It may be possible to reduce cancer mortality by monitoring the concentrations of serum biomarkers over time in men and women to detect their cancer early, when it is most curable. The simplest approach to using a biomarker for screening is to sequentially use fixed thresholds as a means to determine an abnormal test (e.g., PSA exceeding 4 mg/ml, CA 125 exceeding 30 U/ml). Alternatives to the simplest single threshold (ST) rules include more sophisticated algorithms that make use of screening history that accumulates over time and determines abnormal tests using individualized reference ranges. Although in principle longitudinal algorithms should out perform fixed threshold rules, the actual benefit gained will depend on behavior of the biomarker, the screening algorithm, and the screening frequency. Little information has been available to help predict when conditions should compel the adoption of the more sophisticated algorithms and when conditions suggest the simpler algorithms should suffice, or indeed be preferred. In this manuscript we evaluate the conditions under which one should expect great benefit, and when one should not expect benefit, by comparing the ability of simple and complex algorithms to detect cancer early under a variety of biomarker behaviors and screening frequencies.