Effect of disease prevalence on predictive values — 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?

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?

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?

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?

A population is studied for risk factors associated with testicular cancer. Alcohol exposure, smoking, dietary factors, social support, and environmental exposure are all assessed. The researchers are interested in the incidence and prevalence of the disease in addition to other outcomes. Which pair of studies would best assess the 1. incidence and 2. prevalence?

Many large clinics have noticed that the prevalence of primary biliary cholangitis (PBC) has increased significantly over the past 20 years. An epidemiologist is working to identify possible reasons for this. After analyzing a series of nationwide health surveillance databases, the epidemiologist finds that the incidence of PBC has remained stable over the past 20 years. Which of the following is the most plausible explanation for the increased prevalence of PBC?

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

Effect of disease prevalence on predictive values 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: 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. 0.01%
B. 2%
C. 0.5%
D. 1% (Correct Answer)
E. 50%

Explanation: ***Correct Option: 1%*** - The patient's symptoms (difficulty breathing requiring bronchodilators, inhaled corticosteroids, and chest physiotherapy; diarrhea and malabsorption requiring enzyme replacement therapy) are classic for **cystic fibrosis (CF)**, an **autosomal recessive disorder**. - For an autosomal recessive disorder with a prevalence of 1 in 10,000 in the general population, **q² = 1/10,000**, so **q = 1/100 = 0.01**. The carrier frequency **(2pq)** is approximately **2q = 2 × (1/100) = 1/50 = 0.02**. - The affected man is **homozygous recessive (aa)** and will always pass on the recessive allele. His wife has a **1/50 chance of being a carrier (Aa)**. If she is a carrier, she has a **1/2 chance of passing on the recessive allele**. - Therefore, the probability of an affected child = **(Probability wife is a carrier) × (Probability wife passes recessive allele) = 1/50 × 1/2 = 1/100 = 1%**. *Incorrect Option: 0.01%* - This percentage is too low and does not correctly account for the carrier frequency in the population and the probability of transmission from a carrier mother. *Incorrect Option: 2%* - This represents approximately the carrier frequency (1/50 ≈ 2%), but does not account for the additional 1/2 probability that a carrier mother would pass on the recessive allele. *Incorrect Option: 0.5%* - This value would be correct if the carrier frequency were 1/100 instead of 1/50, which does not match the given population prevalence. *Incorrect Option: 50%* - **50%** would be the risk if both parents were carriers of an autosomal recessive disorder (1/4 chance = 25% for affected, but if we know one parent passes the allele, conditional probability changes). More accurately, 50% would apply if the disorder were **autosomal dominant** with one affected parent, which is not the case here.

Question 3: 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 4: 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 5: 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 6: 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 7: A population is studied for risk factors associated with testicular cancer. Alcohol exposure, smoking, dietary factors, social support, and environmental exposure are all assessed. The researchers are interested in the incidence and prevalence of the disease in addition to other outcomes. Which pair of studies would best assess the 1. incidence and 2. prevalence?

A. 1. Prospective cohort study 2. Cross sectional study (Correct Answer)
B. 1. Prospective cohort study 2. Retrospective cohort study
C. 1. Cross sectional study 2. Retrospective cohort study
D. 1. Case-control study 2. Prospective cohort study
E. 1. Clinical trial 2. Cross sectional study

Explanation: ***1. Prospective cohort study 2. Cross sectional study*** - A **prospective cohort study** is ideal for measuring **incidence** (new cases over time) because it follows a group of individuals forward in time to observe who develops the disease. - A **cross-sectional study** is suitable for measuring **prevalence** (existing cases at a specific point in time) as it surveys a population at one moment to determine the proportion with the disease. *1. Prospective cohort study 2. Retrospective cohort study* - A **retrospective cohort study** assesses past exposures and outcomes and can measure incidence, but it is not the primary choice for prevalence. - While a prospective cohort study is appropriate for incidence, a retrospective cohort study is less suited for determining current prevalence. *1. Cross sectional study 2. Retrospective cohort study* - A **cross-sectional study** measures prevalence, not incidence, as it captures disease status at a single point in time. - A **retrospective cohort study** looks back in time to identify past exposures and subsequent outcomes, which is not the best method for current prevalence. *1. Case-control study 2. Prospective cohort study* - A **case-control study** compares exposures between individuals with a disease (cases) and those without (controls) and is best for studying rare diseases and estimating odds ratios, not incidence or prevalence directly. - A **prospective cohort study** is suitable for incidence, but a case-control study is not for incidence or prevalence. *1. Clinical trial 2. Cross sectional study* - A **clinical trial** is an experimental study designed to test the efficacy of interventions and is not primarily used to measure disease incidence or prevalence in a general population. - While a cross-sectional study is appropriate for prevalence, a clinical trial is not designed for incidence measurement.

Question 8: Many large clinics have noticed that the prevalence of primary biliary cholangitis (PBC) has increased significantly over the past 20 years. An epidemiologist is working to identify possible reasons for this. After analyzing a series of nationwide health surveillance databases, the epidemiologist finds that the incidence of PBC has remained stable over the past 20 years. Which of the following is the most plausible explanation for the increased prevalence of PBC?

A. Improved quality of care for PBC (Correct Answer)
B. Increased availability of diagnostic testing for PBC
C. Increased exposure to environmental risk factors for PBC
D. Increased awareness of PBC among clinicians
E. Increased average age of the population at risk for PBC

Explanation: ***Improved quality of care for PBC*** - This leads to a **longer survival time** for patients with PBC. When incidence remains stable but patients live longer, the cumulative number of living cases (prevalence) naturally increases. - An increase in prevalence with stable incidence is a classic indicator of **improved patient survival** due to better management or treatment. *Increased availability of diagnostic testing for PBC* - This would primarily impact the **incidence** of PBC by detecting more cases that were previously undiagnosed. The question states that the incidence has remained stable. - While improved diagnostics might initially increase *reported* incidence, if the true incidence is stable, it wouldn't explain a sustained rise in prevalence without a corresponding change in incidence or survival. *Increased exposure to environmental risk factors for PBC* - This would directly lead to an **increase in the incidence** of PBC, as more people would be developing the disease. - Since the incidence is stable, an increase in environmental risk factors is not the most plausible explanation for increased prevalence. *Increased awareness of PBC among clinicians* - Similar to increased diagnostic testing, increased awareness would likely lead to the diagnosis of more new cases, thus **increasing the incidence** of PBC. - A stable incidence despite increased awareness means that the actual rate of new cases developing the disease has not changed, ruling this out as the primary cause of increased prevalence. *Increased average age of the population at risk for PBC* - An aging population could potentially increase the incidence of age-related diseases. However, if the **incidence has remained stable**, it implies that even with an older population, the rate of new diagnoses has not increased. - While age is a risk factor for PBC, an increase in prevalence without a change in incidence suggests a factor influencing the duration of the disease rather than its onset.

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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