Optimizing cut-off values — MCQs

10 questions

A 40-year-old female volunteers for an invasive study to measure her cardiac function. She has no previous cardiovascular history and takes no medications. With the test subject at rest, the following data is collected using blood tests, intravascular probes, and a closed rebreathing circuit: Blood hemoglobin concentration 14 g/dL Arterial oxygen content 0.22 mL O2/mL Arterial oxygen saturation 98% Venous oxygen content 0.17 mL O2/mL Venous oxygen saturation 78% Oxygen consumption 250 mL/min The patient's pulse is 75/min, respiratory rate is 14/ min, and blood pressure is 125/70 mm Hg. What is the cardiac output of this volunteer?

A group of investigators who are studying individuals infected with Trypanosoma cruzi is evaluating the ELISA absorbance cutoff value of serum samples for diagnosis of infection. The previous cutoff point is found to be too high, and the researchers decide to lower the threshold by 15%. Which of the following outcomes is most likely to result from this decision?

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 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?

A pharmaceutical corporation is developing a research study to evaluate a novel blood test to screen for breast cancer. They enrolled 800 patients in the study, half of which have breast cancer. The remaining enrolled patients are age-matched controls who do not have the disease. Of those in the diseased arm, 330 are found positive for the test. Of the patients in the control arm, only 30 are found positive. What is this test’s sensitivity?

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?

You are reviewing raw data from a research study performed at your medical center examining the effectiveness of a novel AIDS screening examination. The study enrolled 250 patients with confirmed AIDS, and 240 of these patients demonstrated a positive screening examination. The control arm of the study enrolled 250 patients who do not have AIDS, and only 5 of these patients tested positive on the novel screening examination. What is the NPV of this novel test?

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?

Q10

Specificity for breast examination is traditionally rather high among community practitioners. A team of new researchers sets forth a goal to increase specificity in detection of breast cancer from the previously reported national average of 74%. Based on the following results, has the team achieved its goal? Breast cancer screening results: Patients WITH breast cancer | Patients WITHOUT breast cancer Test is Positive (+) 21 | 5 Test is Negative (-) 7 | 23

Optimizing cut-off values US Medical PG Practice Questions and MCQs

Question 1: A 40-year-old female volunteers for an invasive study to measure her cardiac function. She has no previous cardiovascular history and takes no medications. With the test subject at rest, the following data is collected using blood tests, intravascular probes, and a closed rebreathing circuit: Blood hemoglobin concentration 14 g/dL Arterial oxygen content 0.22 mL O2/mL Arterial oxygen saturation 98% Venous oxygen content 0.17 mL O2/mL Venous oxygen saturation 78% Oxygen consumption 250 mL/min The patient's pulse is 75/min, respiratory rate is 14/ min, and blood pressure is 125/70 mm Hg. What is the cardiac output of this volunteer?

A. Body surface area is required to calculate cardiac output.
B. Stroke volume is required to calculate cardiac output.
C. 250 mL/min
D. 5.0 L/min (Correct Answer)
E. 50 L/min

Explanation: ***5.0 L/min*** - Cardiac output can be calculated using the **Fick principle**: Cardiac Output $(\text{CO}) = \frac{{\text{Oxygen Consumption}}}{{\text{Arterial } \text{O}_2 \text{ Content} - \text{Venous O}_2 \text{ Content}}}$. - Given Oxygen Consumption = 250 mL/min, Arterial O$_2$ Content = 0.22 mL/mL, and Venous O$_2$ Content = 0.17 mL/mL. Thus, CO = $\frac{{250 \text{ mL/min}}}{{(0.22 - 0.17) \text{ mL } \text{O}_2/\text{mL blood}}} = \frac{{250 \text{ mL/min}}}{{0.05 \text{ mL } \text{O}_2/\text{mL blood}}} = 5000 \text{ mL/min } = 5.0 \text{ L/min}$. *Body surface area is required to calculate cardiac output.* - **Body surface area (BSA)** is used to calculate **cardiac index**, which is cardiac output normalized to body size, but not cardiac output directly. - While a normal cardiac output might be compared to a patient's BSA for context, it is not a necessary component for calculating the absolute cardiac output. *Stroke volume is required to calculate cardiac output.* - Cardiac output can be calculated as **Stroke Volume (SV) x Heart Rate (HR)**. However, stroke volume is not provided directly in this question. - The Fick principle allows for the calculation of cardiac output **without explicit knowledge of stroke volume** or heart rate, using oxygen consumption and arteriovenous oxygen difference. *250 mL/min* - 250 mL/min represents the **oxygen consumption**, not the cardiac output. - Cardiac output is the volume of blood pumped by the heart per minute, which is influenced by both oxygen consumption and the difference in oxygen content between arterial and venous blood. *50 L/min* - A cardiac output of 50 L/min is an **extremely high and physiologically impossible** value for a resting individual. - This value is 10 times higher than the calculated cardiac output and typically represents a calculation error.

