2x2 contingency tables — 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 27-year-old man interested in pre-exposure therapy for HIV (PrEP) is being evaluated to qualify for a PrEP study. In order to qualify, patients must be HIV- and hepatitis B- and C-negative. Any other sexually transmitted infections require treatment prior to initiation of PrEP. The medical history is positive for a prior syphilis infection and bipolar affective disorder, for which he takes lithium. On his next visit, the liver and renal enzymes are within normal ranges. HIV and hepatitis B and C tests are negative. Which of the following about the HIV test is true?

A novel PET radiotracer is being evaluated for its ability to aid in the diagnosis of Alzheimer’s disease (AD). The study decides to use a sample size of 1,000 patients, and half of the patients enrolled have AD. In the group of patients with AD, 400 are found positive on the novel type of PET imaging examination. In the control group, 50 are found positive. What is the PPV of this novel exam?

A research group wants to assess the safety and toxicity profile of a new drug. A clinical trial is conducted with 20 volunteers to estimate the maximum tolerated dose and monitor the apparent toxicity of the drug. The study design is best described as which of the following phases of a clinical trial?

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?

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 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?

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?

2x2 contingency tables 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 27-year-old man interested in pre-exposure therapy for HIV (PrEP) is being evaluated to qualify for a PrEP study. In order to qualify, patients must be HIV- and hepatitis B- and C-negative. Any other sexually transmitted infections require treatment prior to initiation of PrEP. The medical history is positive for a prior syphilis infection and bipolar affective disorder, for which he takes lithium. On his next visit, the liver and renal enzymes are within normal ranges. HIV and hepatitis B and C tests are negative. Which of the following about the HIV test is true?

A. It is a quantitative test used for screening purposes.
B. It is a qualitative test used for screening purposes. (Correct Answer)
C. A secondary reagent is needed to interpret the results.
D. A known antigen binds directly to the patient's serum.
E. An unknown antigen binds to the known serum.

Explanation: ***It is a qualitative test used for screening purposes.*** - **HIV screening tests** (e.g., 4th generation antibody/antigen combination assays) are typically **qualitative**, meaning they detect the presence or absence of HIV markers, not their exact amount. - These tests are primarily used for broad **screening** of populations to identify potential cases of HIV infection. *It is a quantitative test used for screening purposes.* - **Quantitative tests** for HIV, such as viral load tests, measure the amount of virus in the blood and are typically used for monitoring disease progression or treatment effectiveness, not for initial screening. - Screening tests are designed for high sensitivity to detect infection, even with low viral loads or early antibody responses, making a quantitative measurement less relevant for initial screening. *A secondary reagent is needed to interpret the results.* - While some complex immunoassays might involve multiple steps, modern **HIV screening tests** often use advanced technologies that directly yield results, making a separate secondary reagent for interpretation generally unnecessary. - The results are typically indicated by a color change or a signal detected by an instrument, without requiring an additional interpretive reagent. *A known antigen binds directly to the patient's serum.* - **HIV antibody tests** detect **antibodies** produced by the patient's immune system in response to HIV infection. - In such tests, **known HIV antigens** (from the test kit) bind to **HIV-specific antibodies present in the patient's serum**, not to serum components directly. - This option is incorrect because it omits the critical role of antibodies as the target molecules being detected. *An unknown antigen binds to the known serum.* - This statement describes a different type of immunological assay where an unknown antigen is being identified using a known antibody, which is contrary to how **HIV screening tests** for infection are typically structured. - **HIV screening tests** use known components (e.g., HIV antigens or antibodies) in the test kit to detect unknown components (e.g., HIV antibodies or viral antigens) in the patient's sample.

Question 3: A novel PET radiotracer is being evaluated for its ability to aid in the diagnosis of Alzheimer’s disease (AD). The study decides to use a sample size of 1,000 patients, and half of the patients enrolled have AD. In the group of patients with AD, 400 are found positive on the novel type of PET imaging examination. In the control group, 50 are found positive. What is the PPV of this novel exam?

A. 400 / (400+50) (Correct Answer)
B. 450 / (450 + 100)
C. 400 / (400+100)
D. 450 / (450 + 50)
E. 400 / (400 + 150)

Explanation: ***400 / (400+50)*** - The **Positive Predictive Value (PPV)** is the probability that subjects with a positive test result actually have the disease. It's calculated as **True Positives / (True Positives + False Positives)**. - In this scenario, **True Positives** are 400 (patients with AD who tested positive), and **False Positives** are 50 (control patients without AD who tested positive). *450 / (450 + 100)* - This calculation incorrectly includes **False Negatives** (450, total AD patients - true positives) in the numerator or denominator for PPV, and misidentifies other components. - The formula for PPV specifically focuses on positive test results and the proportion of those that are truly disease-positive. *400 / (400+100)* - This option correctly identifies **True Positives** as 400 but incorrectly assumes **False Positives** are 100. - The problem states that 50 control patients (without AD) tested positive, which are the false positives. *450 / (450 + 50)* - This formula incorrectly uses **450** as the number of **True Positives**, which represents the total number of patients with AD testing positive and negative (400 TP + 100 FN). - PPV only considers those who tested positive in its numerator. *400 / (400 + 150)* - While 400 is correctly identified as **True Positives**, the **False Positives** are incorrectly stated as 150. - The problem explicitly states that 50 control patients were found positive, making 50 the correct number for false positives.

Question 4: A research group wants to assess the safety and toxicity profile of a new drug. A clinical trial is conducted with 20 volunteers to estimate the maximum tolerated dose and monitor the apparent toxicity of the drug. The study design is best described as which of the following phases of a clinical trial?

A. Phase 0
B. Phase III
C. Phase V
D. Phase II
E. Phase I (Correct Answer)

Explanation: ***Phase I*** - **Phase I clinical trials** involve a small group of healthy volunteers (typically 20-100) to primarily assess **drug safety**, determine a safe dosage range, and identify side effects. - The main goal is to establish the **maximum tolerated dose (MTD)** and evaluate the drug's pharmacokinetic and pharmacodynamic profiles. *Phase 0* - **Phase 0 trials** are exploratory studies conducted in a very small number of subjects (10-15) to gather preliminary data on a drug's **pharmacodynamics and pharmacokinetics** in humans. - They involve microdoses, not intended to have therapeutic effects, and thus cannot determine toxicity or MTD. *Phase III* - **Phase III trials** are large-scale studies involving hundreds to thousands of patients to confirm the drug's **efficacy**, monitor side effects, compare it to standard treatments, and collect information that will allow the drug to be used safely. - These trials are conducted after safety and initial efficacy have been established in earlier phases. *Phase V* - "Phase V" is not a standard, recognized phase in the traditional clinical trial classification (Phase 0, I, II, III, IV). - This term might be used in some non-standard research contexts or for post-marketing studies that go beyond Phase IV surveillance, but it is not a formal phase for initial drug development. *Phase II* - **Phase II trials** involve several hundred patients with the condition the drug is intended to treat, focusing on **drug efficacy** and further evaluating safety. - While safety is still monitored, the primary objective shifts to determining if the drug works for its intended purpose and at what dose.

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: 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 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: 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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