A colon cancer screening study is being conducted in Nottingham, England. Individuals 50 to 75 years old will be screened with the Hemoccult test. In this test, a stool sample is tested for the presence of blood. The Hemoccult test has a sensitivity of 70% and a specificity of 75%. If Nottingham has a prevalence of 12/1000 for colon caner, what is the positive predictive value of the test?

The correct answer is 3.3 %.

Explanation:

Based on the given information, the specificity of the test is 75 percent, the sensitivity of the test is 70 percent and the prevalence of the disease is 12/1000 or 1.2 percent.

As 1.2 percent is the prevalence of the disease, therefore, it shows that of the 1000 individuals the infected individuals would be 12. The 70 percent sensitivity of the test shows that of the 12 affected individuals, 8.4 individuals are determined as positive, that is, 12*70/100.

The remaining 988 of 1000 individuals are not affected by the condition. With 75 percent specificity, the test determines 75 % of 988 individuals, that is, 741 as negative for the test, thus, the left 247 are considered positive. When taken together the outcome of the sensitivity and specificity, the total of 255.4 persons, that is, 247+8.4, are determined as positive. Of these positives, the false positive, that is, 247 holds for 96.7 percent of the total positive individuals.

The PPV or the positive predictive value can be calculated by using the formula:

PPV = Number of persons who are true positive for the disease/Total number of persons who are diagnosed to be positive * 100

= 8.4/255.4 * 100

= 3.3%