We propose a model for lifetime data in which all units start out susceptible to the event of interest but may move into a non-susceptible group if another event intervenes. Practical examples include subjects dropping out of a study by leaving the study area. It is supposed that the investigator is unaware of each subject’s status. The model results in the appearance of a cured fraction (long-term survivors). It is shown that certain parametric models for the lifetime and the intervening event are related to a cured fraction mixture model even though the non-susceptible group is fixed from the outset in the latter but not in the new model. A likelihood ratio test and a diagnostic plot are proposed and examples of applications are provided.
"A hidden competing risk model for censored observations." Braz. J. Probab. Stat. 28 (3) 333 - 352, August 2014. https://doi.org/10.1214/12-BJPS210