Question

The American Disease X Foundation reports that 6% of the population over 50 years of age has Disease X. You inquire as to the source of their information, and they cite disease population screening data in the literature which reports that 6% of that population was positive when screened. Referring to the literature, you discover that the screening test used had sensitivity of 95% and specificity of 98%. What proportion of the population over 50 years of age do you think really has the disease?

Answer 1

The 2x2 table for the diagnostic test is define as,

	Present	Absent	Total
Positive	a	c	a+c
Negative	b	d	b+d
Total	a+b	c+d	a+b+c+d

Given:

and

The American Disease X Foundation reports that 6% of the population over 50 years of age has Disease X such that

Required:

We need to find proportion of the population over 50 years of age who really has disease (positive predicted value)

Now, solving the three equation, we get,