A revolution in molecular technology is leading to the discovery of many biomarkers of disease. Monitoring these biomarkers in a population may lead to earlier disease detection, and may prevent death from diseases like cancer that are more curable if found early. For markers whose concentration is associated with disease progression the earliest detection is achieved by monitoring the marker with an algorithm able to detect very small changes. One strategy is to monitor the biomarkers using a longitudinal algorithm that incorporates a subject's screening history into screening decisions. Longitudinal algorithms that have been proposed thus far rely on modeling the behavior of a biomarker from the moment of disease onset until its clinical presentation. Because the data needed to observe the early pre-clinical behavior of the biomarker may take years to accumulate, those algorithms are not appropriate for timely development using new biomarker discoveries. This manuscript presents a computationally simple longitudinal screening algorithm that can be implemented with data that is obtainable in a short period of time. For biomarkers meeting only a few modest assumptions our algorithm uniformly improves the sensitivity compared with simpler screening algorithms but maintains the same specificity. It is unclear what performance advantage more complex methods may have compared with our method, especially when there is doubt about the correct model for describing the behavior of the biomarker early in the disease process. Our method was specifically developed for use in screening for cancer with a new biomarker, but it is appropriate whenever the pre-clinical behavior of the disease and/or biomarker is uncertain.