You have been asked to quantify the relative risk of developing bacterial meningitis following exposure to a patient with active disease. You analyze 200 patients in total, half of which are controls. In the trial arm, 30% of exposed patients ultimately contracted bacterial meningitis. In the unexposed group, only 1% contracted the disease. Which of the following is the relative risk due to disease exposure?
Q2
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?
Q3
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)?
Q4
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?
Q5
You are reading through a recent article that reports significant decreases in all-cause mortality for patients with malignant melanoma following treatment with a novel biological infusion. Which of the following choices refers to the probability that a study will find a statistically significant difference when one truly does exist?
Q6
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?
Q7
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?
Q8
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?
Q9
A first-year medical student is conducting a summer project with his medical school's pediatrics department using adolescent IQ data from a database of 1,252 patients. He observes that the mean IQ of the dataset is 100. The standard deviation was calculated to be 10. Assuming that the values are normally distributed, approximately 87% of the measurements will fall in between which of the following limits?
Q10
The mean, median, and mode weight of 37 newborns in a hospital nursery is 7 lbs 2 oz. In fact, there are 7 infants in the nursery that weigh exactly 7 lbs 2 oz. The standard deviation of the weights is 2 oz. The weights follow a normal distribution. A newborn delivered at 10 lbs 2 oz is added to the data set. What is most likely to happen to the mean, median, and mode with the addition of this new data point?
Confidence intervals for OR and RR US Medical PG Practice Questions and MCQs
Question 1: You have been asked to quantify the relative risk of developing bacterial meningitis following exposure to a patient with active disease. You analyze 200 patients in total, half of which are controls. In the trial arm, 30% of exposed patients ultimately contracted bacterial meningitis. In the unexposed group, only 1% contracted the disease. Which of the following is the relative risk due to disease exposure?
Explanation: ***[30 / (30 + 70)] / [1 / (1 + 99)]***
- This formula correctly calculates the **relative risk (RR)**. The numerator represents the **incidence rate in the exposed group** (30% of 100 exposed patients = 30 cases out of 100), and the denominator represents the **incidence rate in the unexposed group** (1% of 100 unexposed patients = 1 case out of 100).
- Relative risk is the ratio of the **risk of an event** in an **exposed group** to the **risk of an event** in an **unexposed group**.
*[(30 * 99) / (70 * 1)]*
- This formula is for calculating the **odds ratio (OR)**, specifically using a 2x2 table setup where 30 represents exposed cases, 70 represents exposed non-cases, 1 represents unexposed cases, and 99 represents unexposed non-cases.
- The odds ratio is a measure of association between an exposure and an outcome, representing the **odds of an outcome** given exposure compared to the odds of the outcome without exposure.
*[70 / (30 + 70)] / [99 / (1 + 99)]*
- This formula calculates the **relative risk of *not* developing the disease**, which is the inverse of what the question asks for.
- It compares the proportion of exposed individuals who *do not* contract the disease to the proportion of unexposed individuals who *do not* contract the disease.
*[[1 / (1 + 99)] / [30 / (30 + 70)]]*
- This formula calculates the **inverse of the relative risk**, which is not what the question asks for.
- It would represent the ratio of the incidence in the unexposed group to the incidence in the exposed group.
*[(70 * 1) / (30 * 99)]*
- This is an **incorrect variation** of the odds ratio calculation, with the terms in the numerator and denominator swapped compared to the standard formula.
- Therefore, it does not represent the relative risk or a correctly calculated odds ratio.
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: You are reading through a recent article that reports significant decreases in all-cause mortality for patients with malignant melanoma following treatment with a novel biological infusion. Which of the following choices refers to the probability that a study will find a statistically significant difference when one truly does exist?
A. Type II error
B. Type I error
C. Confidence interval
D. p-value
E. Power (Correct Answer)
Explanation: ***Power***
- **Power** is the probability that a study will correctly reject the null hypothesis when it is, in fact, false (i.e., will find a statistically significant difference when one truly exists).
- A study with high power minimizes the risk of a **Type II error** (failing to detect a real effect).
*Type II error*
- A **Type II error** (or **beta error**) occurs when a study fails to reject a false null hypothesis, meaning it concludes there is no significant difference when one actually exists.
- This is the **opposite** of what the question describes, which asks for the probability of *finding* a difference.
*Type I error*
- A **Type I error** (or **alpha error**) occurs when a study incorrectly rejects a true null hypothesis, concluding there is a significant difference when one does not actually exist.
- This relates to the **p-value** and the level of statistical significance (e.g., p < 0.05).
*Confidence interval*
- A **confidence interval** provides a range of values within which the true population parameter is likely to lie with a certain degree of confidence (e.g., 95%).
