Definition and interpretation of p-values — MCQs

10 questions

A research team develops a new monoclonal antibody checkpoint inhibitor for advanced melanoma that has shown promise in animal studies as well as high efficacy and low toxicity in early phase human clinical trials. The research team would now like to compare this drug to existing standard of care immunotherapy for advanced melanoma. The research team decides to conduct a non-randomized study where the novel drug will be offered to patients who are deemed to be at risk for toxicity with the current standard of care immunotherapy, while patients without such risk factors will receive the standard treatment. Which of the following best describes the level of evidence that this study can offer?

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 randomized control double-blind study is conducted on the efficacy of 2 sulfonylureas. The study concluded that medication 1 was more efficacious in lowering fasting blood glucose than medication 2 (p ≤ 0.05; 95% CI: 14 [10-21]). Which of the following is true regarding a 95% confidence interval (CI)?

A researcher is conducting a study to compare fracture risk in male patients above the age of 65 who received annual DEXA screening to peers who did not receive screening. He conducts a randomized controlled trial in 900 patients, with half of participants assigned to each experimental group. The researcher ultimately finds similar rates of fractures in the two groups. He then notices that he had forgotten to include 400 patients in his analysis. Including the additional participants in his analysis would most likely affect the study's results in which of the following ways?

An investigator is measuring the blood calcium level in a sample of female cross country runners and a control group of sedentary females. If she would like to compare the means of the two groups, which statistical test should she use?

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 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?

You submit a paper to a prestigious journal about the effects of coffee consumption on mesothelioma risk. The first reviewer lauds your clinical and scientific acumen, but expresses concern that your study does not have adequate statistical power. Statistical power refers to which of the following?

The height of American adults is expected to follow a normal distribution, with a typical male adult having an average height of 69 inches with a standard deviation of 0.1 inches. An investigator has been informed about a community in the American Midwest with a history of heavy air and water pollution in which a lower mean height has been reported. The investigator plans to sample 30 male residents to test the claim that heights in this town differ significantly from the national average based on heights assumed be normally distributed. The significance level is set at 10% and the probability of a type 2 error is assumed to be 15%. Based on this information, which of the following is the power of the proposed study?

Q10

A prospective cohort study was conducted to assess the relationship between LDL and the incidence of heart disease. The patients were selected at random. Results showed a 10-year relative risk of 2.3 for people with elevated LDL levels compared to individuals with normal LDL levels. The 95% confidence interval was 1.05-3.50. This study is most likely to have which of the following p values?

Definition and interpretation of p-values US Medical PG Practice Questions and MCQs

Question 1: A research team develops a new monoclonal antibody checkpoint inhibitor for advanced melanoma that has shown promise in animal studies as well as high efficacy and low toxicity in early phase human clinical trials. The research team would now like to compare this drug to existing standard of care immunotherapy for advanced melanoma. The research team decides to conduct a non-randomized study where the novel drug will be offered to patients who are deemed to be at risk for toxicity with the current standard of care immunotherapy, while patients without such risk factors will receive the standard treatment. Which of the following best describes the level of evidence that this study can offer?

A. Level 1
B. Level 3 (Correct Answer)
C. Level 5
D. Level 4
E. Level 2

Explanation: ***Level 3*** - A **non-randomized controlled trial** like the one described, where patient assignment to treatment groups is based on specific characteristics (risk of toxicity), falls into Level 3 evidence. - This level typically includes **non-randomized controlled trials** and **well-designed cohort studies** with comparison groups, which are prone to selection bias and confounding. - The study compares two treatments but lacks randomization, making it Level 3 evidence. *Level 1* - Level 1 evidence is the **highest level of evidence**, derived from **systematic reviews and meta-analyses** of multiple well-designed randomized controlled trials or large, high-quality randomized controlled trials. - The described study is explicitly stated as non-randomized, ruling out Level 1. *Level 2* - Level 2 evidence involves at least one **well-designed randomized controlled trial** (RCT) or **systematic reviews** of randomized trials. - The current study is *non-randomized*, which means it cannot be classified as Level 2 evidence, as randomization is a key criterion for this level. *Level 4* - Level 4 evidence includes **case series**, **case-control studies**, and **poorly designed cohort or case-control studies**. - While the study is non-randomized, it is a controlled comparative trial rather than a case series or retrospective case-control study, placing it at Level 3. *Level 5* - Level 5 evidence is the **lowest level of evidence**, typically consisting of **expert opinion** without explicit critical appraisal, or based on physiology, bench research, or animal studies. - While the drug was initially tested in animal studies, the current human comparative study offers a higher level of evidence than expert opinion or preclinical data.

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: A randomized control double-blind study is conducted on the efficacy of 2 sulfonylureas. The study concluded that medication 1 was more efficacious in lowering fasting blood glucose than medication 2 (p ≤ 0.05; 95% CI: 14 [10-21]). Which of the following is true regarding a 95% confidence interval (CI)?

