Question

A study was perform in the Albuquerque, New Mexico metropolitan area to evaluate the diagnostic accuracy of Prostate Specific Antigen (PSA) testing as a screening tool for detecting prostate cancer in community practice. Subjects were 2,620 men 40 years and older undergoing (PSA) testing and prostate biopsy. A total of 1,932 men tested positive with the initial PSA testing and among them cancer was detected in 800 subjects with a subsequent prostate biopsy. In addition, 130 cases of prostate cancer were detected among men who screened negative with the initial PSA test.

a) Using the information above, create a 2x2 table to assess the accuracy of the test.

b) Calculate and interpret the sensitivity of the PSA test.

c) What will be the specificity of this screening test? Calculate and interpret.

d) Calculate and interpret the predictive value positive of the PSA test.

e) Calculate and interpret the predictive value negative of the PSA test

Answer 1

a) 2X2 table to assess the accuracy of the test is as follows:

Initial PSA	Cancer Yes	Cancer No	Row Total
Positive	800	1132	1932
Negative	130	558	688
Column Total	930	1690	2620

b)

From above table, we can get

True positive (a)=800, False positive (c)=1132

False negative (b)=130 and True negative (d)=558

Sensitivity= a / a+b = 800 / (800+130) = 0.8602

Hence Sensitivity is 86.02%.

Interpretation: Above number suggest that ~86% cases are correctly identified as positive by the test.

c)

Specificity= d / c+d = 558 / (1132+558) = 0.3301

Hence Specificity is 33%.

Interpretation: Above number suggest that ~33% cases are correctly identified as negative by the test.

d)

Positive predictive value = a / a+c = 800 / (800+1132) = 0.4140

Hence Positive predictive value is 41%

Interpretation: Above number suggest that ~41% people are test positive who actually have disease.

e)

Negative predictive value = d / b+d = 558 / (130+558) = 0.8110

Hence Positive predictive value is 81%

Interpretation: Above number suggest that ~81% people are test negative who actually do not have disease.