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Longitudinal changepoint data naturally arise in many applications. Examples include transition of core body temperature following the hypothermia therapy and prostate-specific antigen levels following treatment. Note that the trend change occurs due to a shock (e.g., treatment) to the system. Thus, an individual exhibiting a linear trend could be an indication of insignificant effects of the shock. One of the goals of this type of study is to investigate whether the shock is significantly associated in changing the trend of a trajectory. The bent-cable model characterizes the shock-through data using three phases: (a) an incoming phase characterizing the trend before the shock comes into effect, (b) a transition due to the shock, and (c) an outgoing phase due to the after-shock effects. In this article, we develop bent-cable methodology accounting for trajectories exhibiting either a linear trend or a trend change characterized by gradual or abrupt transition.

Modeling a Mixture of Linear and Changepoint Trajectories for Longitudinal Time-Series Data