Background Estimation of incidence of the state of undiagnosed chronic disease provides a crucial missing link for the monitoring of chronic disease epidemics and determining the degree to which changes in prevalence are affected or biased by detection. Methods We developed a four-part compartment model for undiagnosed cases of irreversible chronic diseases with a preclinical state that precedes the diagnosis. Applicability of the model is tested in a simulation study of a hypothetical chronic disease and using diabetes data from the Health and Retirement Study (HRS). Results A two dimensional system of partial differential equations forms the basis for estimating incidence of the undiagnosed and diagnosed disease states from the prevalence of the associated states. In the simulation study we reach very good agreement between the estimates and the true values. Application to the HRS data demonstrates practical relevance of the methods. Discussion We have demonstrated the applicability of the modeling framework in a simulation study and in the analysis of the Health and Retirement Study. The model provides insight into the epidemiology of undiagnosed chronic diseases. Electronic supplementary material The online version of this article (doi:10.1186/s12874-015-0094-y) contains supplementary material, which is available to authorized users.