Robust Combination Testing: Methods and Application to COVID-19 Detection

Situations where simple and affordable testing tools are available but not accurate enough to be operationally relevant are ubiquitous. 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 provides a structured way for policymakers to break this trade-off by optimally combining results from cheap tests for increased predictive 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 specificity of at least 0.9 can improve sensitivity by 14% and 10% 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.