A flexible parametric model for combining current status and age at first diagnosis data

In some cross-sectional studies of chronic disease, data consist of the age at examination, whether the disease was present at the exam, and recall of the age at first diagnosis. This article describes a flexible parametric approach for combining current status and age at first diagnosis data. We assume that the log odds of onset by a given age and of detection by a given age conditional on onset by that age are nondecreasing functions of time plus linear combinations of covariates. Piecewise linear models are used to characterize changes across time in the baseline odds. Methods are described for accommodating informatively missing current status data and inferences based on the age-specific incidence of disease prior to a landmark event (e.g., puberty, menopause). Our formulation enables straightforward maximum likelihood estimation without requiring restrictive parametric or Markov assumptions. The methods are applied to data from a study of uterine fibroids.