Area under the curve (AUC) interpretation — MCQs

10 questions

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?

You are developing a new diagnostic test to identify patients with disease X. Of 100 patients tested with the gold standard test, 10% tested positive. Of those that tested positive, the experimental test was positive for 90% of those patients. The specificity of the experimental test is 20%. What is the positive predictive value of this new test?

A scientist in Boston is studying a new blood test to detect Ab to the parainfluenza virus 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 even greater than what she had originally hoped for. She travels to South America 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 the parainfluenza virus. The scientist tests these 1,200 patients’ blood and finds that only 120 of them tested negative with her new test. Of the following options, which describes the sensitivity of the test?

You conduct a medical research study to determine the screening efficacy of a novel serum marker for colon cancer. The study is divided into 2 subsets. In the first, there are 500 patients with colon cancer, of which 450 are found positive for the novel serum marker. In the second arm, there are 500 patients who do not have colon cancer, and only 10 are found positive for the novel serum marker. What is the overall sensitivity of this novel test?

A 20-year-old college student is brought to the ED after a motor vehicle accident. Primary and secondary surveys reveal no significant compromise to his airway, his cardiovascular system, or to his motor function. However, his conjunctiva appear injected and he maintains combative behavior towards staff. What is the gold standard confirmatory test for substance use?

A 32-year-old woman presented for her annual physical examination. She mentioned that her family history had changed since her last visit: her mother was recently diagnosed with breast cancer and her sister tested positive for the BRCA2 mutation. The patient, therefore, requested testing as well. If the patient tests positive for the BRCA1 or BRCA2 mutation, which of the following is the best screening approach?

During an evaluation of a new diagnostic imaging modality for detecting salivary gland tumors, 90 patients tested positive out of the 100 patients who tested positive with the gold standard test. A total of 80 individuals tested negative with the new test out of the 100 individuals who tested negative with the gold standard test. What is the positive likelihood ratio for this test?

In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?

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?

Q10

You are tasked with analyzing the negative predictive value of an experimental serum marker for ovarian cancer. You choose to enroll 2,000 patients across multiple clinical sites, including both 1,000 patients with ovarian cancer and 1,000 age-matched controls. From the disease and control subgroups, 700 and 100 are found positive for this novel serum marker, respectively. Which of the following represents the NPV for this test?

Area under the curve (AUC) interpretation US Medical PG Practice Questions and MCQs

Question 1: 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. 45%
B. 63.75%
C. 67.5%
D. 20%
E. 65% (Correct Answer)

Explanation: ***65%*** - To find the **95% confidence interval (CI) of the mean**, we use the formula: Mean ± (Z-score × Standard Error). For a 95% CI, the Z-score is approximately **1.96**. - The **Standard Error (SE)** is calculated as SD/√n, where n is the sample size (100 students). So, SE = 25%/√100 = 25%/10 = **2.5%**. - The 95% CI is 70% ± (1.96 × 2.5%) = 70% ± 4.9%. The lower bound is 70% - 4.9% = **65.1%**, which rounds to **65%** as the minimum passing score. *45%* - This value is significantly lower than the calculated lower bound of the 95% confidence interval (approximately 65.1%). - It would represent a score far outside the defined passing range. *63.75%* - This value falls below the calculated lower bound of the 95% confidence interval (approximately 65.1%). - While close, this score would not meet the professor's criterion for passing. *67.5%* - This value is within the 95% confidence interval (65.1% to 74.9%) but is **not the minimum score**. - Lower scores within the interval would still qualify as passing. *20%* - This score is extremely low and falls significantly outside the 95% confidence interval for a mean of 70%. - It would indicate performance far below the defined passing threshold.

Question 2: You are developing a new diagnostic test to identify patients with disease X. Of 100 patients tested with the gold standard test, 10% tested positive. Of those that tested positive, the experimental test was positive for 90% of those patients. The specificity of the experimental test is 20%. What is the positive predictive value of this new test?

