Question

In this hypothetical case study, a new rapid test kit nicknamed Alpha is being reviewed. The sensitivity of Alpha is 93.0% (0.93) and the specificity is 96.0% (0.96). Assume that the actual prevalence of the Zika antibody among the United States population of blood donors is 4% (0.04) and that of the hurricane disaster relief volunteers returning from Puerto Rico is 20.0% (0.20).

Construct a 2 x 2 table, to calculate the positive predictive value (PPV) and the negative predictive value (NPV) of the Alpha test kit in a national network of 1,000,000 donors who donated to ABC Blood banks across the United States. (10 points)

Construct a separate 2 x 2 table, to calculate the PPV and NPV for a population of 2,500 volunteers who aided in the recent hurricane relief efforts in the Caribbean. (10 points)

Answer 1

In the present scenario, or in the Hypothetical case study of a new rapid test or Alpha being reviewed. The sensitivity of alpha is 0.93 and the specificity is 0.96 and the prevalence of zika antibody among the united population of blood donor is 0.04.

*We can construct 2 x 2 to calculate the Positive Predictive Value (PPV) and Negative Predictive Value of Alpha test Kit in a national network of 1,000,000 donors who are donated to ABC Blood Banks across the United States as:

	Diseased	Not Diseased	Total
Test Positive	930000	70000	1000000
Test Negative	960000	40000	1000000
Column Total	1890000	110000	2000000

Eg: for calculating the PPV and NPV

=0.93 x0.04/(0.037) + (1-0.96) x (1-0.04)

=0.37/ (0.037)+ (1-0.96) x (1-0.04)

=0.037/( 0.037) + (0.04 x0.96)

=0.037/ (0.037 + 0.03)

=0.037/0.067

=0.55

=0.96 x (1-0.04)/ (1-0.93) x 1 x (1-0.04)

=(0.096 x 0.096) /0.07 x 1x (0.96)

=0.92/0.06

=15.3

* In the present scenario, or in the Hypothetical case study of Hurricane disaster relief volunteers returning from Puerto Rico where the sensitivity is (93.0%) 0.93 and the specificity is (96.0%) 0.96 and the Hurricane disaster relief volunteers returning from Puerto Rico is (20.0%) 0.20

*We can construct 2 x 2 to calculate the Positive Predictive Value (PPV) and Negative Predictive Value of Hurricane disaster relief volunteers returning from Puerto Rico for a population of 2,500 volunteers who aided in the hurricane relief efforts in the Caribbean as :

	Returned	Not Returned	Total
Sensitivity	2325	175	2500
Specificity	2400	100	2500
Column Total	4725	275	5000

Thus 2 x2 contingency table can be very useful when testing the validity of a screening test.Here we can prepare the table as in rows and columns and observed for the total of two