Summary. We present a Bayesian model to estimate the time-varying sensitivity of a diagnostic assay when the assay is given repeatedly over time, disease status is changing, and the gold standard is only partially observed. The model relies on parametric assumptions for the distribution of the latent time of disease onset and the time-varying sensitivity. Additionally, we illustrate the incorporation of historical data for constructing prior distributions. We apply the new methods to data collected in a study of mother-to-child transmission of HIV and include a covariate for sensitivity to assess whether two different assays have different sensitivity profiles.