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Abstract:
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Proportional hazards (PH) regression is an established methodology for analyzing survival and time-to-event data. The proportional hazards assumption of PH regression, however, is not always appropriate and, thus, statistical researchers have explored many alternatives. Threshold regression (TR) is one of these alternative methodologies (see Lee and Whitmore, 2006, for a review). The connection between PH regression and TR has been examined in previous published work but the investigations have been limited in scope. In this article, we study the connections between these two regression methodologies in greater depth and show that, in fact, PH regression is, for most purposes, a special case of TR. We show two methods of construction by which TR models can yield PH functions for survival times, one based on altering the TR time scale and the other based on varying the TR bound.
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