摘要：In carcinogenicity experiments with animals where the tumor is not palpable it is common to observe only the time of death of the animal, the cause of death (the tumor or another independent cause, as sacrifice) and whether the tumor was present at the time of death. These last two indicator variables are evaluated after an autopsy. Defining the non-negative variables $T_{1}$ (time of tumor onset), $T_{2}$ (time of death from the tumor) and $C$ (time of death from an unrelated cause), we observe $(Y,\Delta_{1},\Delta_{2})$, where $Y=\min\left\{T_{2},C\right\}$, $\Delta_{1}=1_{\left\{T_{1}\leq C\right\}}$, and $\Delta_{2}=1_{\left\{T_{2}\leq C\right\}}$. The random variables $T_{1}$ and $T_{2}$ are independent of $C$ and have a joint distribution such that $P(T_{1}\leq T_{2})=1$. Some authors call this model a “survival-sacrifice model”.
关键词：MLE; survival sacrifice model; self-consistency equation; Volterra integral equation; primal-dual interior point algorithm; EM algorithm; smooth functionals
