Suppose the pdfs of the test result for patients with and without a disease are mode...

Suppose the pdfs of the test result for patients with and without a disease are modeled as Gaussian with different mean values and variances, as shown in Figure 3.18. We design a diagnostic test by selecting a threshold t₀. For a patient whose test value is below t₀, we call it normal. If the test value is above t₀, we call is diseased. By selecting different thresholds, we obtain different diagnostic tests. Denote the means and variances of the test result of the normal and diseased subjects as And assume

(a) Find expressions for the pdfs of the test value for normal and diseased subjects.

(b) If we choose compute the sensitivity and the specificity.

(c) Derive an expression for the sensitivity as a function of the threshold value.

(d) Derive an expression for the diagnostic accuracy as a function of the threshold value