Survival curves — 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 researcher is trying to determine whether a newly discovered substance X can be useful in promoting wound healing after surgery. She conducts this study by enrolling the next 100 patients that will be undergoing this surgery and separating them into 2 groups. She decides which patient will be in which group by using a random number generator. Subsequently, she prepares 1 set of syringes with the novel substance X and 1 set of syringes with a saline control. Both of these sets of syringes are unlabeled and the substances inside cannot be distinguished. She gives the surgeon performing the surgery 1 of the syringes and does not inform him nor the patient which syringe was used. After the study is complete, she analyzes all the data that was collected and performs statistical analysis. This study most likely provides which level of evidence for use of substance X?

A pharmaceutical company conducts a randomized clinical trial to demonstrate that their new anticoagulant drug, Aclotsaban, prevents more thrombotic events following total knee arthroplasty than the current standard of care. A significant number of patients are lost to follow-up, and many fail to complete treatment according to the study arm to which they were assigned. Despite these protocol deviations, the results for the patients who completed the course of Aclotsaban are encouraging. Which of the following analytical approaches is most appropriate for the primary analysis to establish the efficacy of Aclotsaban?

A neuro-oncology investigator has recently conducted a randomized controlled trial in which the addition of a novel alkylating agent to radiotherapy was found to prolong survival in comparison to radiotherapy alone (HR = 0.7, p < 0.01). A number of surviving participants who took the alkylating agent reported that they had experienced significant nausea from the medication. The investigator surveyed all participants in both the treatment and the control group on their nausea symptoms by self-report rated mild, moderate, or severe. The investigator subsequently compared the two treatment groups with regards to nausea level. | | Mild nausea | Moderate nausea | Severe nausea | |---|---|---|---| | Treatment group (%) | 20 | 30 | 50 | | Control group (%) | 35 | 35 | 30 | Which of the following statistical methods would be most appropriate to assess the statistical significance of these results?

A biostatistician is processing data for a large clinical trial she is working on. The study is analyzing the use of a novel pharmaceutical compound for the treatment of anorexia after chemotherapy with the outcome of interest being the change in weight while taking the drug. While most participants remained about the same weight or continued to lose weight while on chemotherapy, there were smaller groups of individuals who responded very positively to the orexic agent. As a result, the data had a strong positive skew. The biostatistician wishes to report the measures of central tendency for this project. Just by understanding the skew in the data, which of the following can be expected for this data set?

A resident in the department of obstetrics and gynecology is reading about a randomized clinical trial from the late 1990s that was conducted to compare breast cancer mortality risk, disease localization, and tumor size in women who were randomized to groups receiving either annual mammograms starting at age 40 or annual mammograms starting at age 50. One of the tables in the study compares the two experimental groups with regard to socioeconomic demographics (e.g., age, income), medical conditions at the time of recruitment, and family history of breast cancer. The purpose of this table is most likely to evaluate which of the following?

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 28-year-old male presents to his primary care physician with complaints of intermittent abdominal pain and alternating bouts of constipation and diarrhea. His medical chart is not significant for any past medical problems or prior surgeries. He is not prescribed any current medications. Which of the following questions would be the most useful next question in eliciting further history from this patient?

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?

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?

Survival curves 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 researcher is trying to determine whether a newly discovered substance X can be useful in promoting wound healing after surgery. She conducts this study by enrolling the next 100 patients that will be undergoing this surgery and separating them into 2 groups. She decides which patient will be in which group by using a random number generator. Subsequently, she prepares 1 set of syringes with the novel substance X and 1 set of syringes with a saline control. Both of these sets of syringes are unlabeled and the substances inside cannot be distinguished. She gives the surgeon performing the surgery 1 of the syringes and does not inform him nor the patient which syringe was used. After the study is complete, she analyzes all the data that was collected and performs statistical analysis. This study most likely provides which level of evidence for use of substance X?

