Medical machine learning algorithms are typically evaluated based on accuracy vs. a clinician-defined ground truth, a reasonable choice because trained clinicians are usually better classifiers than ML models. However, this metric does not fully reflect the clinical task: it neglects the fact that humans, even with perfect accuracy, are subject to sometimes significant error from the Poisson statistics of rare events, because clinical protocols often specify that a relatively small sample be examined. 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 variation in actual number of parasites present due to Poisson variability, so that a perfect human's count can differ substantially from the true average load. In contrast, ML systems may be less accurate on an object level, but they also may have the option to examine more blood (e.g. 0.1 uL, or 250x). So while their accuracy as to parasite count in a particular sample is lower, the Poisson variability of their estimate is also lower due to larger sample size. Crucially, when an ML system moves out of the proof-of-concept stage and targets deployment in a clinical setting, its performance must match current standard of care. To this end, it may have the option to offset its lower accuracy by increasing 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 analyze the mathematics of the trade-off between these two types of error, to enable teams developing 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.

在医疗机器学习算法中，通过比较与临床医生定义的标准结果的准确性来评估该算法往往是合理的选择。然而，这并不能完全反映临床任务的实际情况：它忽视了人类由于罕见事件的 Poisson 统计学规律而产生的有时相当大的误差以及临床协议通常要求只检查相对较小样本的事实。相比之下，机器学习系统可以通过检查更多的血液样本来弥补其准确性上的不足，因此达到与仅限于较小样本的准确人工判读相同的实际临床表现。本文分析了这两种错误之间的权衡数学关系，以帮助开发机器学习系统的团队利用相对优势（更大的样本量）来弥补相对劣势（分类准确性），并以疟疾的诊断和定量为例说明了这些方法。

降低泊松误差可以抵消临床任务中的分类误差