Distributed Lag Regression Methods and Compartmental Models for Analysis of Disease Progression

Abstract

ANCA vasculitis is an autoimmune disease characterised by relapses, or flares, that can have a severe detrimental impact on patient health. Flares can be prevented by suppressing the immune system but this exposes the patient to infection. It is hard to prepare patients for flares since clinicians are still unclear on how to predict flare events. Some attention has been given on uncovering any environmental predictors but so far results have been inconclusive. Investigating this for ourselves is the main focus of this thesis.

We construct a distributed lag / MIDAS model to analyse the accumulation of environmental exposure over time in a parsimonious manner, and how that may impact the probability of a flare occurring. Our model employs Bayesian variable selection and adjustment for imbalanced response data using latent variable representation and reversible-jump MCMC. The construction of this model is the primary novel contribution of this thesis.

The method is validated via simulation study, and then applied to real data comprising of clinical information for flare events and satellite data that tracks weather and pollution indices for the region of residence of each patient. Despite our focus on vasculitis, we believe this model is applicable to many similar research problems.

We also look at a compartmental model to estimate the effect of lockdowns of combating the COVID--19 pandemic in Dublin, Ireland. The compartments are split into age groups and the flow between/within each compartment is adjusted to account for non-homogeneous age mixing between/within age groups. Uncertainty estimates are constructed using parametric bootstraps. With these, we can create projections of compartmental growth under different lockdown measures; a proof-of-concept app is discussed to demonstrate this.