Question

A new test has been developed for diagnosing Rheumatoid Arthritis. The test was evaluated in four communities with the following results Table-1:

            Table 1: Results of a new screening test for Rheumatoid Arthritis in Four Communities

Community A	Rheumatoid Arthritis
	Present	Absent	Total
Test Result +	887	888	1775
Test Result --	99	7989	8088
	986	8877	9863

Community B	Rheumatoid Arthritis
	Present	Absent	Total
Test Result +	1485	385	1870
Test Result --	165	3465	3630
	1650	3850	5500

Community C	Rheumatoid Arthritis
	Present	Absent	Total
Test Result +	3634	269	3903
Test Result --	404	2423	2827
	4038	2692	6730

Community D	Rheumatoid Arthritis
	Present	Absent	Total
Test Result +	2866	56	2922
Test Result --	318	506	824
	3184	562	3746

2.1.      Calculate the prevalence of Rheumatoid Arthritis in each of these four communities.

            (4 points)

            2.2.      Calculate the sensitivity of the test for each community. (4 points)

                       2.3.      Graph the sensitivity percentages against the prevalence for the communities. No need to        use a graph paper! (1 point)

            2.4.      Calculate the specificity of the test for each community. (4 points)

2.5.      Graph the specificity percentages against the prevalence for the communities. No need to use a graph paper! (1 point)

            2.6.      Calculate the positive predictive value of the test for each community. (4 points)

2.7.      Graph the positive predictive values against the prevalence for the communities. No need to use a graph paper! (1 point)

2.8.      What problems might one have in applying the positive predictive value if, as is usually done, a test is first evaluated in a hospital population and then used in the community? (2 points)

Answer 1

Data:

	community A	community B	community C	community D
	Present	Absent	Present	Absent	Present	Absent	Present	Absent
	887	888	1485	385	3634	269	2866	56
	99	7989	165	3465	404	2423	318	506
Total	986	8877	1650	3850	4038	2692	3184	562

2.1

Prevalence = no. of cases / population size

Population size = 25839

Community A : 9863/25839 =38%

Community B : 5500/ 25839 = 21%

Community C : 6730/ 25839 =26%

Community D : 3746/ 25839 =14%

2.2

Sensitivity

Community A : 986/9863 =10%

Community B :1650/ 5500 = 30%

Community C : 408/ 6730 =60%

Community D : 3184/3746 =85%

2.3

Community	prevalence	sensitivity
A	38%	10%
B	21%	30%
C	26%	60%
D	14%	85%

2.4

Specificity

Community A : 8877/25839 =34%

Community B :3850/ 25839 = 15%

Community C : 2692/ 25839 =10%

Community D : 562/25839 =2%

2.5

Community	prevalence	specificity
A	38%	34%
B	21%	15%
C	26%	10%
D	14%	2%

2.6

Community	prevalence	sensitivity	specificity	Positive predicated value
A	38%	10%	34%	9%
B	21%	30%	15%	9%
C	26%	60%	10%	19%
D	14%	85%	2%	13%

2.7