleatoric uncertainties are modeled as random variables. In this framework, the Z-score itself is random, and clinicians receive both an expected value and a high density interval quantifying epistemic uncertainty. Trained on a merged dataset of 1,947 healthy subjects, our Bayesian Z-score detects more dilatations in at-risk patients, identifies uncertain cases, and offers a more reliable basis for clinical decision-making.