A nonparametric method for penetrance function estimation

In diseases caused by a deleterious gene mutation, knowledge of age-specific cumulative risks is necessary for medical management of mutation carriers. When pedigrees are ascertained through at least one affected individual, ascertainment bias can be corrected by using a parametric method such as the Proband's phenotype Exclusion Likelihood, or PEL, that uses a survival analysis approach based on the Weibull model. This paper proposes a nonparametric method for penetrance function estimation that corrects for ascertainment on at least one affected: the Index Discarding EuclideAn Likelihood or IDEAL. IDEAL is compared with PEL, using family samples simulated from a Weibull distribution and under alternative models. We show that, under Weibull assumption and asymptotic conditions, IDEAL and PEL both provide unbiased risk estimates. However, when the true risk function deviates from a Weibull distribution, we show that the PEL might provide biased estimates while IDEAL remains unbiased.