In analyzing time-to-event data, proportional hazards (PH) regression is an ubiquitous model used in many fields. PH regression, however, requires a strong assumption that is not always appropriate. Threshold regression (TR) is one of the alternative models. A first-hitting-time (FHT) survival model postulates a health status process for a patient that gradually declines until the patient dies when the health level first reaches a critical threshold. In this article, we review the development of threshold regression models and their applications.
"A Survey of Threshold Regression for Time-to-event Analysis and Applications." Taiwanese J. Math. 23 (2) 293 - 305, April, 2019. https://doi.org/10.11650/tjm/190107