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A cutoff value is a standard value used to separate quantitative data. In the medical field, this value distinguishes between positive and negative results in a test and is also called the “pathological identification value.”
We will explain with some examples.
- The cutoff value for body mass index (BMI) to determine obesity is 30 or higher.
- The cutoff value for the fecal occult blood test to screen for colorectal cancer is approximately 120 ng/mL.
- The Japan Atherosclerosis Society considers dyslipidemia to be suspected when LDL cholesterol levels are 140 mg/dL or higher and when HDL cholesterol levels are less than 40 mg/dL.
For example, obesity (1) has serious negative effects on health. BMI is calculated by dividing weight (kg) by the square of height (m) and is widely used to indicate obesity/thinness. Many studies have reported that BMI is closely associated with health risks and mortality rates. The WHO international standard (cutoff value) is that a BMI of 25 or more is overweight, and that of 30 or more is obese.
True positives, false positives, false negatives, and true negatives
The cutoff value for being overweight is 25, but the BMI cutoff value for screening for certain lifestyle-related diseases is not necessarily 25.
Twenty patients were tested to calculate the BMI cutoff value for lifestyle-related diseases. The results are summarized in Tables 1–3.
[Table 1] BMI and presence of disease
[Table 2] Positive/negative
[Table 3] Number of patients with positive and negative BMI values
Table 2: Data from Table 1 sorted by BMI in descending order according to whether the test was positive or negative.
Table 3: Number of patients by BMI value for positive and negative cases for the data in Table 2.
We set the cutoff value at 27 and tabulated the number of patients with a BMI of 27 or more and less than 27, divided into positive and negative groups.
[Table 4] Number of positive and negative cases when the cutoff value was set at 27
The values of the four cells are listed in Table 4. (Table 5)
[Table 5]
True positive (A): A person with the disease is considered positive.
False positive (B): A person without the disease is considered positive.
False negative (C): A person with the disease is considered negative.
True negative (D): A person without the disease is considered negative.
Sensitivity and specificity
The ideal cutoff value is a test that can determine whether all positive test results have the disease and all negative test results do not. However, regardless of the cutoff value, some patients will be judged as false negatives and false positives. Therefore, an appropriate cutoff value is set such that the number of patients judged as false negatives and false positives is small. The appropriate cutoff value leads to more patients being judged as true positives and true negatives.
As shown in Table 4, there were 3 true positives and 13 true negatives.
Whether there are many true positives can be determined by calculating the proportion of patients with the disease who test positive (true positives/positives with or without the disease). The calculated value is called “sensitivity.”
The sensitivity for Table 4 is 3 ÷ (3 + 3) = 0.5 (50%).
Whether there are many true negatives can be determined by calculating the proportion of patients who test negative among those without the disease (true negatives/disease presence/absence negatives). The calculated value is called “specificity.”
The specificity for Table 4 is 13 ÷ (13 + 1) = 0.929 (92.9%).
If sensitivity and specificity are high, the cutoff value is considered good. In this case, the specificity (92.9%) was high, but the sensitivity (50%) was not. Therefore, a cutoff value of 27 or more was not considered appropriate.
The cutoff value was set at 26 or more, and the number of patients with positive and negative results was calculated for the data in Table 3.
[Table 6] Number of positive and negative cases with a cutoff value of 26 or more
The sensitivity and specificity in Table 6 are 83.3% and 92.9%, respectively. As sensitivity and specificity are high, a cutoff value of 26 or more is considered appropriate.
We must calculate the sensitivity and specificity for all other cutoff values and determine the appropriate cutoff value.
[Table 7] Sensitivity and specificity
Sensitivity and specificity were high for a BMI of 26 or higher. The BMI cutoff value for determining the presence or absence of lifestyle-related diseases is 26 or higher.
Next, we introduce other methods for calculating cutoff values.
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