  When considering a genetic disease with variable age at onset (ex: diabetes ,
familial amyloid neuropathy, cancers, etc.), computing the individual risk of
the disease based on family history (FH) is of critical interest both for
clinicians and patients. Such a risk is very challenging to compute because: 1)
the genotype X of the individual of interest is in general unknown; 2) the
posterior distribution P(X|FH, T > t) changes with t (T is the age at disease
onset for the targeted individual); 3) the competing risk of death is not
negligible. In this work, we present a modeling of this problem using a
Bayesian network mixed with (right-censored) survival outcomes where hazard
rates only depend on the genotype of each individual. We explain how belief
propagation can be used to obtain posterior distribution of genotypes given the
FH, and how to obtain a time-dependent posterior hazard rate for any individual
in the pedigree. Finally, we use this posterior hazard rate to compute
individual risk, with or without the competing risk of death. Our method is
illustrated using the Claus-Easton model for breast cancer (BC). This model
assumes an autosomal dominant genetic risk factor such as non-carriers
(genotype 00) have a BC hazard rate $\lambda$ 0 (t) while carriers (genotypes
01, 10 and 11) have a (much greater) hazard rate $\lambda$ 1 (t). Both hazard
rates are assumed to be piecewise constant with known values (cuts at 20, 30,.
.. , 80 years). The competing risk of death is derived from the national French
registry.
