This paper addresses challenges in developing liquid biopsies for early-stage cancer detection through active sequential hypothesis testing (ASHT). In the problem of ASHT, a learner seeks to identify the true hypothesis (true cancer type) from a known set of hypotheses (candidate cancer types). The learner is given a set of actions (sequencing genetic intervals) and knows the distribution of the random outcome (whether a mutation is detected) of any action under any true hypothesis. Given a target error Formula: see text, the goal is to sequentially select the fewest number of actions to identify the true hypothesis with probability at least Formula: see text. Motivated by applications in which the number of hypotheses or actions is massive (e.g., genomics-based cancer detection), we propose efficient greedy algorithms and provide the first approximation guarantees for ASHT, under two types of adaptivity. Our guarantees are independent of the number of actions and logarithmic in the number of hypotheses. Numerical tests on synthetic and real DNA mutation data show that our algorithms significantly outperform previous heuristic policies. This paper was accepted by David Simchi-Levi, healthcare management. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2023.00829 .
Gan et al. (2025) studied this question.