Estimation in Multi-State Semi-Markov Models with a Cured Fraction and Masked Causes of Deaths

Analyses of disease-free survival data for certain cancer types indicate that cohorts of patients treated for cancer consist of individuals who are susceptible to experience cancer-related events and individuals who are cured. Cured individuals do not experience any cancer-related event and eventually die due to other causes. Individuals who are not cured may die after experiencing cancer recurrence or without experiencing any recurrence. Cure status is a partially latent variable and is only known if a disease-related event, cancer recurrence, or cancer death is observed. Causes of some observed deaths may be masked. To model disease progression events, which are cancer recurrence and cancer death, we consider a multi-state model including partially latent cured and not cured states. We describe our modeling approach and discuss an inference method incorporating masked causes of deaths. Our method allows to identify factors associated with the risk of experiencing a disease-related event and with timing of disease events after the treatment of cancer.