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?
Q2
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?
Q3
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?
Q4
A physician attempts to study cirrhosis in his state. Using a registry of admitted patients over the last 10 years at the local hospital, he isolates all patients who have been diagnosed with cirrhosis. Subsequently, he contacts this group of patients, asking them to complete a survey assessing their prior exposure to alcohol use, intravenous drug abuse, blood transfusions, personal history of cancer, and other medical comorbidities. An identical survey is given to an equal number of patients in the registry who do not carry a prior diagnosis of cirrhosis. Which of the following is the study design utilized by this physician?
Q5
You are currently employed as a clinical researcher working on clinical trials of a new drug to be used for the treatment of Parkinson's disease. Currently, you have already determined the safe clinical dose of the drug in a healthy patient. You are in the phase of drug development where the drug is studied in patients with the target disease to determine its efficacy. Which of the following phases is this new drug currently in?
Q6
In a randomized controlled trial studying a new treatment, the primary endpoint (mortality) occurred in 14.4% of the treatment group and 16.7% of the control group. Which of the following represents the number of patients needed to treat to save one life, based on the primary endpoint?
Q7
In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?
Q8
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?
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
A health system implements a new sepsis protocol across 20 hospitals. A researcher plans to evaluate effectiveness using a stepped-wedge cluster randomized design where hospitals sequentially adopt the protocol every 3 months. She calculates sample size based on individual patient outcomes (mortality) needing 2,000 patients total. The biostatistician identifies a critical error. Evaluate what modification is needed.
Sample size calculation for different study designs 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 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 3: 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 4: A physician attempts to study cirrhosis in his state. Using a registry of admitted patients over the last 10 years at the local hospital, he isolates all patients who have been diagnosed with cirrhosis. Subsequently, he contacts this group of patients, asking them to complete a survey assessing their prior exposure to alcohol use, intravenous drug abuse, blood transfusions, personal history of cancer, and other medical comorbidities. An identical survey is given to an equal number of patients in the registry who do not carry a prior diagnosis of cirrhosis. Which of the following is the study design utilized by this physician?
A. Randomized controlled trial
B. Case-control study (Correct Answer)
C. Cross-sectional study
D. Cohort study
E. Meta-analysis
Explanation: ***Case-control study***
- This study design **identifies subjects based on their outcome (cases with cirrhosis, controls without cirrhosis)** and then retrospectively investigates their past exposures.
- The physician selected patients with cirrhosis (cases) and patients without cirrhosis (controls), then assessed their prior exposures to risk factors like alcohol use and intravenous drug abuse.
*Randomized controlled trial*
- This design involves randomly assigning participants to an **intervention group** or a **control group** to assess the effect of an intervention.
- There is no intervention being tested or randomization occurring in this study; it is observational.
*Cross-sectional study*
- A cross-sectional study measures the **prevalence of disease and exposure at a single point in time** in a defined population.
- This study collects retrospective exposure data and compares two distinct groups (cases and controls), rather than assessing prevalence at one time point.
*Cohort study*
- A cohort study **follows a group of individuals over time** to see if their exposure to a risk factor is associated with the development of a disease.
- This study starts with the outcome (cirrhosis) and looks backward at exposures, which is the opposite direction of a cohort study.
*Meta-analysis*
- A meta-analysis is a statistical method that **combines the results of multiple independent studies** to produce a single, more powerful estimate of treatment effect or association.
- This is an original research study collecting new data, not a systematic review or synthesis of existing studies.
Question 5: You are currently employed as a clinical researcher working on clinical trials of a new drug to be used for the treatment of Parkinson's disease. Currently, you have already determined the safe clinical dose of the drug in a healthy patient. You are in the phase of drug development where the drug is studied in patients with the target disease to determine its efficacy. Which of the following phases is this new drug currently in?
A. Phase 4
B. Phase 1
C. Phase 2 (Correct Answer)
D. Phase 0
E. Phase 3
Explanation: ***Phase 2***
- **Phase 2 trials** involve studying the drug in patients with the target disease to assess its **efficacy** and further evaluate safety, typically involving a few hundred patients.
- The question describes a stage after safe dosing in healthy patients (Phase 1) and before large-scale efficacy confirmation (Phase 3), focusing on efficacy in the target population.
*Phase 4*
- **Phase 4 trials** occur **after a drug has been approved** and marketed, monitoring long-term effects, optimal use, and rare side effects in a diverse patient population.
- This phase is conducted post-market approval, whereas the question describes a drug still in development prior to approval.
*Phase 1*
- **Phase 1 trials** primarily focus on determining the **safety and dosage** of a new drug in a **small group of healthy volunteers** (or sometimes patients with advanced disease if the drug is highly toxic).
- The question states that the safe clinical dose in a healthy patient has already been determined, indicating that Phase 1 has been completed.
*Phase 0*
- **Phase 0 trials** are exploratory, very early-stage studies designed to confirm that the drug reaches the target and acts as intended, typically involving a very small number of doses and participants.
- These trials are conducted much earlier in the development process, preceding the determination of safe clinical doses and large-scale efficacy studies.
*Phase 3*
- **Phase 3 trials** are large-scale studies involving hundreds to thousands of patients to confirm **efficacy**, monitor side effects, compare it to commonly used treatments, and collect information that will allow the drug to be used safely.
- While Phase 3 does assess efficacy, it follows Phase 2 and is typically conducted on a much larger scale before submitting for regulatory approval.
Question 6: In a randomized controlled trial studying a new treatment, the primary endpoint (mortality) occurred in 14.4% of the treatment group and 16.7% of the control group. Which of the following represents the number of patients needed to treat to save one life, based on the primary endpoint?
