An analysis of the recurrence–progression process in bladder carcinoma by means of joint frailty models

Multiple sequential recurrences are one of the most important characteristics of superficial transitional cell carcinoma of the bladder, more than 50% of the patients will have recurrences (reappearance of a new superficial tumor). When in the same subject recurrent events are considered and these observed events are clustered into groups, independence between the clustered survival times cannot be assumed. A natural way to model the dependence of clustered event times is through the introduction of a cluster-specific random effect: the frailty term. On the other hand, between 10% and 30% of patients diagnosed with bladder carcinoma will present a muscle invasive progression, so the observation process of recurrences could be interrupted by a major failure event (progression). In this regard, a joint modelling of the two processes could make the study of a joint evolution over time possible, giving unbiased and efficient parameters. We jointly analyze recurrences and progression processes by means of the joint frailty model.