Nonparametric estimation of bivariate distribution under right truncation with application to panic disorder

In several studies, investigators are interested in estimating the bivariate distribution of the onset ages of a generic disorder in successive generations. The empirical distribution is inappropriate for this purpose due to truncation: only parent–child pairs with onset ages prior to the ages at interview were included in the sample. In this paper, we propose a simple nonparametric estimator for the underlying bivariate distribution of the onset ages. Compared with the existing estimators, the proposed estimator has a closed form and smaller biases when estimating marginal distributions. A real example is used to illustrate this estimator.