Using interpretable random forest to determine observational-data-based cutoff points in medical measurements

Regular checkups are crucial in health management of a general population. Part of a checkup includes monitoring substances in blood, in urine, as well as physical measurements related to health. It is often taken for granted that normal ranges, specified by cutoff points, of these measurements are rigorously determined by scientific evidence. In reality, there is a degree of uncertainty due to possible change of the definition of being healthy, small sample sizes in intervention trials, and gender, ethnic group, and individual differences. One conceptual difficulty in setting a cutoff point is that generally there is no evidence for a threshold effect – quantum jump of risk for detrimental medical outcome once the measurement level crosses the cutoff point – for almost all physical checkup measurements. A solution in unambiguously determining a cutoff point at the population level, even though the risk changes continuously, is by minimizing the sum of two false classification rates (false positive and false negative rates), as one false rate will increase whereas another decrease with the change of the measurement level. Another problem in cutoff determination is that cutoff of a measurement may depend on the context of other variables such as gender or other components in blood. We use interpretable random forests (IRF) to tackle this latter problem. The output from an IRF is a set of node split rules involving one or multiple variables. Each rule is a possible cutoff point, and a composite rule provides a cutoff point conditional on other variables. We use the National Health and Nutrition Examination Survey (NHANES) data to illustrate this approach, as well as to show that the observational-data-determined cutoff point depends on the data used, the medical outcome chosen, and the cost or objection function employed.