A. 10%
B. 90%
C. 95%
D. 11% (Correct Answer)
E. 20%

Explanation: ***11%*** - The positive predictive value (PPV) is calculated as **true positives / (true positives + false positives)**. - From 100 patients, 10 have disease (prevalence 10%). With 90% sensitivity, the test correctly identifies **9 true positives** (90% of 10). - Of 90 patients without disease, specificity of 20% means 20% are correctly identified as negative (18 true negatives), so **72 false positives** = 90 × (1 - 0.20). - Therefore, PPV = 9 / (9 + 72) = 9/81 = **11.1% ≈ 11%**. *10%* - This value represents the **prevalence** of the disease in the population, not the positive predictive value of the test. - Prevalence is the proportion of individuals who have the disease (10 out of 100 patients). *90%* - This figure represents the **sensitivity** of the test, which is the percentage of true positives correctly identified by the experimental test. - Sensitivity = true positives / (true positives + false negatives) = 9/10 = 90%. *95%* - This value is not directly derivable from the given data and does not represent any standard test characteristic in this context. - It would imply a much higher PPV than what can be calculated given the low specificity of 20%. *20%* - This is the stated **specificity** of the test, which measures the proportion of true negatives correctly identified. - Specificity = true negatives / (true negatives + false positives) = 18/90 = 20%.

Question 3: A scientist in Boston is studying a new blood test to detect Ab to the parainfluenza virus 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 even greater than what she had originally hoped for. She travels to South America 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 the parainfluenza virus. The scientist tests these 1,200 patients’ blood and finds that only 120 of them tested negative with her new test. Of the following options, which describes the sensitivity of the test?

A. 82%
B. 86%
C. 98%
D. 90% (Correct Answer)
E. 84%

Explanation: ***90%*** - **Sensitivity** is calculated as the number of **true positives** divided by the total number of individuals with the disease (true positives + false negatives). - In this scenario, there were 1200 infected patients (total diseased), and 120 of them tested negative (false negatives). Therefore, 1200 - 120 = 1080 patients tested positive (true positives). The sensitivity is 1080 / 1200 = 0.90, or **90%**. *82%* - This value was the **original sensitivity** of the test before the scientist improved it. - The question states that the scientist believes she has achieved a sensitivity "even greater than what she had originally hoped for." *86%* - This value is not directly derivable from the given data for the new test's sensitivity. - It might represent an intermediate calculation or an incorrect interpretation of the provided numbers. *98%* - This would imply only 24 false negatives out of 1200 true disease cases, which is not the case (120 false negatives). - A sensitivity of 98% would be significantly higher than the calculated 90% and the initial stated values. *84%* - This value is not derived from the presented data regarding the new test's performance. - It could be mistaken for an attempt to add 2% to the original 82% sensitivity, but the actual data from the new test should be used.

Question 4: You conduct a medical research study to determine the screening efficacy of a novel serum marker for colon cancer. The study is divided into 2 subsets. In the first, there are 500 patients with colon cancer, of which 450 are found positive for the novel serum marker. In the second arm, there are 500 patients who do not have colon cancer, and only 10 are found positive for the novel serum marker. What is the overall sensitivity of this novel test?

