Abstract: Bivariate truncated data arise from the study of age-of-onset anticipation for diseases with variable age of onset in which children tend to develop clinical disease at younger ages than their affected parents. To test for age-of-onset anticipation using affected parent-child pair data, it is of interest to estimate the marginal distributions of the age-of-onset for both parents and children. However, the observed ages of onset in both parents and children are right-truncated by their current ages. In this report, we proposed a nonparametric estimator of the marginal distributions of a bivariate distribution based on right-truncated data. This estimator is shown to be consistent under appropriate conditions. A noniterative algorithm is given to compute the proposed estimator. Finite sample behavior of the estimator is investigated via simulation. An example is given to illustrate the use of the proposed estimator in testing of age-of-onset anticipation in bipolar affective disorder.
Key words and phrases: Age of onset, anticipation, bivariate data, consistency, marginal distribution, truncation.