Question

1. Construct a 2 by 2 table, calculate the predictive value positive and predictive value negative of the EIA in a hypothetical population of 1,000,000 blood donors. Using a separate 2-by-2 table, calculate PVP and PVN for a population of ill patients. Assume that the actual prevalence of S. Heidelberg among blood donors is 0.04% (.0004) and that of people who ate Foster's chicken is 10.00% (.10).

2. Do you think that the EIA is a good screening test for the hospital? Why or why not?

3. DO you think that the EIA performs well enough to justify using the test outcomes in court cases? Why or why not?

4. If sensitivity and specificity remain constant, what is the relationship of the prevalence of predicative-value positive and predicative value negative?

Given their success with the EIA for S. Heidelberg, Meridian Diagnostics decided to perfect their design, and use it to produce an EIA test for E.coli 0157 H7.

Answer 1

1) Actual prevalence of S. Heidelberg among blood donors is 0.04% (0.0004)

Total number of cases (a+ c) = 0.0004 X 1,000,000 = 400

Sensitivity of the test is 95% or .095

Number of true positives (a) = number of cases X sensitivity of the test

Number of true positives (a) = 400 X 0.95 = 380

Number of true negatives (d) = (number of diagnosed negatives (b + d) – number of cases) X specificity of the test

Number of true negatives (d) = (1,000,000 – 400) X 0.98

= 999,600 X 0.98 = 979,608

Number of false negative (c) = 400 – 380 = 20

Number of false Positive (b) = 999,600 – 979,608 = 19, 992

Test results	Present	Absent	Total
Positive	380(a)	19992(b)	20372(a + b)
Negative	20 (c)	979608(d)	979628 (c+d)
Total	400(a +c)	999600(c+d)	1,000,000

Predictive value plus (PVP) = a/ (a+ b) X 100

= 380/ 20,372 X 100 = 1.865%

PVP = 2%

Predictive value negative (PVN) = d/ (c+ d) X100

= 979,608/ 979,628 X 100

PVN = 99. 99%

2) Based on the PVP and PVN values, EIA is not a good screening test for blood bank because it has high sensitivity and specificity to identify the individuals with S. Heidelberg. It requires an additional test to confirm the positive EIA of blood donors.

3) EIA does not perform very well to identify positive clients in court cases. Because it has high specificity and sensitivity, so it needs a further test and counseling.

4) If the sensitivity and specificity remain constant, then the antibody becomes fall, which results in decreased Predict value positive and increased Predict value Negative. Low PVP means Low prevalence of the disease.