A. 450 / (450 + 10)
B. 490 / (10 + 490)
C. 490 / (50 + 490)
D. 450 / (450 + 50) (Correct Answer)
E. 490 / (450 + 490)

Explanation: ***450 / (450 + 50)*** - **Sensitivity** is defined as the proportion of actual positive cases that are correctly identified by the test. - In this study, there are **500 patients with colon cancer** (actual positives), and **450 of them tested positive** for the marker, while **50 tested negative** (500 - 450 = 50). Therefore, sensitivity = 450 / (450 + 50) = 450/500 = 0.9 or 90%. *450 / (450 + 10)* - This formula represents **Positive Predictive Value (PPV)**, which is the probability that a person with a positive test result actually has the disease. - It incorrectly uses the total number of **test positives** in the denominator (450 true positives + 10 false positives) instead of the total number of diseased individuals, which is needed for sensitivity. *490 / (10 + 490)* - This is actually the correct formula for **specificity**, not sensitivity. - Specificity = TN / (FP + TN) = 490 / (10 + 490) = 490/500 = 0.98 or 98%, which measures the proportion of actual negative cases correctly identified. - The question asks for sensitivity, not specificity. *490 / (50 + 490)* - This formula incorrectly mixes **true negatives (490)** with **false negatives (50)** in an attempt to calculate specificity. - The correct specificity formula should use false positives (10), not false negatives (50), in the denominator: 490 / (10 + 490). *490 / (450 + 490)* - This calculation incorrectly combines **true negatives (490)** and **true positives (450)** in the denominator, which does not correspond to any standard epidemiological measure. - Neither sensitivity nor specificity uses both true positives and true negatives in the denominator.

Question 5: A 20-year-old college student is brought to the ED after a motor vehicle accident. Primary and secondary surveys reveal no significant compromise to his airway, his cardiovascular system, or to his motor function. However, his conjunctiva appear injected and he maintains combative behavior towards staff. What is the gold standard confirmatory test for substance use?

A. Gas chromatography / mass spectrometry (GC/MS) (Correct Answer)
B. Urine immunoassay
C. Western blot
D. Breath alcohol test
E. Polymerase chain reaction

Explanation: ***Gas chromatography / mass spectrometry (GC/MS)*** - **GC/MS** is considered the **gold standard** for confirming substance use due to its high specificity and sensitivity in identifying and quantifying various substances. - It effectively separates individual compounds in a complex mixture and identifies them based on their unique mass spectra, making it highly reliable for forensic and clinical toxicology. *Urine immunoassay* - **Urine immunoassays** are typically used as **screening tests** for substances because they are rapid and relatively inexpensive, but they can produce false positives. - While useful for initial detection, they require confirmatory testing, often by GC/MS, due to their lower specificity. *Western blot* - **Western blot** is primarily used to detect **specific proteins** in a sample, especially in the diagnosis of infectious diseases or autoimmune conditions, not for substance identification. - It involves separating proteins by gel electrophoresis and then transferring them to a membrane for antibody-based detection. *Breath alcohol test* - A **breath alcohol test** is specifically designed to measure **alcohol concentration** in the breath, which correlates with blood alcohol content. - It is not used for detecting other illicit substances and would not provide a comprehensive toxicology profile. *Polymerase chain reaction* - **Polymerase chain reaction (PCR)** is a molecular biology technique used to amplify **DNA or RNA sequences**, primarily for detecting genetic material from pathogens or for genetic analysis. - It has no role in the direct detection of drugs or their metabolites in biological samples.

Question 6: A 32-year-old woman presented for her annual physical examination. She mentioned that her family history had changed since her last visit: her mother was recently diagnosed with breast cancer and her sister tested positive for the BRCA2 mutation. The patient, therefore, requested testing as well. If the patient tests positive for the BRCA1 or BRCA2 mutation, which of the following is the best screening approach?

A. Order magnetic resonance imaging of the breast
B. Annual ultrasound, annual mammography, and monthly self-breast exams
C. Twice-yearly clinical breast exams, annual mammography, annual breast MRI, and breast self-exams (Correct Answer)
D. Annual clinical breast exams, annual mammography, and monthly self-breast exams
E. Refer to radiation therapy

