  In genetic epidemiological studies, family history data are collected on
relatives of study participants and used to estimate the age-specific risk of
disease for individuals who carry a causal mutation. However, a family member's
genotype data may not be collected due to the high cost of in-person interview
to obtain blood sample or death of a relative. Previously, efficient
nonparametric genotype-specific risk estimation in censored mixture data has
been proposed without considering covariates. With multiple predictive risk
factors available, risk estimation requires a multivariate model to account for
additional covariates that may affect disease risk simultaneously. Therefore,
it is important to consider the role of covariates in the genotype-specific
distribution estimation using family history data. We propose an estimation
method that permits more precise risk prediction by controlling for individual
characteristics and incorporating interaction effects with missing genotypes in
relatives, and thus gene-gene interactions and gene-environment interactions
can be handled within the framework of a single model. We examine performance
of the proposed methods by simulations and apply them to estimate the
age-specific cumulative risk of Parkinson's disease (PD) in carriers of LRRK2
G2019S mutation using first-degree relatives who are at genetic risk for PD.
The utility of estimated carrier risk is demonstrated through designing a
future clinical trial under various assumptions. Such sample size estimation is
seen in the Huntington's disease literature using the length of abnormal
expansion of a CAG repeat in the HTT gene, but is less common in the PD
literature.
