The performance of diagnostic tests for disease classification is often measured by accuracy (e.g., sensitivity or specificity); however, costs of the diagnostic test are a concern as well. Combinations of multiple diagnostic tests may improve accuracy, but incur additional costs. Here, we consider serial testing approaches that maintain accuracy while controlling costs of the diagnostic tests. We present a serial risk score classification approach. The basic idea is to sequentially test with additional diagnostic tests just until persons are classified. In this way, it is not necessary to test all persons with all tests. The methods are studied in simulations and compared with logistic regression. We applied the methods to data from HIV cohort studies to identify HIV infected individuals who are recently infected (<1>year) by testing with assays for multiple biomarkers. We find that the serial risk score classification approach can maintain accuracy while achieving a reduction in cost compared to testing all individuals with all assays.