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Abstract:
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In cancer studies, multiple events of interests such as diagnosis and metastasis can be observed in any order before the patient's death or end of the study. Sometimes, a particular event is unobserved and the exact time that it occurs is only known to be between other observed events, which leads to marked-endpoint type of data. In a previous paper, we proposed the use of a semi-parametric regression model to simultaneously model time to diagnosis, latent metastasis, and death. This paper proposes the use of a shared frailty term to model the latent correlation between the sequential events that is not accounted for by the shared baseline hazards and covariates. We derive the estimation procedure for the frailty term's parameters and other covariate effects via nonparametric maximum likelihood and Laplace transformation. This proposed model's estimation procedure is tested via Monte Carlo simulation and applied to the analysis of breast cancer data from SEER registry. The proposed model's ability to capture the correlation between time-of-diagnosis and time-of-death are demonstrated graphically via plots of post-diagnosis survivals conditioning on time-of-diagnosis.
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