Robust combination testing: methods and application to COVID-19 detection

Simple and affordable testing tools are often not accurate enough to be operationally relevant. For COVID-19 detection, rapid point-of-care tests are cheap and provide results in minutes, but largely fail policymakers’ accuracy requirements. We propose an analytical methodology, based on robust optimization, that identifies optimal combinations of results from cheap tests for increased predictive accuracy. This methodological tool allows policymakers to credibly quantify the benefits from combination testing and thus break the trade-off between cost and accuracy. Our methodology is robust to noisy and partially missing input data and incorporates operational constraints—relevant considerations in practice. We apply our methodology to two datasets containing individual-level results of multiple COVID-19 rapid antibody and antigen tests, respectively, to generate Pareto-dominating receiver operating characteristic (ROC) curves. We find that combining only three rapid tests increases out-of-sample area under the curve (AUC) by 4% (6%) compared with the best performing individual test for antibody (antigen) detection. We also find that a policymaker who requires a specificity of at least 0.95 can improve sensitivity by 8% and 2% for antibody and antigen testing, respectively, relative to available combination testing heuristics. Our numerical analysis demonstrates that robust optimization is a powerful tool to avoid overfitting, accommodate missing data, and improve out-of-sample performance. Based on our analytical and empirical results, policymakers should consider approving and deploying a curated combination of cheap point-of-care tests in settings where ‘gold standard’ tests are too expensive or too slow.