  By reducing core body temperature, T_c, induced hypothermia is a therapeutic
tool to prevent brain damage resulting from physical trauma. However, all
physiological systems begin to slow down due to hypothermia that in turn can
result in increased risk of mortality. Therefore, quantification of the
transition of T_c to early hypothermia is of great clinical interest.
Conceptually, T_c may exhibit an either gradual or abrupt transition.
Bent-cable regression is an appealing statistical tool to model such data due
to the model's flexibility and greatly interpretable regression coefficients.
It handles more flexibly models that traditionally have been handled by
low-order polynomial models (for gradual transition) or piecewise linear
changepoint models (for abrupt change). We consider a rat model for humans to
quantify the temporal trend of T_c to primarily address the question: What is
the critical time point associated with a breakdown in the compensatory
mechanisms following the start of hypothermia therapy? To this end, we develop
a Bayesian modelling framework for bent-cable regression of longitudinal data
to simultaneously account for gradual and abrupt transitions. Our analysis
reveals that: (a) about 39% of rats exhibit a gradual transition in T_c; (b)
the critical time point is approximately the same regardless of transition
type; (c) both transition types show a significant increase of T_c followed by
a significant decrease.
