Over the course of 5 years, a pediatric endocrinologist has seen a marked increase in the prevalence of depression among patients with obesity in her practice. She partners with a pediatric psychiatrist to devise a short screening test for depression for this specific population. The new screening test is found to be 90% sensitive and 84% specific. If this test is used on a sample of patients with obesity in which 35% are known to have depression, what is the chance that a patient with obesity who tests negative is actually free from depression?
A)0)12
B)0)75
C)0)94
D)2)97
E)5)63

Question

Over the course of 5 years, a pediatric endocrinologist has seen a marked increase in the prevalence of depression among patients with obesity in her practice.  She partners with a pediatric psychiatrist to devise a short screening test for depression for this specific population.  The new screening test is found to be 90% sensitive and 84% specific.  If this test is used on a sample of patients with obesity in which 35% are known to have depression, what is the chance that a patient with obesity who tests negative is actually free from depression?
A)0)12
B)0)75
C)0)94
D)2)97
E)5)63

Quizplus · Accepted Answer

Explanation: The negative predictive value (NPV) is the probability of not having a disease given a negative test result. Predictive values are affected by the prevalence of the condition being studied, unlike sensitivity and specificity, which are prevalence-independent. NPV can be calculated from data summarized in a standard 2 × 2 table, which can be reconstructed using disease prevalence and test sensitivity and specificity. 2 × 2 table Consider a hypothetical sample of 1,000 subjects. Based on the prevalence (35%), 350 of these subjects will have depression; therefore, 1,000 - 350 = 650 will not have depression. Given the sensitivity of 90%, 0.9 × 350 = 315 of the 350 subjects with depression will test positive (true positives); given the specificity of 84%, 0.84 × 650 = 546 of the 650 without depression will test negative (true negatives). Then the NPV can be calculated as: True negatives / (False negatives + True negatives) = d / (c + d). In this case: NPV = d / (c + d) = 546 / (35 + 546) = (546 / 581) = ~0.94 Therefore, there is a 94% chance that a patient with obesity who tests negative for depression on the screening test is actually free of this disease. (Choices A and E) The negative likelihood ratio (LR−) is the probability of a patient with the disease testing negative divided by the probability of a patient without the disease testing negative. LR− = (1 − sensitivity) / specificity = (1 − 0.90) / 0.84 = (0.10 / 0.84) = ~0.12. The positive likelihood ratio (LR+) is the probability of a patient with the disease testing positive divided by the probability of a patient without the disease testing positive. LR+ = sensitivity / (1 − specificity) = 0.90 / (1 − 0.84) = (0.90 / 0.16) = ~5.63. (Choice B) Positive predictive value (PPV) is the probability of having a disease given a positive test result. PPV = a / (a + b) = 315 / (315 + 104) = ~0.75. (Choice D) The ratio of false-positive to false-negative findings (FP:FN ratio) is an informative metric that denotes how likely the screening test is to result in a false positive as compared to a false negative; it can be expressed as follows: b / c = 104 / 35 = 2.97 or ~3:1. Therefore, a false positive test result is almost 3 times more likely than a false negative test result. Educational objective: Predictive values are affected by the prevalence of disease in the target population. They can be calculated based on sensitivity, specificity, and prevalence of disease.

Over the Course of 5 Years, a Pediatric Endocrinologist Has