# WBR0038

Author [[PageAuthor::Gonzalo A. Romero, M.D.  (Reviewed by Yazan Daaboul, M.D.)]]
Exam Type USMLE Step 1
Main Category Biostatistics/Epidemiology
Sub Category General Principles
Prompt CG-23 is a bloodborne infectious organism that causes a self-limited acute infection among healthy adults. A group of investigators has developed a new diagnostic test for the detection of a serum marker, TAK, which is a structural component of the CG-23 capsule. A study is evaluating the performance of the new test among 500 healthy subjects who are followed-up for the development of symptoms. Blood is also withdrawn for real-time polymerase chain reaction (RT-PCR) analysis, the gold standard test for the detection of CG-23 DNA. The infectious organism's DNA is detected in 100 individuals by RT-PCR. The sensitivity and specificity of the novel test are 90% and 80%, respectively. What is the probability that a subject with a positive result in the new diagnostic test truly has the disease?
Answer A Explanation [[AnswerAExp::The sensitivity is the probability of a positive test result when the subjects actually have the disease. The sensitivity can be calculated as follows:

In this case, sensitivity=90/(90+10)= 90/100]]

Answer B Explanation [[AnswerBExp::The specificity is the probability of a negative test result when the subjects do not have the disease. The specificity can be calculated as follows:

In this case, specificity=320/(320+10)= 320/330]]

Answer C Explanation [[AnswerCExp::The positive predictive value (PPV) is the proportion of individuals with a positive test result who actually have the disease. The PPV can be calculated as follows:

In this case, PPV= 90/(90+80)= 90/170]]

Answer D Explanation [[AnswerDExp::The negative predictive value is the proportion of individuals without the disease who test negative using the specified testing modality. The NPV can be calculated as follows:

In this case, NPV= 320/(320+10)= 320/330]]

Answer E Explanation [[AnswerEExp::The accuracy of a test is the proportion of true results (both true positives and true negatives) in the population.

Accuracy= (True positive + True negative) / Total number of subject tested

In this case, accuracy=90+320/500= 410/500]]

Explanation [[Explanation::In order to calculate the positive predictive value (PPV), a 2x2 table containing the true positive, false positive, true negative, and false negative needs to be constructed. The sample size is 500 and the total number of subjects with disease is 100. Therefore, the total number of subjects without the disease is 400. Since the sensitivity is 90%, 90 subjects of the 100 who have the disease have true positive results; while 10 have false negative results. Similarly, since the specificity is 80%, 320 subjects out of the 400 have true negative results, and 400-32=80 have false negative results.

The positive predictive value (PPV) is the proportion of individuals with a positive test result who actually have the disease. The PPV can be calculated as follows:

 Disease No disease Positive test True positive False negative Negative test False positive True negative

In this case, PPV= 90/(90+80)= 90/170

 Disease No disease Total Positive test 90 80 170 Negative test 10 320 330 Total 100 400 500

Educational Objective: The positive predictive value (PPV) is the proportion of individuals with a positive test result who actually have the disease. PPV= True positive/(True positive + False positive)
References: First Aid 2014 page 51]]

Approved Yes
Keyword Biostatistics, Positive predictive value