A group of scientists developed a new quantitative test to diagnose a childhood disease that is lethal if left untreated. The distribution of patients who have the disease and who are disease-free according to their values on the new test are shown below. If the treatment for the disease is safe and inexpensive, which of the points labeled on the graph represents the best diagnostic cutoff for the disease?

Question

A group of scientists developed a new quantitative test to diagnose a childhood disease that is lethal if left untreated.  The distribution of patients who have the disease and who are disease-free according to their values on the new test are shown below.  If the treatment for the disease is safe and inexpensive, which of the points labeled on the graph represents the best diagnostic cutoff for the disease?

Quizplus · Accepted Answer

In this example, scientists developed a new quantitative test to diagnose a childhood disease that is lethal if left untreated. For this type of disease, the consequences of a false-negative diagnostic error are catastrophic because a patient incorrectly diagnosed as not having the disease will certainly die as a result. Therefore, the cutoff for diagnosis should be set at a point that guarantees that among all subjects with disease, the proportion who have a positive test result is as high as possible (ie, maximum sensitivity) given the safety and cost of available treatments. The treatment for the disease under study is safe and inexpensive, which means that treating patients who are disease-free causes little to no harm. In this case, a false-positive diagnostic error (which may lead to inappropriate but safe and inexpensive treatment) is less consequential than a false-negative diagnostic error (which leads to death). Therefore, the best cutoff for the quantitative test would be a point that guarantees all patients who have the disease are correctly diagnosed (100% sensitivity). On the graph given, the cutoff that guarantees 100% sensitivity is point B. If this point is selected as a cutoff, test values higher than B will be considered a positive test result. All patients with the disease have values higher than B; therefore, they will all be correctly diagnosed as having the disease (100% sensitivity). Similarly, if points C, D, or E are selected as cutoff points, values higher than these will be considered a positive test but some patients with the disease will be missed (false negatives) (Choices D and E). If point A is selected as a cutoff point, many patients without the disease will be incorrectly diagnosed as having the disease (false positives) (Choice A). (Choice C) Point C also misses some patients with the disease (ie, those who have values lower than C). Given its location in the middle of the disease and disease-free symmetric curves, it represents the cutoff that results in the greatest diagnostic accuracy (ie, greatest proportion of patients with and without the disease are correctly identified). Educational objective: The cutoff of a test used to diagnose a lethal disease should guarantee the maximum sensitivity possible, considering the safety and cost of available treatments.

A Group of Scientists Developed a New Quantitative Test to Diagnose