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Many researchers have investigated first hitting times as models for survivaldata. First hitting times arise naturally in many types of stochasticprocesses, ranging from Wiener processes to Markov chains. In a survivalcontext, the state of the underlying process represents the strength of an itemor the health of an individual. The item fails or the individual experiences aclinical endpoint when the process reaches an adverse threshold state for thefirst time. The time scale can be calendar time or some other operationalmeasure of degradation or disease progression. In many applications, theprocess is latent (i.e., unobservable). Threshold regression refers tofirst-hitting-time models with regression structures that accommodate covariatedata. The parameters of the process, threshold state and time scale may dependon the covariates. This paper reviews aspects of this topic and discussesfruitful avenues for future research.

Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary