Suppose the probability distributions of a test results for patients disease wit

Question

Suppose the probability distributions of a test results for patients disease with and without diseases are modeled as Gaussian distribution as shown in the figure below. The means are variance odf the result of the normal and subjects with disease are respectively E_infinity = sigma_n = 5, x_d = 20, sigma_d = 4. A diagnostic test is performed the decision the signal is above t then the with patient is threshold below t then the patient is diagnosed as having cancer, whereas if the signal is below t then the patients is diabolized as normal. The following integrals are given: integral_-infinity^t rho_normal (x) dx = 0.65654 integral_-infinity^t rho_diseasced(x) dx = 0.0228 The distribution are normalized such that: integral_-infinity^infinity rho_normal(x) dx = 1 integral_-infinity^infinity rh0_diseaseced (x) dx = 1 What is the sensitivity for the diagnostic test What is the specificity for the diagnostic test lf the threshold t was increased to 60, estimate what happens to the values sensitivity and specificity?

Explanation / Answer

a) Sensitivity = True Positive Rate= True positive/Total positive

This is basically the probability of detecting Normal when it is actually Normal= 0.6554

b) Specificity = True Negative Rate= True negative / Total negative=1-.0228= 0.9772

c) If t is increased from 12 to 60 then:

Sensitivity= 1 (almost)

Specificity=0 (almost)

Excel formula:

Sensitivity Specificity =NORM.DIST(60,10,5,TRUE) =1-NORM.DIST(60,20,4,TRUE)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.