A. If the same study were repeated multiple times, approximately 95% of the calculated confidence intervals would contain the true population parameter. (Correct Answer)
B. The 95% confidence interval is the probability chosen by the researcher to be the threshold of statistical significance.
C. When a 95% CI for the estimated difference between groups contains the value ‘0’, the results are significant.
D. It represents the probability that chance would not produce the difference shown, 95% of the time.
E. The study is adequately powered at the 95% confidence interval.

Explanation: ***If the same study were repeated multiple times, approximately 95% of the calculated confidence intervals would contain the true population parameter.*** - This statement accurately defines the **frequentist interpretation** of a confidence interval (CI). It reflects the long-run behavior of the CI over hypothetical repetitions of the study. - A 95% CI means that if you were to repeat the experiment many times, 95% of the CIs calculated from those experiments would capture the **true underlying population parameter**. *The 95% confidence interval is the probability chosen by the researcher to be the threshold of statistical significance.* - The **alpha level (α)**, typically set at 0.05 (or 5%), is the threshold for statistical significance (p ≤ 0.05), representing the probability of a Type I error. - The 95% confidence level (1-α) is related to statistical significance, but it is not the *threshold* itself; rather, it indicates the **reliability** of the interval estimate. *When a 95% CI for the estimated difference between groups contains the value ‘0’, the results are significant.* - If a 95% CI for the difference between groups **contains 0**, it implies that there is **no statistically significant difference** between the groups at the 0.05 alpha level. - A statistically significant difference (p ≤ 0.05) would be indicated if the 95% CI **does NOT contain 0**, suggesting that the intervention had a real effect. *It represents the probability that chance would not produce the difference shown, 95% of the time.* - This statement misinterprets the meaning of a CI and probability. The chance of not producing the observed difference is typically addressed by the **p-value**, not directly by the CI in this manner. - A CI provides a **range of plausible values** for the population parameter, not a probability about the role of chance in producing the observed difference. *The study is adequately powered at the 95% confidence interval.* - **Statistical power** is the probability of correctly rejecting a false null hypothesis, typically set at 80% or 90%. It is primarily determined by sample size, effect size, and alpha level. - A 95% CI is a measure of the **precision** of an estimate, while power refers to the **ability of a study to detect an effect** if one exists. They are related but distinct concepts.

Question 4: A researcher is conducting a study to compare fracture risk in male patients above the age of 65 who received annual DEXA screening to peers who did not receive screening. He conducts a randomized controlled trial in 900 patients, with half of participants assigned to each experimental group. The researcher ultimately finds similar rates of fractures in the two groups. He then notices that he had forgotten to include 400 patients in his analysis. Including the additional participants in his analysis would most likely affect the study's results in which of the following ways?

A. Wider confidence intervals of results
B. Increased probability of committing a type II error
C. Decreased significance level of results
D. Increased external validity of results
E. Increased probability of rejecting the null hypothesis when it is truly false (Correct Answer)

Explanation: ***Increased probability of rejecting the null hypothesis when it is truly false*** - Including more participants increases the **statistical power** of the study, making it more likely to detect a true effect if one exists. - A higher sample size provides a more precise estimate of the population parameters, leading to a greater ability to **reject a false null hypothesis**. *Wider confidence intervals of results* - A larger sample size generally leads to **narrower confidence intervals**, as it reduces the standard error of the estimate. - Narrower confidence intervals indicate **greater precision** in the estimation of the true population parameter. *Increased probability of committing a type II error* - A **Type II error** (false negative) occurs when a study fails to reject a false null hypothesis. - Increasing the sample size typically **reduces the probability of a Type II error** because it increases statistical power. *Decreased significance level of results* - The **significance level (alpha)** is a pre-determined threshold set by the researcher before the study begins, typically 0.05. - It is independent of sample size and represents the **acceptable probability of committing a Type I error** (false positive). *Increased external validity of results* - **External validity** refers to the generalizability of findings to other populations, settings, or times. - While a larger sample size can enhance the representativeness of the study population, external validity is primarily determined by the **sampling method** and the study's design context, not just sample size alone.

Question 5: An investigator is measuring the blood calcium level in a sample of female cross country runners and a control group of sedentary females. If she would like to compare the means of the two groups, which statistical test should she use?

A. Chi-square test
B. Linear regression
C. t-test (Correct Answer)
D. ANOVA (Analysis of Variance)
E. F-test

Explanation: ***t-test*** - A **t-test** is appropriate for comparing the means of two independent groups, such as the blood calcium levels between runners and sedentary females. - It assesses whether the observed difference between the two sample means is statistically significant or occurred by chance. *Chi-square test* - The **chi-square test** is used to analyze categorical data to determine if there is a significant association between two variables. - It is not suitable for comparing continuous variables like blood calcium levels. *Linear regression* - **Linear regression** is used to model the relationship between a dependent variable (outcome) and one or more independent variables (predictors). - It aims to predict the value of a variable based on the value of another, rather than comparing means between groups. *ANOVA (Analysis of Variance)* - **ANOVA** is used to compare the means of **three or more independent groups**. - Since there are only two groups being compared in this scenario, a t-test is more specific and appropriate. *F-test* - The **F-test** is primarily used to compare the variances of two populations or to assess the overall significance of a regression model. - While it is the basis for ANOVA, it is not the direct test for comparing the means of two groups.

