Abstract: Motivated by a design for discovering associations between inherited childhood risk factors and adult-onset disease, the problem of estimating the distribution of age at onset of the disease from a case-control sample of subjects who have and have not yet experienced onset is examined. An embedding of the distribution function of age at onset in a multiplicative intercept model simplifies estimation by allowing the distribution function of age at enrollment to be conditioned out of the likelihood. A class of estimators of the distribution function of age at onset is developed and it is argued that a member of the class is efficient. Standard error calculations and an approach to approximating the efficient member of the class are described.
Key words and phrases: Efficiency, Lynden-Bell estimator, multiplicative intercept, one sample problem, truncated data.