**1. Introduction**

Survival analysis arises in many applications where we want to reason about the amount of time until the considered event happens. A common assumption in standard survival modeling is that all individuals can experience the event if observed for a sufficient amount of time. Cure models [1] have been developed because there might be situations where the standard survival model is not true, for example, in the event of a recurrence in some diseases or death from some types of cancer. One challenge with time-to-event data is that the event is not always observed (censored observations). Standard cure models typically make inferences based on the assumption that the cure status information is an unobserved (latent) variable as the event is only known for the uncensored (uncured) subjects, but it is unknown for the censored observations whether it is cured or not. There are situations where cure status information is known for some of the censored individuals as they can be identified to be insusceptible to the considered event, that is, known to be cured. For example, when a medical test ascertains that a disease has entirely disappeared after treatment.

In this paper, we present kernel methods to estimate the conditional survival function, cure probability and latency function in the presence of cure status information. The proposed approach contributes to state-of-the-art in time-to-event data, as it extends previous works in the mixture cure model.