Question 6: 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 7: 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 8: You submit a paper to a prestigious journal about the effects of coffee consumption on mesothelioma risk. The first reviewer lauds your clinical and scientific acumen, but expresses concern that your study does not have adequate statistical power. Statistical power refers to which of the following?

A. The probability of detecting an association when no association exists.
B. The probability of not detecting an association when an association does exist.
C. The probability of detecting an association when an association does exist. (Correct Answer)
D. The first derivative of work.
E. The square root of the variance.

Explanation: ***The probability of detecting an association when an association does exist.*** - **Statistical power** is defined as the probability that a study will correctly reject a false null hypothesis, meaning it will detect a true effect or association if one exists. - A study with **adequate statistical power** is less likely to miss a real effect. *The probability of detecting an association when no association exists.* - This describes a **Type I error** or **false positive**, often represented by **alpha (α)**. - It is the probability of incorrectly concluding an effect or association exists when, in reality, there is none. *The probability of not detecting an association when an association does exist.* - This refers to a **Type II error** or **false negative**, represented by **beta (β)**. - **Statistical power** is calculated as **1 - β**, so this option describes the complement of power. *The first derivative of work.* - The first derivative of work with respect to time represents **power** in physics, which is the rate at which work is done. - This option is a **distractor** from physics and is unrelated to statistical power in research. *The square root of the variance.* - The **square root of the variance** is the **standard deviation**, a measure of the dispersion or spread of data. - This is a statistical concept but is not the definition of statistical power.

Question 9: The height of American adults is expected to follow a normal distribution, with a typical male adult having an average height of 69 inches with a standard deviation of 0.1 inches. An investigator has been informed about a community in the American Midwest with a history of heavy air and water pollution in which a lower mean height has been reported. The investigator plans to sample 30 male residents to test the claim that heights in this town differ significantly from the national average based on heights assumed be normally distributed. The significance level is set at 10% and the probability of a type 2 error is assumed to be 15%. Based on this information, which of the following is the power of the proposed study?

A. 0.10
B. 0.85 (Correct Answer)
C. 0.90
D. 0.15
E. 0.05

Explanation: ***0.85*** - **Power** is defined as **1 - β**, where β is the **probability of a Type II error**. - Given that the probability of a **Type II error (β)** is 15% or 0.15, the power of the study is 1 - 0.15 = **0.85**. *0.10* - This value represents the **significance level (α)**, which is the probability of committing a **Type I error** (rejecting a true null hypothesis). - The significance level is distinct from the **power of the study**, which relates to Type II errors. *0.90* - This value would be the power if the **Type II error rate (β)** was 0.10 (1 - 0.10 = 0.90), but the question specifies a β of 0.15. - It is also the complement of the significance level (1 - α), which is not the definition of power. *0.15* - This value is the **probability of a Type II error (β)**, not the power of the study. - **Power** is the probability of correctly rejecting a false null hypothesis, which is 1 - β. *0.05* - While 0.05 is a common significance level (α), it is not given as the significance level in this question (which is 0.10). - This value also does not represent the power of the study, which would be calculated using the **Type II error rate**.

Question 10: A prospective cohort study was conducted to assess the relationship between LDL and the incidence of heart disease. The patients were selected at random. Results showed a 10-year relative risk of 2.3 for people with elevated LDL levels compared to individuals with normal LDL levels. The 95% confidence interval was 1.05-3.50. This study is most likely to have which of the following p values?

A. 0.20
B. 0.06
C. 0.08
D. 0.04 (Correct Answer)
E. 0.10

Explanation: ***0.04*** - A 95% confidence interval that **does not include 1 (one)** suggests a **statistically significant** association, meaning the p-value is likely to be **less than 0.05**. - The given CI of 1.05-3.50 for the relative risk (RR) is entirely above 1, indicating a significant positive association, and therefore, a p-value less than 0.05. *0.20* - A p-value of 0.20 is **greater than 0.05**, which would imply the finding is **not statistically significant**. - If the p-value were 0.20, the 95% confidence interval would likely **include 1**, suggesting no significant difference in risk. *0.06* - A p-value of 0.06 is **greater than 0.05**, indicating that the association is **not statistically significant at the conventional alpha level**. - If the p-value were 0.06, the 95% confidence interval would likely **include 1**, or be very close to including it, contradicting the given CI of 1.05-3.50. *0.08* - A p-value of 0.08 is **greater than 0.05**, indicating that the finding is **not statistically significant**. - If the p-value were 0.08, the 95% confidence interval would almost certainly **include 1**, which is inconsistent with the provided interval. *0.10* - A p-value of 0.10 is **greater than 0.05**, which signifies that the finding is **not statistically significant**. - If the p-value were 0.10, the 95% confidence interval for the relative risk would typically **include 1**, contradicting the given confidence interval.

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