Estimating Disease Onset Distribution Functions from Censored Mixture Data

We consider nonparametric estimation of disease onset distribution functions in multiple populations using censored data with unknown population identifiers. The problem is motivated from studies aiming at estimating the disease risk distribution in deleterious mutation carriers for the purpose of genetic counseling and design of therapeutic intervention trials to modify disease onset progression. In these studies, the distribution of disease risk in subjects assumes a mixture form. Although the population identifiers are missing, design and scientific knowledge allow easy calculation of the probability of an observation belonging to each population. We propose a general family of simple weighted least squares estimators and show that the existing consistent nonparametric methods belong to this family. We further show that this family also includes a class of imputation estimators that is not known in the literature for this type of problems. We identify a computationally effortless estimator in the family, study its asymptotic properties, and show its significant efficiency gain comparing to the existing estimators in the literature. The application to a large genetic epidemiological study of Huntington’s disease reveals information on the age-at-onset distribution of HD not previously available in the clinical literature which may generate new clinical hypothesis.