Threshold Regression and First Hitting Time Models

First hitting time models are a technique of modeling a stochastic process as it approaches or avoids a boundary, also known as a threshold. The process itself may be unobservable, making this a difficult problem. Regression techniques, however, can be employed to model the data as it compares to the threshold, creating a class of first hitting time models called threshold regression models. Survival data, measuring the amount of time before an event occurs, is widely used in modeling medical and manufacturing data. To analyze and model the data at hand, one commonly used method is the proportional hazards model, but this requires a strong proportional hazards assumption, one that is often lacking in practice. In place of the proportional hazards model, first hitting time models can be employed. First hitting time models do not require such strong assumptions and can be extended to become threshold regression models. Threshold regression has many advantages over the proportional hazards model, including its flexibility in both its assumptions and utilization and its application to stochastic processes so often evident in measuring survival. This paper describes the process of threshold regression modeling and compares its results and utility against that of the proportional hazards model.