An identifiability problem in a state model for partly undetected chronic diseases

TL;DR

This paper investigates the limitations of using cross-sectional studies with mortality follow-up to estimate true disease incidence in a model of chronic diseases with undiagnosed states, demonstrating that it is generally not feasible.

Contribution

It provides a counterexample showing that the true incidence rate cannot be identified from such data in the proposed disease progression model.

Findings

Counterexample proves non-identifiability of incidence rate

Estimation of true incidence from cross-sectional data is generally impossible

Highlights limitations in epidemiological modeling of undiagnosed diseases

Abstract

Recently, we proposed an state model (compartment model) to describe the progression of a chronic disease with an pre-clinical (undiagnosed) state before clinical diagnosis. It is an open question, if a sequence of cross-sectional studies with mortality follow-up is sufficient to estimate the true incidence rate of the disease, i.e. the incidence of the undiagnosed and diagnosed disease. In this note, we construct a counterexample and show that this cannot be achieved in general.