An 89-year-old man is brought to a geriatric clinic by family members who are concerned that he is developing dementia due to recent worsening of his memory. The attending physician uses a new cognitive test (test X) to help rule out the possibility of dementia. The patient's test result is negative. A study evaluating the efficacy of test X in a sample of 200 individuals age 85, in which the prevalence of dementia is 50%, has determined that the test has a specificity of 80% and a sensitivity of 90%. Assuming that this patient's pretest probability of having dementia is equivalent to the disease prevalence in the study population, what is the probability that this patient truly does not have dementia?

Question

An 89-year-old man is brought to a geriatric clinic by family members who are concerned that he is developing dementia due to recent worsening of his memory.  The attending physician uses a new cognitive test (test X) to help rule out the possibility of dementia.  The patient's test result is negative.  A study evaluating the efficacy of test X in a sample of 200 individuals age >85, in which the prevalence of dementia is 50%, has determined that the test has a specificity of 80% and a sensitivity of 90%.  Assuming that this patient's pretest probability of having dementia is equivalent to the disease prevalence in the study population, what is the probability that this patient truly does not have dementia?

Quizplus · Accepted Answer

The negative predictive value (NPV) of a diagnostic test is the probability that a patient truly does not have the disease when the patient receives a negative test result. It can be calculated from study data as follows: NPV = number of true negatives / total number of negative tests To determine the NPV in this case, it helps to summarize the results of the efficacy study in a 2 × 2 table. The study evaluated 200 individuals in a population with a 50% prevalence of dementia (ie, 100 patients had dementia while 100 did not). Knowing that specificity (ie, true negatives/total disease negatives) and sensitivity (ie, true positives/total disease positives) are 80% and 90%, respectively, the following 2 × 2 table can be created: 11ec160b_3725_37f3_9249_d71f0b1e11f9_MD0001_00 The NPV can now be estimated as follows: NPV = number of true negatives (d) / total number of negative tests (c + d) NPV = d / (c + d) = 80 / (10 + 80) = 0.889 = ~ 89% Unlike sensitivity and specificity, positive and negative predictive values vary based on the prevalence of the disease. In fact, the NPV is inversely proportional to the prevalence of a disease (eg, NPV ↓ as disease prevalence ↑). For the NPV to be applicable to an individual patient, that patient's pretest probability (eg, probability of having the disease before testing) must be similar to the prevalence of disease in the population where the study was conducted. The question says to assume that the patient's pretest probability is equivalent to the disease prevalence in the study population, so the NPV calculated in the study is generalizable to this patient. Educational objective: Negative predictive value (NPV) represents the probability of not having a disease given a negative test result. NPV is inversely proportional to the prevalence of a disease. When a patient has characteristics similar to the overall population (eg, age, sex, risk factor status), the disease prevalence is a valid estimate of the pretest probability of disease.

An 89-Year-Old Man Is Brought to a Geriatric Clinic by Family