Non‐parametric estimation of the age‐at‐onset distribution from a cross‐sectional sample.

This article focuses on a novel non-parametric method to estimate the age-of-onset distribution of a disease from cross-sectional population samples that include prevalent cases, addressing biases inherent in such data. The approach jointly models the bivariate distribution of age at disease onset and survival time after onset, using a computationally efficient expectation–maximization (EM) algorithm that accounts for left truncation due to survival until sampling. The method accommodates categorical covariates, such as BRCA1/2 mutation status, and provides unbiased estimates of age-specific penetrance and mutation prevalence without requiring prospective follow-up or parametric assumptions. Simulation studies demonstrate that the EM-based estimates outperform traditional life-table methods, especially under truncation, and an application to the Washington Ashkenazi Study data yields penetrance estimates for breast cancer consistent with those obtained from relatives’ data, indicating effective bias correction. The method is broadly applicable to cross-sectional studies and prevalent surveys where only retrospective disease onset information is available.