Explanation: ***Twice-yearly clinical breast exams, annual mammography, annual breast MRI, and breast self-exams*** - For patients with **BRCA1 or BRCA2 mutations**, an intensive breast cancer screening protocol is recommended due to their highly increased lifetime risk of breast cancer. - This typically includes **semiannual clinical breast exams**, **annual mammography**, and **annual breast MRI**, often starting at a young age. *Order magnetic resonance imaging of the breast* - While MRI is a crucial part of screening for high-risk individuals, it is **not sufficient as a standalone screening modality**. - A comprehensive approach combining multiple screening methods is needed to maximize detection rates. *Annual ultrasound, annual mammography, and monthly self-breast exams* - **Breast ultrasound** is generally used as an adjunct to mammography when specific abnormalities are found or in women with dense breasts, not as a routine primary screening tool for BRCA carriers. - While **mammography** and **self-breast exams** are included, this option lacks the crucial **annual MRI** and **twice-yearly clinical breast exams** recommended for BRCA carriers. *Annual clinical breast exams, annual mammography, and monthly self-breast exams* - This protocol is **less intensive** than what is recommended for women with BRCA mutations. - It omits the essential **annual breast MRI** and the **twice-yearly clinical breast exams** that are critical for early detection in this high-risk population. *Refer to radiation therapy* - **Radiation therapy** is a treatment modality for existing cancer, not a screening approach for cancer prevention or early detection. - Referring for radiation therapy would be appropriate only after a diagnosis of breast cancer, not as a primary screening strategy.

Question 7: During an evaluation of a new diagnostic imaging modality for detecting salivary gland tumors, 90 patients tested positive out of the 100 patients who tested positive with the gold standard test. A total of 80 individuals tested negative with the new test out of the 100 individuals who tested negative with the gold standard test. What is the positive likelihood ratio for this test?

A. 80/90
B. 90/100
C. 90/20 (Correct Answer)
D. 90/110
E. 10/80

Explanation: ***90/20*** - The **positive likelihood ratio (LR+)** is calculated as **sensitivity / (1 - specificity)**. To calculate this, we first need to determine the values for true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). - Given that 90 out of 100 actual positive patients tested positive, **TP = 90** and **FN = 100 - 90 = 10**. Also, 80 out of 100 actual negative patients tested negative, so **TN = 80** and **FP = 100 - 80 = 20**. - **Sensitivity** is the true positive rate (TP / (TP + FN)) = 90 / (90 + 10) = 90 / 100. - **Specificity** is the true negative rate (TN / (TN + FP)) = 80 / (80 + 20) = 80 / 100. - Therefore, LR+ = (90/100) / (1 - 80/100) = (90/100) / (20/100) = **90/20**. *80/90* - This option incorrectly represents the components for the likelihood ratio. It seems to misinterpret the **true negative** count and the **true positive** count. - It does not follow the formula for LR+ which is **sensitivity / (1 - specificity)**. *90/100* - This value represents the **sensitivity** of the test, which is the proportion of true positives among all actual positives. - It does not incorporate the **false positive rate** (1 - specificity) in the denominator required for the positive likelihood ratio. *90/110* - This option incorrectly combines different values, possibly by confusing the denominator for sensitivity or specificity calculations. - It does not correspond to the formula for the **positive likelihood ratio**. *10/80* - This value seems to relate to the inverse of the **false negative rate** (10/100) or misrepresents the relationship between false negatives and true negatives. - It is not correctly structured to represent the **positive likelihood ratio (LR+)**.

Question 8: In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?

A. 5,100 (Correct Answer)
B. 4,500
C. 6,000
D. 3,750
E. 6,750

Explanation: ***5,100*** - To solve this, first calculate the **z-score** for 250: (250 - 227) / 22 = 1.045. - Using a **z-table**, the area under the curve from the mean (z=0) to z=1.045 is approximately 0.353. Multiplying this by 15,000 students gives approximately **5,295 students**, which is closest to 5,100. *4,500* - This answer would imply a smaller proportion of students between the mean and 250 (around 30%), which is lower than the calculated z-score of 1.045 suggests. - It does not accurately reflect the area under the **normal distribution curve** for the given range. *6,000* - This option would mean that approximately 40% of students scored in this range, which would correspond to a z-score much higher than 1.045 or a different standard deviation. - This calculation overestimates the number of students within the specified range. *3,750* - This value represents 25% of the total students (15,000 * 0.25), indicating that only a quarter of the distribution lies in this range. - This significantly underestimates the proportion of students scoring between the mean and 250 for the given standard deviation. *6,750* - This option reflects approximately 45% of the total student population (15,000 * 0.45), which would correspond to a much larger z-score or a different distribution. - This value is an overestimation and does not align with the standard normal distribution probabilities for the given parameters.