- It does not directly represent the probability of finding a statistically significant difference when one truly exists.
*p-value*
- The **p-value** is the probability of observing data as extreme as, or more extreme than, that obtained in the study, assuming the null hypothesis is true.
- It is used to determine statistical significance, but it is not the probability of detecting a true effect.
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 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 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: A first-year medical student is conducting a summer project with his medical school's pediatrics department using adolescent IQ data from a database of 1,252 patients. He observes that the mean IQ of the dataset is 100. The standard deviation was calculated to be 10. Assuming that the values are normally distributed, approximately 87% of the measurements will fall in between which of the following limits?
A. 85–115 (Correct Answer)
B. 95–105
C. 65–135
D. 80–120
E. 70–130
Explanation: ***85–115***
- For a **normal distribution**, approximately 87% of data falls within **±1.5 standard deviations** from the mean.
- With a mean of 100 and a standard deviation of 10, the range is 100 ± (1.5 * 10) = 100 ± 15, which gives **85–115**.
*95–105*
- This range represents **±0.5 standard deviations** from the mean (100 ± 5), which covers only about 38% of the data.
- This is a much narrower range and does not encompass 87% of the observations as required.
*65–135*
- This range represents **±3.5 standard deviations** from the mean (100 ± 35), which would cover over 99.9% of the data.
- Thus, this interval is too wide for 87% of the measurements.
*80–120*
- This range represents **±2 standard deviations** from the mean (100 ± 20), which covers approximately 95% of the data.
- While a common interval, it is wider than necessary for 87% of the data.
*70–130*
- This range represents **±3 standard deviations** from the mean (100 ± 30), which covers approximately 99.7% of the data.
- This interval is significantly wider than required to capture 87% of the data.
Question 10: The mean, median, and mode weight of 37 newborns in a hospital nursery is 7 lbs 2 oz. In fact, there are 7 infants in the nursery that weigh exactly 7 lbs 2 oz. The standard deviation of the weights is 2 oz. The weights follow a normal distribution. A newborn delivered at 10 lbs 2 oz is added to the data set. What is most likely to happen to the mean, median, and mode with the addition of this new data point?
A. The mean will increase; the median will increase; the mode will stay the same
B. The mean will increase; the median will stay the same; the mode will stay the same (Correct Answer)
C. The mean will stay the same; the median will increase; the mode will stay the same
D. The mean will increase; the median will increase; the mode will increase
E. The mean will stay the same; the median will increase; the mode will increase
Explanation: ***The mean will increase; the median will stay the same; the mode will stay the same***
- The **mean** is highly sensitive to outliers. Adding a newborn weighing 10 lbs 2 oz (significantly heavier than the original mean of 7 lbs 2 oz) will increase the total sum of weights, thus **increasing the mean**.
- The **median** is the middle value in an ordered dataset. With 37 newborns, the median is the 19th value. Adding one more (38 total) makes the median the average of the 19th and 20th values. Since the new value (10 lbs 2 oz) is added at the extreme high end of the distribution, the 19th and 20th positions contain the same values as before. Therefore, the median will **stay the same**.
- The **mode** is the most frequent value. Since there are 7 infants already at 7 lbs 2 oz, adding a single infant at 10 lbs 2 oz will not change the most frequent weight in the dataset. The mode will **stay the same** at 7 lbs 2 oz.
*The mean will increase; the median will increase; the mode will stay the same*
- While the **mean will increase** due to the added outlier, the **median will not change**. With 38 observations, the median becomes the average of the 19th and 20th values, which remain unchanged since the outlier is added at position 38.
- The **mode** correctly stays at 7 lbs 2 oz as the new data point does not become the most frequent value.
*The mean will stay the same; the median will increase; the mode will stay the same*
- The **mean will not stay the same** because an outlier significantly higher than the current mean will always pull the mean higher.
- The **median will also not increase** as the middle values (19th and 20th positions) remain unchanged when adding an extreme outlier.
*The mean will increase; the median will increase; the mode will increase*
- While the **mean will increase**, the **median will not change** because the middle positions are unaffected by adding one extreme outlier.
- The **mode will not change** as the new data point (10 lbs 2 oz) is unique and doesn't become the most frequent value; 7 lbs 2 oz remains most frequent with 7 occurrences.
*The mean will stay the same; the median will increase; the mode will increase*
- This option is incorrect because the **mean will definitely increase** with the addition of a much larger value.
- The **median will not increase** as it depends on the middle positions, not extreme values.
- The **mode will not increase** as adding one 10 lb 2 oz infant won't make that weight the most frequent.
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