Sensitivity and Specificity

1
Sensitivity and Specificity

• Assuming a low risk population where the
  prevalence of HIV infection is 1/10,000 and
• given an ELISA test with sensitivity of 97.7,
  and specificity of 92.6
• how would the Positive Predictive Value be
  calculated?

2
Sensitivity and Specificity

• STEP 1 Arbitrarily select a population, in this
  case a population of 1,000,000
• STEP 2 Given an estimated prevalence of
  disease, calculate the number of diseased and
  non-diseased that you would expect to find in
  that population.

3
Sensitivity and Specificity

• Diseased .0001 X 1,000,000 100
• Non-diseased 1,000,000 - 100
• 999,900

4
Sensitivity and Specificity

• STEP 3 Calculate true positives, false
  positives, true negatives, and false negatives.
• TP 100 x .977 98
• FN 100 - 98 2
• TN 999,900 x .926 925,907
• FP 999,900 - 925,907 73,993

5
Sensitivity and Specificity

• STEP 4 Fill in a hypothetical screening table
  and calculate the expected Positive Predictive
  Value
• ELISA HIV
• Ratio Present Absent Total
• gt3 98 73,993 74,091
• lt3 2 925,907 925,909
• Total 100 999,900 1,000,000

Positive Predictive Value 98/74,091 .1
6
Sensitivity and Specificity

• Assuming a high risk population where the
  prevalence of HIV is 40, and
• given an ELISA test with sensitivity of 97.7,
  and specificity of 92.6
• how would the Positive Predictive Value be
  calculated?

7
Sensitivity and Specificity

• STEP 1 Arbitrarily select a population, in this
  case a population of 10,000.
• STEP 2 Given an estimated prevalence of disease
  calculate the number of diseased and
  non-diseased that you would expect to find in the
  population

8
Sensitivity and Specificity

• Diseased
• .40 x 10,000 4,000
• Non-diseased
• 10,000 - 4,000 6,000

9
Sensitivity and Specificity

• STEP 3 Calculate the number of true positives,
  false positives, true negatives, and false
  negatives.
• TP 4,000 x .977 3,908
• FN 4,000 - 3,908 92
• TN 6,000 x .926 5,556
• FP 6,000 - 5,556 444

10
Sensitivity and Specificity

• STEP 4 Fill in a hypothetical screening table
  and calculate the expected Positive Predictive
  Value
• ELISA HIV
• Ratio Present Absent Total
• lt3 92 5,556 5,648
• gt3 3,908 444 4,352
• Total 4,000 6,000 10,000

Positive Predictive Value 3,908/4,352 89.9
11
Sensitivity and Specificity

• If the ELISA screening test was applied to a low
  risk population (a prevalence of 0.1), 0.1 of
  all those who tested positive would actually be
  HIV.
• OR
• If the ELISA screening test was applied to a high
  risk population (a prevalence of 40), 89.9 of
  all those that tested positive would actually be
  HIV.

12
Sensitivity and Specificity

• Positive Predictive Values of the ELISA test for
  HIV Infection For Two Cutpoints, in Populations
  with Varying Prevalence of HIV

13
PV for two cut points
PV decreases as the P decreases
14
PV and Prevalence

• Effect of Prevalence on Predictive Value
• Positive Predictive Value of Prostatic Acid
  Phosphatase for Prostatic Cancer
• Sensitivity 70
• Specificity 90
• Various Clinical Settings

15
PV and Prevalence

16
Glaucoma