Abstract
First hitting times arise naturally in survival analysis where the underlying stochastic counting process represents the strength of the health of an individual. The patient experiences a clinical endpoint when this process reaches a critical point for the first time. We propose a very flexible and unified first hitting time density function in a stochastic carcinogenesis counting process, and its mathematical properties are investigated. The Poisson and negative binomial first hitting time models are addressed and two examples with real data are presented.
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