Probabilistic broken-stick model: A regression algorithm for irregularly sampled data with application to eGFR

In order for clinicians to manage disease progression and make effective decisions about drug dosage, treatment regimens or scheduling follow up appointments, it is necessary to be able to identify both short and long-term trends in repeated biomedical measurements. However, this is complicated by the fact that these measurements are irregularly sampled and influenced by both genuine physiological changes and external factors. In their current forms, existing regression algorithms often do not fulfil all of a clinician's requirements for identifying short-term (acute) events while still being able to identify long-term, chronic, trends in disease progression. Therefore, in order to balance both short term interpretability and long term flexibility, an extension to broken-stick regression models is proposed in order to make them more suitable for modelling clinical time series. The proposed probabilistic broken-stick model can robustly estimate both short-term and long-term trends simultaneously, while also accommodating the unequal length and irregularly sampled nature of clinical time series. Moreover, since the model is parametric and completely generative, its first derivative provides a long-term non-linear estimate of the annual rate of change in the measurements more reliably than linear regression. The benefits of the proposed model are illustrated using estimated glomerular filtration rate as a case study used to manage patients with chronic kidney disease.