A. 1/(0.144 - 0.167)
B. 1/(0.167 - 0.144) (Correct Answer)
C. 1/(0.300 - 0.267)
D. 1/(0.267 - 0.300)
E. 1/(0.136 - 0.118)
Explanation: ***1/(0.167 - 0.144)***
- The **Number Needed to Treat (NNT)** is calculated as **1 / Absolute Risk Reduction (ARR)**.
- The **Absolute Risk Reduction (ARR)** is the difference between the event rate in the control group (16.7%) and the event rate in the treatment group (14.4%), which is **0.167 - 0.144**.
*1/(0.144 - 0.167)*
- This calculation represents 1 divided by the **Absolute Risk Increase**, which would be relevant if the treatment increased mortality.
- The **NNT should always be a positive value**, indicating the number of patients to treat to prevent one adverse event.
*1/(0.300 - 0.267)*
- This option uses arbitrary numbers (0.300 and 0.267) that do not correspond to the given **mortality rates** in the problem.
- It does not reflect the correct calculation for **absolute risk reduction** based on the provided data.
*1/(0.267 - 0.300)*
- This option also uses arbitrary numbers not derived from the problem's data, and it would result in a **negative value** for the denominator.
- The difference between event rates of 0.267 and 0.300 is not present in the given information for this study.
*1/(0.136 - 0.118)*
- This calculation uses arbitrary numbers (0.136 and 0.118) that are not consistent with the reported **mortality rates** of 14.4% and 16.7%.
- These values do not represent the **Absolute Risk Reduction** required for calculating NNT in this specific scenario.
Question 7: In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?
A. 5,100 (Correct Answer)
B. 4,500
C. 6,000
D. 3,750
E. 6,750
Explanation: ***5,100***
- To solve this, first calculate the **z-score** for 250: (250 - 227) / 22 = 1.045.
- Using a **z-table**, the area under the curve from the mean (z=0) to z=1.045 is approximately 0.353. Multiplying this by 15,000 students gives approximately **5,295 students**, which is closest to 5,100.
*4,500*
- This answer would imply a smaller proportion of students between the mean and 250 (around 30%), which is lower than the calculated z-score of 1.045 suggests.
- It does not accurately reflect the area under the **normal distribution curve** for the given range.
*6,000*
- This option would mean that approximately 40% of students scored in this range, which would correspond to a z-score much higher than 1.045 or a different standard deviation.
- This calculation overestimates the number of students within the specified range.
*3,750*
- This value represents 25% of the total students (15,000 * 0.25), indicating that only a quarter of the distribution lies in this range.
- This significantly underestimates the proportion of students scoring between the mean and 250 for the given standard deviation.
*6,750*
- This option reflects approximately 45% of the total student population (15,000 * 0.45), which would correspond to a much larger z-score or a different distribution.
- This value is an overestimation and does not align with the standard normal distribution probabilities for the given parameters.
Question 8: 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.
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: A health system implements a new sepsis protocol across 20 hospitals. A researcher plans to evaluate effectiveness using a stepped-wedge cluster randomized design where hospitals sequentially adopt the protocol every 3 months. She calculates sample size based on individual patient outcomes (mortality) needing 2,000 patients total. The biostatistician identifies a critical error. Evaluate what modification is needed.
A. Adjust for multiple time periods using Bonferroni correction
B. Use hospital-level outcomes instead of patient-level outcomes as unit of analysis
C. Increase alpha to 0.10 to account for cluster randomization reducing power
D. Include random effects for both hospital and time period in power calculation
E. Account for intra-cluster correlation coefficient (ICC) requiring substantial sample size inflation (Correct Answer)
Explanation: ***Account for intra-cluster correlation coefficient (ICC) requiring substantial sample size inflation***
- In cluster-randomized designs, observations within the same cluster (hospital) are not independent; the **Intra-cluster Correlation Coefficient (ICC)** quantifies this correlation and must be used to calculate a **design effect**.
- Neglecting the ICC leads to an **underpowered study** because the effective sample size is smaller than the total number of individual patients measured.
*Adjust for multiple time periods using Bonferroni correction*
- **Bonferroni correction** is used to control for **Type I error** when performing multiple independent hypothesis tests, not for determining sample size in nested longitudinal designs.
- While the stepped-wedge design involves multiple time points, the primary analysis typically uses a **single model** (e.g., GEE or GLMM) that accounts for time as a fixed effect.
*Use hospital-level outcomes instead of patient-level outcomes as unit of analysis*
- While the hospital is the **unit of randomization**, using hospital-level means as the unit of analysis simplifies the data and causes a significant loss of **statistical information** and precision.
- Modern biostatistical methods utilize **multilevel modeling** to maintain the richness of patient-level data while adjusting for the cluster-level randomization.
*Include random effects for both hospital and time period in power calculation*
- While random effects are important for the **analysis phase**, the "critical error" identified in the prompt refers to the initial failure to inflate the sample size based on **clustering (ICC)**.
- Power calculations for stepped-wedge designs are complex and certainly involve time parameters, but **ICC-based inflation** is the most fundamental adjustment required when moving from individual to cluster randomization.
*Increase alpha to 0.10 to account for cluster randomization reducing power*
- Increasing the **alpha level** (significance threshold) is not a standard or scientifically acceptable method to compensate for the loss of power due to **clustering**.
- Standard practice mandates maintaining an **alpha of 0.05** while appropriately increasing the **sample size** or number of clusters to reach the desired power (usually 80-90%).
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