A common phenomenon in cancer syndromes is for an individual to have multiple primary cancers (MPC) at different sites during his/her lifetime. Patients with Li-Fraumeni syndrome (LFS), a rare pediatric cancer syndrome mainly caused by germline TP53 mutations, are known to have a higher probability of developing a second primary cancer than those with other cancer syndromes. In this context, it is desirable to model the development of MPC to enable better clinical management of LFS. Here, we propose a Bayesian recurrent event model based on a non-homogeneous Poisson process in order to obtain penetrance estimates for MPC related to LFS. We employed a familywise likelihood that facilitates using genetic information inherited through the family pedigree and properly adjusted for the ascertainment bias that was inevitable in studies of rare diseases by using an inverse probability weighting scheme. We applied the proposed method to data on LFS, using a family cohort collected through pediatric sarcoma patients at MD Anderson Cancer Center from 1944 to 1982. Both internal and external validation studies showed that the proposed model provides reliable penetrance estimates for MPC in LFS, which, to the best of our knowledge, have not been reported in the LFS literature.

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