An Exact Formula for Estimation of Age-Specific Sensitivity for Screening Tests

Abstract

There has been a growing interest in screening programs designed to detect chronic progressive cancers in the asymptomatic stage, with the expectation that early detection will result in a better prognosis. One key element of early detection programs is a screening test. An accurate screening test is more effective in finding cases with early-stage diseases. Sensitivity, the conditional probability of getting a positive test result when one truly has a disease, represents one measure of accuracy for a screening test. Since the true disease status is unknown, it is not straightforward to estimate the sensitivity directly from observed data. Furthermore, the sensitivity is associated with other parameters related to the disease progression. This feature introduces additional numerical complexity and limitations, especially when the sensitivity depends on age. In this paper, we propose a new approach that, through combinatorial manipulation of probability statements, formulates the age-dependent sensitivity. This formulation has an exact and simple expression and can be estimated based on directly observable probabilities. This approach also helps evaluate other parameters associated with the natural history of disease more accurately. The proposed method was applied to estimate the mammography sensitivity for breast cancer using the data from the Health Insurance Plan trial.