A strictly increasing sequence of time points at which the event rate changes. The first element of tchange must be zero. It must have the same length as rate.
Author
Xiaodong Luo
Details
Let \(\lambda(t)=\sum_{j=1}^m \lambda_j I(t_{j-1}\le t<t_j)\) be the hazard function, where \(\lambda_1,\ldots,\lambda_m\) are the corresponding elements of rate and \(t_0,\ldots,t_{m-1}\) are the corresponding elements of tchange, \(t_m=\infty\). The cumulative hazard function
$$\Lambda(t)=\sum_{j=1}^m \lambda_j(t\wedge t_j-t\wedge t_{j-1}),$$
the survival function \(S(t)=\exp\{-\Lambda(t)\}\), the distribution function \(F(t)=1-S(t)\) and the density function
\(f(t)=\lambda(t)S(t)\).