# Sensitivity and Specificity – HPHA 5330 Homework #2

1. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true positive numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the false positive numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the false negative numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the sensitivity will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the specificity will _____________________ .

(3 points)

1. Increase
2. Decrease

1. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the diseased population (higher numbers in this example), the true positive numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the diseased population (higher numbers in this example), the true negative numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the diseased population (higher numbers in this example), the false positive numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the diseased population (higher numbers in this example), the false negative numbers will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the diseased population (higher numbers in this example), sensitivity will _____________________ .

(3 points)

1. Increase
2. Decrease
3. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the diseased population (higher numbers in this example), the specificity will _____________________ .

(3 points)

1. Increase
2. Decrease

13.

A new test for strep throat is developed. 500 children with sore throat are tested with the new test and also have throat cultures taken. Assume that the throat cultures are 100% accurate in determining whether or not a child has a strep infection.

The following data are collected:

The new test showed positive results (strep throat) in 210 children out of the 276 children who had positive strep cultures

The new test showed negative results (no strep throat) in 190 children out of 224 children who had negative strep cultures.

Construct and fill in a complete “2×2” table for this study. (15 points)

 Strep Throat (Yes) Strep Throat (No) Totals Test result + TP = 210 FP = 34 (TP + FP) = 244 Test result – FN = 66 TN = 190 (TN + FN) = 256 Totals (TP + FN) = 276 (TN + FP) = 224 (TP + TN + FP + FN) = 500

What is the sensitivity of the new test? Show all work.  (7 points)

Sensitivity = TP / (TP + FN)

210 / 276 = 0.76 0r 76%

What is the specificity of the new test? Show all work. (7 points)

Specificity = TN / (TN + FP)

190 / 224 = 0.85 or 85%

What is the false positive rate of the new test? Show all work. (7 points)

FPR = FP / (FP + TN)

34 / 224 = 0.15 or 15%

What is the false negative rate of the new test? Show all work. (7 points)

FNR = FN / (FN + TP)

66 / 276 = 0.24 or 24%

If the prevalence (pre-test probability) of strep throat among children in the population is 2%, what is the probability that a child has strep throat if the new test result for that child is positive? (Hint: This is a problem using Bayes’ Theorem). Show all work. (7 points)

p[D|+] = p[D] x TPR / [(p[D] x TPR) + ((1 – p[D]) x FPR)]

p[D|+] = 0.02 x 0.76 / [(0.02 x 0.76) + ((1 – 0.02) x 0.15)]

p[D|+] = 0.0152 / [(0.0152) + ((0.98) x 0.15)]

p[D|+] = 0.0152 / [(0.0152) + (0.98 x 0.15)]

p[D|+] = 0.0152 / 0.1622

p[D|+] = 0.09

14.

There are an equal number of males and females in your community, 15% of the population are indigent. At any one time, 45% of the males have high blood pressure. Assume that there is no causal relationship between gender, hypertension, and indigent status.

What is the probability that the next person who comes to your emergency room will be a hypertensive, indigent, man? Show all work. (7 points)

P = P (hypertensive / males) * P (indigent / population) * P (gender / male)

P = 0.45 x 0.15 x 0.50

P  = 0.03

15.

There are an equal number of males and females in your community. At any one time, 45% of the males have high blood pressure. At any one time, 4% of the women are pregnant.

What is the probability that the next person who comes into your emergency room will be either a hypertensive man or a pregnant woman? Show all work. (7 points)

P = [P (hypertensive / males) * P (gender / female)] OR [P (pregnant / female) * P (gender / female)]

P = [0.50 x 0.45] + [0.50 x 0.04]

P = 0.225 + 0.02

P = 0.25