Question 9: 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. 400 / (400 + 0) (Correct Answer)
B. 700 / (700 + 300)
C. 400 / (400 + 300)
D. 700 / (700 + 0)
E. 700 / (400 + 400)

Explanation: ***400 / (400 + 0) = 1.0 or 100%*** - The **positive predictive value (PPV)** is calculated as **True Positives / (True Positives + False Positives)**. - In this scenario, **True Positives (TP)** are the 400 patients with NHL who tested positive, and **False Positives (FP)** are 0, as no control patients tested positive. - This gives a PPV of 400/400 = **1.0 or 100%**, indicating that all patients who tested positive actually had the disease. *700 / (700 + 300)* - This calculation does not align with the formula for PPV based on the given data. - The denominator `(700+300)` suggests an incorrect combination of various patient groups. *400 / (400 + 300)* - The denominator `(400+300)` incorrectly includes 300, which is the number of **False Negatives** (patients with NHL who tested negative), not False Positives. - PPV focuses on the proportion of true positives among all positive tests, not all diseased individuals. *700 / (700 + 0)* - This calculation incorrectly uses the total number of patients with NHL (700) as the numerator, rather than the number of positive test results in that group. - The numerator should be the **True Positives** (400), not the total number of diseased individuals. *700 / (400 + 400)* - This calculation uses incorrect values for both the numerator and denominator, not corresponding to the PPV formula. - The numerator 700 represents the total number of patients with the disease, not those who tested positive, and the denominator incorrectly sums up values that don't represent the proper PPV calculation.

Question 10: You are tasked with analyzing the negative predictive value of an experimental serum marker for ovarian cancer. You choose to enroll 2,000 patients across multiple clinical sites, including both 1,000 patients with ovarian cancer and 1,000 age-matched controls. From the disease and control subgroups, 700 and 100 are found positive for this novel serum marker, respectively. Which of the following represents the NPV for this test?

A. 700 / (700 + 300)
B. 700 / (300 + 900)
C. 700 / (700 + 100)
D. 900 / (900 + 100)
E. 900 / (900 + 300) (Correct Answer)

Explanation: ***900 / (900 + 300)*** - The **Negative Predictive Value (NPV)** is the probability that a person with a **negative test result** does not have the disease. It is calculated as **true negatives (TN)** divided by the sum of true negatives and **false negatives (FN)**, i.e., TN / (TN + FN). - In this scenario: there are 1,000 ovarian cancer patients, and 700 tested positive, meaning **300 tested negative (false negatives)**. There are 1,000 controls, and 100 tested positive, meaning **900 tested negative (true negatives)**. Therefore, NPV = 900 / (900 + 300). *700 / (700 + 300)* - This calculation represents the sensitivity of the test, which is the proportion of true positives among all individuals with the disease (700 true positives / 1000 diseased individuals). - It does not account for the true negatives or false positives, which are crucial for determining predictive values. *700 / (300 + 900)* - This formula mixes elements and does not correspond to a standard measure of test validity. - The numerator (700) is the number of true positives, and the denominator incorrectly combines false negatives (300) and true negatives (900). *700 / (700 + 100)* - This calculation represents the **Positive Predictive Value (PPV)**, which is the probability that a person with a **positive test result** actually has the disease (700 true positives / (700 true positives + 100 false positives)). - It does not assess the negative predictive power of the test. *900 / (900 + 100)* - This calculation represents the **specificity** of the test, which is the proportion of true negatives among all individuals without the disease (900 true negatives / 1000 controls). - While this involves true negatives, it does not account for false negatives, which are essential for calculating NPV.

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