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Hierarchical dynamic time-to-event models for post-treatment preventive care data on breast cancer survivors

This paper considers modelling data arising in post-treatment preventive care settings, where cancer patients who have undergone disease-directed treatment discontinue seeking preventive care services. Clinicians and public health researchers are interested in explaining such behavioural patterns by modelling the time-to-receiving care while accounting for several patient and treatment attributes. A key feature of such data is that a noticeable number of patients would never return for screening, a concept subtly different from censoring, where an individual does not return for screening in the given time frame of the study. Models distinguishing between these two concepts are known as cure rate models and are often preferred for data where a significant part of the population never experienced the endpoint. Building upon recent work on hierarchical cure model framework we propose modelling a sequence of latent events with a piecewise exponential distribution that remedies oversmoothing encountered in existing models with different latent distributions. We investigate simultaneous regression on the cure fraction and the latent event distribution and derive a flexible class of semiparametric cure rate models.