A new serologic test has been developed for the detection of active pulmonary tuberculosis and is compared to the gold standard of sputum mycobacterial culture. A total of 1000 subjects are randomly selected for testing from a population with a high prevalence of tuberculosis. Results of the study are given below: Which of the following is the positive predictive value of the test under study?

Question

A new serologic test has been developed for the detection of active pulmonary tuberculosis and is compared to the gold standard of sputum mycobacterial culture.  A total of 1000 subjects are randomly selected for testing from a population with a high prevalence of tuberculosis.  Results of the study are given below:  Which of the following is the positive predictive value of the test under study?

Quizplus · Accepted Answer

11ec160b_3724_c2c0_9249_611d458bf99e_MD0001_00 The positive predictive value (PPV) of a test answers the question: If the test result is positive, what is the probability that a patient has the disease? PPV is calculated as the proportion of subjects who truly have the disease among all those with a positive test result. In contrast, the negative predictive value (NPV) of a test answers the question: If the test result is negative, what is the probability that a patient does not have the disease? It is calculated as the proportion of subjects who are truly free of disease among all those with a negative test result. Predictive values are of prime importance to physicians because, in clinical practice, patients will present more often with a positive or negative test than with a defined diseased or disease-free state. Consider the following 2 × 2 (contingency) table: PPV = TP / (TP + FP), where TP is true positives and FP is false positives. NPV = TN / (TN + FN), where TN is true negatives and FN is false negatives. In this case, PPV = 130 / (130 + 60) = 130/190. (Choices A and E) Sensitivity is a test's ability to correctly identify individuals with the disease. Sensitivity = TP / (TP + FN) = 130 / (130 + 50) = 130/180. Specificity is a test's ability to correctly identify individuals without the disease. Specificity = TN / (TN + FP) = 760 / (760 + 60) = 760/820. (Choice C) The total number of individuals who have tuberculosis (based on the gold standard of positive sputum culture) is 180. The total number of individuals in this sample is 1000. Therefore, the prevalence of tuberculosis in this sample is 180/1000. (Choice D) NPV = 760 / (760 + 50) = 760/810. Educational objective: The positive predictive value (PPV) of a test answers the question: If the test result is positive, what is the probability that a patient has the disease? PPV = true positives / (true positives + false positives).

A New Serologic Test Has Been Developed for the Detection