Question 2: A group of investigators who are studying individuals infected with Trypanosoma cruzi is evaluating the ELISA absorbance cutoff value of serum samples for diagnosis of infection. The previous cutoff point is found to be too high, and the researchers decide to lower the threshold by 15%. Which of the following outcomes is most likely to result from this decision?

A. Increased negative predictive value (Correct Answer)
B. Unchanged true positive results
C. Decreased sensitivity
D. Increased specificity
E. Increased positive predictive value

Explanation: ***Increased negative predictive value*** - Lowering the absorbance cutoff for the ELISA test makes it **easier to test positive**, which increases **sensitivity** (more true positives are detected, fewer false negatives occur). - **Negative predictive value (NPV)** is the probability that a person who tests negative truly does not have the disease: NPV = TN / (TN + FN). - When the cutoff is lowered, **fewer infected individuals will be missed** (false negatives decrease). This reduction in false negatives improves the NPV because there are fewer disease-positive individuals in the "test-negative" group. - Therefore, a negative test result becomes **more reliable at ruling out infection**, increasing the NPV. *Unchanged true positive results* - Lowering the cutoff means that samples with lower absorbance values (previously below threshold) from truly infected individuals will now be classified as positive. - This directly **increases the number of true positive results**, not keeps them unchanged. - The whole purpose of lowering the threshold is to capture more infected cases. *Decreased sensitivity* - **Sensitivity** = TP / (TP + FN), the ability to correctly identify those with disease. - Lowering the cutoff **increases sensitivity** by making it easier to test positive, thereby capturing more true positives and reducing false negatives. - A lower threshold would never decrease sensitivity—it does the opposite. *Increased specificity* - **Specificity** = TN / (TN + FP), the ability to correctly identify those without disease. - Lowering the cutoff causes some uninfected individuals to now test positive (false positives increase). - This **decreases specificity**, not increases it, as fewer true negatives remain. *Increased positive predictive value* - **PPV** = TP / (TP + FP), the probability that a positive test indicates true disease. - While lowering the cutoff increases true positives, it also **increases false positives more substantially**. - The increased false positives dilute the proportion of true positives among all positive results, thereby **decreasing the PPV**.

Question 3: 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 4: 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 5: 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?

A. Test A on the entire student body followed by Test B on those who are positive
B. Test A on the entire student body followed by Test C on those who are positive
C. Test C on the entire student body followed by Test B on those who are positive
D. Test C on the entire student body followed by Test A on those who are positive (Correct Answer)
E. Test B on the entire student body followed by Test A on those who are positive

Explanation: ***Test C on the entire student body followed by Test A on those who are positive*** - To "capture as many correct HIV diagnoses as possible" (maximize true positives), the initial screening test should have the **highest sensitivity**. Test C has the highest sensitivity (0.98). - To "capture as few false positives as possible" (maximize true negatives and confirm diagnoses), the confirmatory test should have the **highest specificity**. Test A has the highest specificity (0.99). *Test A on the entire student body followed by Test B on those who are positive* - Starting with Test A (sensitivity 0.92) would miss more true positive cases than starting with Test C (sensitivity 0.98), failing the goal of **capturing as many cases as possible**. - Following with Test B (specificity 0.96) would result in more false positives than following with Test A (specificity 0.99). *Test A on the entire student body followed by Test C on those who are positive* - This scheme would miss many true positive cases initially due to Test A's lower sensitivity compared to Test C. - Following with Test C would introduce more false positives than necessary, as it has a lower specificity (0.93) than Test A (0.99). *Test C on the entire student body followed by Test B on those who are positive* - While Test C is a good initial screen for its high sensitivity, following it with Test B (specificity 0.96) is less optimal than Test A (specificity 0.99) for minimizing false positives in the confirmation step. - This combination would therefore yield more false positives in the confirmatory stage than using Test A. *Test B on the entire student body followed by Test A on those who are positive* - Test B has a sensitivity of 0.95, which is lower than Test C's sensitivity of 0.98, meaning it would miss more true positive cases at the initial screening stage. - While Test A provides excellent specificity for confirmation, the initial screening step is suboptimal for the goal of capturing as many diagnoses as possible.

Question 6: A pharmaceutical corporation is developing a research study to evaluate a novel blood test to screen for breast cancer. They enrolled 800 patients in the study, half of which have breast cancer. The remaining enrolled patients are age-matched controls who do not have the disease. Of those in the diseased arm, 330 are found positive for the test. Of the patients in the control arm, only 30 are found positive. What is this test’s sensitivity?

