  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 events while still being able to
identify long-term 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 for managing patients with
chronic kidney disease.
