Driving down Poisson error can offset classification error in clinical tasks

Medical machine learning algorithms are typically evaluated based on accuracy vs. a clinician-defined ground truth, a reasonable initial choice since trained clinicians are usually better classifiers than ML models. However, this metric does not fully capture the actual clinical task: it neglects the fact that humans, even with perfect accuracy, are subject to non-trivial error from the Poisson statistics of rare events, because clinical protocols often specify a relatively small sample size. For example, to quantitate malaria on a thin blood film a clinician examines only 2000 red blood cells (0.0004 uL), which can yield large Poisson variation in the actual number of parasites present, so that a perfect human's count can differ substantially from the true average load. In contrast, an ML system may be less accurate on an object level, but it may also have the option to examine more blood (e.g. 0.1 uL, or 250x). Then while its parasite identification error is higher, the Poisson variability of its estimate is lower due to larger sample size. To qualify for clinical deployment, an ML system's performance must match current standard of care, typically a very demanding target. To achieve this, it may be possible to offset the ML system's lower accuracy by increasing its sample size to reduce Poisson error, and thus attain the same net clinical performance as a perfectly accurate human limited by smaller sample size. In this paper, we analyse the mathematics of the relationship between Poisson error, classification error, and total error. This mathematical toolkit enables teams optimizing ML systems to leverage a relative strength (larger sample sizes) to offset a relative weakness (classification accuracy). We illustrate the methods with two concrete examples: diagnosis and quantitation of malaria on blood films.