A. 330 / (330 + 30)
B. 330 / (330 + 70) (Correct Answer)
C. 370 / (30 + 370)
D. 370 / (70 + 370)
E. 330 / (400 + 400)

Explanation: ***330 / (330 + 70)*** - **Sensitivity** measures the proportion of actual **positives** that are correctly identified as such. - In this study, there are **400 diseased patients** (half of 800). Of these, 330 tested positive (true positives), meaning 70 tested negative (false negatives). So sensitivity is **330 / (330 + 70)**. *330 / (330 + 30)* - This calculation represents the **positive predictive value**, which is the probability that subjects with a positive screening test truly have the disease. It uses **true positives / (true positives + false positives)**. - It does not correctly calculate **sensitivity**, which requires knowing the total number of diseased individuals. *370 / (30 + 370)* - This expression is attempting to calculate **specificity**, which is the proportion of actual negatives that are correctly identified. It would be **true negatives / (true negatives + false positives)**. - However, the numbers used are incorrect for specificity in this context given the data provided. *370 / (70 + 370)* - This formula is an incorrect combination of values and does not represent any standard epidemiological measure like **sensitivity** or **specificity**. - It is attempting to combine false negatives (70) and true negatives (370 from control arm) in a non-standard way. *330 / (400 + 400)* - This calculation attempts to divide true positives by the total study population (800 patients). - This metric represents the **prevalence of true positives within the entire study cohort**, not the test's **sensitivity**.

Question 7: 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 8: You are reviewing raw data from a research study performed at your medical center examining the effectiveness of a novel AIDS screening examination. The study enrolled 250 patients with confirmed AIDS, and 240 of these patients demonstrated a positive screening examination. The control arm of the study enrolled 250 patients who do not have AIDS, and only 5 of these patients tested positive on the novel screening examination. What is the NPV of this novel test?

A. 240 / (240 + 15)
B. 240 / (240 + 5)
C. 240 / (240 + 10)
D. 245 / (245 + 10) (Correct Answer)
E. 245 / (245 + 5)

Explanation: ***245 / (245 + 10)*** - The **negative predictive value (NPV)** is calculated as **true negatives (TN)** divided by the sum of **true negatives (TN)** and **false negatives (FN)**. - In this study, there are 250 patients with AIDS; 240 tested positive (true positives, TP), meaning 10 tested negative (false negatives, FN = 250 - 240). There are 250 patients without AIDS; 5 tested positive (false positives, FP), meaning 245 tested negative (true negatives, TN = 250 - 5). Therefore, NPV = 245 / (245 + 10). *240 / (240 + 15)* - This calculation incorrectly uses the number of **true positives** (240) in the numerator and denominator, which is relevant for **positive predictive value (PPV)**, not NPV. - The denominator `(240 + 15)` does not correspond to a valid sum for calculating NPV from the given data. *240 / (240 + 5)* - This calculation incorrectly uses **true positives** (240) in the numerator, which is not part of the NPV formula. - The denominator `(240 + 5)` mixes true positives and false positives, which is incorrect for NPV. *240 / (240 + 10)* - This incorrectly places **true positives** (240) in the numerator instead of **true negatives**. - The denominator `(240+10)` represents **true positives + false negatives**, which is related to sensitivity, not NPV. *245 / (245 + 5)* - This calculation correctly identifies **true negatives** (245) in the numerator but incorrectly uses **false positives** (5) in the denominator instead of **false negatives**. - The denominator for NPV should be **true negatives + false negatives**, which is 245 + 10.

Question 9: 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.

Question 10: Specificity for breast examination is traditionally rather high among community practitioners. A team of new researchers sets forth a goal to increase specificity in detection of breast cancer from the previously reported national average of 74%. Based on the following results, has the team achieved its goal? Breast cancer screening results: Patients WITH breast cancer | Patients WITHOUT breast cancer Test is Positive (+) 21 | 5 Test is Negative (-) 7 | 23

A. No, the research team’s results lead to nearly the same specificity as the previous national average.
B. Yes, the team has achieved an increase in specificity of over 15%.
C. It can not be determined, as the prevalence of breast cancer is not listed.
D. It can not be determined, since the numbers affiliated with the first trial are unknown.
E. Yes, the team has achieved an increase in specificity of approximately 8%. (Correct Answer)

Explanation: ***Yes, the team has achieved an increase in specificity of approximately 8%.*** - Specificity is calculated as **True Negatives / (True Negatives + False Positives)**. In this case, specificity = 23 / (23 + 5) = 23 / 28 = 0.8214 or **82.14%**. - Comparing this to the national average of 74%, the increase is 82.14% - 74% = **8.14%**. *No, the research team’s results lead to nearly the same specificity as the previous national average.* - The calculated specificity is **82.14%**, which is significantly higher than the 74% national average, not nearly the same. - An **8% increase** represents a substantial improvement in the ability of the test to correctly identify individuals without the disease. *Yes, the team has achieved an increase in specificity of over 15%.* - The calculated increase in specificity is **8.14%**, which is less than 15%. - This option incorrectly overestimates the magnitude of the improvement. *It can not be determined, as the prevalence of breast cancer is not listed.* - Prevalence is used to calculate **positive and negative predictive values**, but not sensitivity or specificity. - Specificity can be directly calculated from the provided data on true negatives and false positives. *It can not be determined, since the numbers affiliated with the first trial are unknown.* - To answer the question, we only need the **original national average specificity (74%)** for comparison and the current trial's results to calculate the new specificity. - The raw numbers from the "first trial" (national average) are not required to determine if the goal was met.

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