Analyses of disease-free survival data in some types of cancer studies indicate that cohorts of patients treated for cancer are mixtures of cured individuals and individuals susceptible to experience a cancer related event. Cured individuals do not experience any disease related events, and eventually die due to other causes. Individuals who are not cured may die after experiencing a cancer recurrence or may die due to cancer without experiencing recurrence caused, for example, by adverse effects of cancer treatment. Cure status is partially latent. When time-to-first event is censored or the cause of observed death is unknown, the cure status is unknown. To model progression events with possibly masked causes of death, we consider a semi-Markov multi-state model including partially latent cured and not cured states. We propose inference methods which allow us to identify genetic markers associated with the risk of experiencing a disease related event and timing of disease events.