Estimating and comparing the distribution of onset of disease from prevalence case-control data

Age at ascertainment from prevalence case-control data identifies the age-specific odds of disease. When age at onset is available from the cases, the conditional distribution of age at onset, given that disease occurs, is identifiable. Combining both kinds of information by introducing a multiplicative intercept allows identification of the marginal distribution of age at onset. Here, the approach is extended to the two-sample setting through a generalization of the multiplicative intercept model. The efficiency of the approach is explored and a test statistic based on the integrated difference between distribution function estimates is proposed. An approach to regularization of the likelihood is discussed. The methods are illustrated through an application to data on colorectal polyps obtained from a case-control study of individuals undergoing colonoscopy.