  In certain genetic studies, clinicians and genetic counselors are interested
in estimating the cumulative risk of a disease for individuals with and without
a rare deleterious mutation. Estimating the cumulative risk is difficult,
however, when the estimates are based on family history data. Often, the
genetic mutation status in many family members is unknown; instead, only
estimated probabilities of a patient having a certain mutation status are
available. Also, ages of disease-onset are subject to right censoring. Existing
methods to estimate the cumulative risk using such family-based data only
provide estimation at individual time points, and are not guaranteed to be
monotonic or nonnegative. In this paper, we develop a novel method that
combines Expectation-Maximization and isotonic regression to estimate the
cumulative risk across the entire support. Our estimator is monotonic,
satisfies self-consistent estimating equations and has high power in detecting
differences between the cumulative risks of different populations. Application
of our estimator to a Parkinson's disease (PD) study provides the age-at-onset
distribution of PD in PARK2 mutation carriers and noncarriers, and reveals a
significant difference between the distribution in compound heterozygous
carriers compared to noncarriers, but not between heterozygous carriers and
noncarriers.
