ABSTRACT
In Chapter 1 the “fixed width failure” function Fw(t) = 1− S(t +w|t) = P(T ≤ t+w |T ≥ t) has been defined as a measure that could be used to describe dynamic prediction. For larger values of w it could help to answer the patient’s question, “Am I cured?” For small values of w it describes the instantaneous risk of dying for those still alive. This function is known as the “force of mortality” or, in more neutral terms, the hazard function. Under the assumption of a continuous distribution with differentiable survival function, it can be defined by
h(t)dt = P(T < t+dt |T ≥ t) .
