Question

The Hemoccult test and the colonoscopy test for colon cancer screening are being conducted in 5000 people in a community. The Hemoccult test has a sensitivity of 78% and a specificity of 75%. The colonoscopy test has a sensitivity of 80% and a specificity of 90%. If the community has a prevalence of 12/1,000 for colon cancer, what is the positive predictive value (PPV) of the hemoccult test and the colonoscopy test, respectively? Which one would be good to recommend for screening test in a large population?

Answer 1

We know that , Positive Predictive Value is defined as the probability that the person has the disease given that the test results in positive .

PPV = (sensitivity * prevalence) / ( sensitivity *prevalence + (1-specificity)*(1-prevalence)

For Hemoccult

sensitivity= 0.78 , prevalence = 12/1000=0.012, specificity =0.75

PPV = (0.78*0.012) / (0.78 *0.012 + (1-0.75)*(1-0.012) = 0.00936/ (0.00936+0.247) = 0.0365

Thus PPV for Hemoccult = 0.0365 or 3.65%

That is probability that the person has colon cancer given that the Hemoccult test results in positive is 3.65%

For Colonoscopy

sensitivity= 0.80 , prevalence = 12/1000=0.012, specificity =0.90

PPV = (0.80*0.012) / (0.80 *0.012 + (1-0.90)*(1-0.012) = 0.0096/ (0.0096+0.0988) = 0.0885

Thus PPV for Hemoccult = 0.0885 or 8.85%

That is probability that the person has colon cancer given that the Colonoscopy test results in positive is 8.85%

Positive predictive value or colonoscopy is more . Thus colonoscopy is recommended for screening test in a large population. As for colonoscopy the probability that the person has cancer if the test is positive is high.