Suppose we want both the sensitivity and specificity to be at least 70%. Use the ROC curve

Question:

Suppose we want both the sensitivity and specificity to be at least 70%. Use the ROC curve to identify the possible value(s) to use as the cutoff for identifying people with dementia, based on these criteria?

Mental Health
The Chinese Mini-Mental Status Test (CMMS) consists of 114 items intended to identify people with Alzheimer€™s disease and senile dementia among people in China [14]. An extensive clinical evaluation of this instrument was performed, whereby participants were interviewed by psychiatrists and nurses and a definitive diagnosis of dementia was made. Table 3.13 shows the results obtained for the subgroup of people with at least some formal education. Suppose a cutoff value of ‰¤ 20 on the test is used to identify people with dementia.

Table 3.13: Relationship of clinical dementia to outcome on the Chinese Mini-Mental Status Test

CMMS score Nondemented Demented 0-5 2 6-10 11-15 3 16-20 21-25 16 3 26-30 18 Total 16 46