Probabilistic reasoning — MCQs

A scientist in Chicago is studying a new blood test to detect Ab to EBV with increased sensitivity and specificity. So far, her best attempt at creating such an exam reached 82% sensitivity and 88% specificity. She is hoping to increase these numbers by at least 2 percent for each value. After several years of work, she believes that she has actually managed to reach a sensitivity and specificity much greater than what she had originally hoped for. She travels to China to begin testing her newest blood test. She finds 2,000 patients who are willing to participate in her study. Of the 2,000 patients, 1,200 of them are known to be infected with EBV. The scientist tests these 1,200 patients' blood and finds that only 120 of them tested negative with her new exam. Of the patients who are known to be EBV-free, only 20 of them tested positive. Given these results, which of the following correlates with the exam's specificity?

Group of 100 medical students took an end of the year exam. The mean score on the exam was 70%, with a standard deviation of 25%. The professor states that a student's score must be within the 95% confidence interval of the mean to pass the exam. Which of the following is the minimum score a student can have to pass the exam?

A 25-year-old man with a genetic disorder presents for genetic counseling because he is concerned about the risk that any children he has will have the same disease as himself. Specifically, since childhood he has had difficulty breathing requiring bronchodilators, inhaled corticosteroids, and chest physiotherapy. He has also had diarrhea and malabsorption requiring enzyme replacement therapy. If his wife comes from a population where 1 in 10,000 people are affected by this same disorder, which of the following best represents the likelihood a child would be affected as well?

A mother presents to the family physician with her 16-year-old son. She explains, "There's something wrong with him doc. His grades are getting worse, he's cutting class, he's gaining weight, and his eyes are often bloodshot." Upon interviewing the patient apart from his mother, he seems withdrawn and angry at times when probed about his social history. The patient denies abuse and sexual history. What initial test should be sent to rule out the most likely culprit of this patient's behavior?

A 26-year-old medical student comes to the physician with a 3-week history of night sweats and myalgias. During this time, he has also had a 3.6-kg (8-lb) weight loss. He returned from a 6-month tropical medicine rotation in Cambodia 1 month ago. A chest x-ray (CXR) shows reticulonodular opacities suggestive of active tuberculosis (TB). The student is curious about his likelihood of having active TB. He reads a study that compares sputum testing results between 2,800 patients with likely active TB on a basis of history, clinical symptoms, and CXR pattern and 2,400 controls. The results are shown: Sputum testing positive for TB Sputum testing negative for TB Total Active TB likely on basis of history, clinical symptoms, and CXR pattern 700 2100 2,800 Active TB not likely on basis of history, clinical symptoms, and CXR pattern 300 2100 2,400 Total 1000 4200 5,200 Which of the following values reflects the probability that a patient with a diagnosis of active TB on the basis of history, clinical symptoms, and CXR pattern actually has active TB?

A 52-year-old man comes to the physician because of a 3-week history of a cough and hoarseness. He reports that the cough is worse when he lies down after lunch. His temperature is 37.5°C (99.5°F); the remainder of his vital signs are within normal limits. Because the physician has recently been seeing several patients with the common cold, the diagnosis of a viral upper respiratory tract infection readily comes to mind. The physician fails to consider the diagnosis of gastroesophageal reflux disease, which the patient is later found to have. Which of the following most accurately describes the cognitive bias that the physician had?

A research study is comparing 2 novel tests for the diagnosis of Alzheimer’s disease (AD). The first is a serum blood test, and the second is a novel PET radiotracer that binds to beta-amyloid plaques. The researchers intend to have one group of patients with AD assessed via the novel blood test, and the other group assessed via the novel PET examination. In comparing these 2 trial subsets, the authors of the study may encounter which type of bias?

A 57-year-old man presents to the clinic for a chronic cough over the past 4 months. The patient reports a productive yellow/green cough that is worse at night. He denies any significant precipitating event prior to his symptoms. He denies fever, chest pain, palpitations, weight changes, or abdominal pain, but endorses some difficulty breathing that waxes and wanes. He denies alcohol usage but endorses a 35 pack-year smoking history. A physical examination demonstrates mild wheezes, bibasilar crackles, and mild clubbing of his fingertips. A pulmonary function test is subsequently ordered, and partial results are shown below: Tidal volume: 500 mL Residual volume: 1700 mL Expiratory reserve volume: 1500 mL Inspiratory reserve volume: 3000 mL What is the functional residual capacity of this patient?

A medical research study is beginning to evaluate the positive predictive value of a novel blood test for non-Hodgkin’s lymphoma. The diagnostic arm contains 700 patients with NHL, of which 400 tested positive for the novel blood test. In the control arm, 700 age-matched control patients are enrolled and 0 are found positive for the novel test. What is the PPV of this test?

A student health coordinator plans on leading a campus-wide HIV screening program that will be free for the entire undergraduate student body. The goal is to capture as many correct HIV diagnoses as possible with the fewest false positives. The coordinator consults with the hospital to see which tests are available to use for this program. Test A has a sensitivity of 0.92 and a specificity of 0.99. Test B has a sensitivity of 0.95 and a specificity of 0.96. Test C has a sensitivity of 0.98 and a specificity of 0.93. Which of the following testing schemes should the coordinator pursue?