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

Explanation: ***Level 1*** - The study design described is a **randomized controlled trial (RCT)**, which is considered the **highest level of evidence (Level 1)** in the hierarchy of medical evidence. - Key features like **randomization**, **control group**, and **blinding (double-blind)** help minimize bias and strengthen the validity of the findings. *Level 2* - Level 2 evidence typically comprises **well-designed controlled trials without randomization** (non-randomized controlled trials) or **high-quality cohort studies**. - While strong, they do not possess the same level of internal validity as randomized controlled trials. *Level 3* - Level 3 evidence typically includes **case-control studies** or **cohort studies**, which are observational designs and carry a higher risk of bias compared to RCTs. - These studies generally do not involve randomization or intervention assignment by the researchers. *Level 4* - Level 4 evidence is usually derived from **case series** or **poor quality cohort and case-control studies**. - These studies provide descriptive information or investigate associations without strong control for confounding factors. *Level 5* - Level 5 evidence is the **lowest level of evidence**, consisting of **expert opinion** or **animal research/bench research**. - This level lacks human clinical data or systematic investigative rigor needed for higher evidence levels.

Question 3: A pharmaceutical company conducts a randomized clinical trial to demonstrate that their new anticoagulant drug, Aclotsaban, prevents more thrombotic events following total knee arthroplasty than the current standard of care. A significant number of patients are lost to follow-up, and many fail to complete treatment according to the study arm to which they were assigned. Despite these protocol deviations, the results for the patients who completed the course of Aclotsaban are encouraging. Which of the following analytical approaches is most appropriate for the primary analysis to establish the efficacy of Aclotsaban?

A. Intention-to-treat analysis (Correct Answer)
B. Sub-group analysis
C. Per-protocol analysis
D. As-treated analysis
E. Non-inferiority analysis

Explanation: ***Intention-to-treat analysis*** - **Intention-to-treat (ITT) analysis** is the gold standard for the **primary analysis in superiority trials** and includes all patients in the groups to which they were originally randomized, regardless of protocol deviations, loss to follow-up, or treatment discontinuation. - ITT preserves **randomization balance**, prevents bias from selective dropout (patients may drop out due to adverse effects or lack of efficacy), and provides a **conservative, realistic estimate** of treatment effect in actual clinical practice. - For **regulatory approval and establishing efficacy**, ITT is the most appropriate primary analysis method even when dropout rates are high, as it maintains the integrity of the randomized comparison. *Per-protocol analysis* - **Per-protocol analysis** includes only patients who completed the study exactly as planned without protocol deviations. - While the encouraging results in completers are noted, per-protocol analysis can **introduce significant bias** by excluding patients who dropped out due to adverse events or lack of efficacy, potentially **overestimating treatment benefit**. - Per-protocol is typically used as a **secondary/supportive analysis**, not the primary method for establishing superiority. *As-treated analysis* - **As-treated analysis** categorizes patients according to the treatment they actually received rather than their randomized assignment. - This violates the principle of randomization and can introduce **confounding bias**, as actual treatment received may be influenced by prognostic factors. *Sub-group analysis* - **Sub-group analysis** evaluates treatment effects within specific patient subsets. - This is **hypothesis-generating** rather than confirmatory and increases the risk of false-positive findings (multiple comparisons problem) unless pre-specified in the protocol. *Non-inferiority analysis* - **Non-inferiority analysis** tests whether a new treatment is not worse than control by more than a pre-specified margin. - The goal here is to demonstrate **superiority** (better than standard care), not non-inferiority, making this approach inappropriate.

Question 4: A neuro-oncology investigator has recently conducted a randomized controlled trial in which the addition of a novel alkylating agent to radiotherapy was found to prolong survival in comparison to radiotherapy alone (HR = 0.7, p < 0.01). A number of surviving participants who took the alkylating agent reported that they had experienced significant nausea from the medication. The investigator surveyed all participants in both the treatment and the control group on their nausea symptoms by self-report rated mild, moderate, or severe. The investigator subsequently compared the two treatment groups with regards to nausea level. | | Mild nausea | Moderate nausea | Severe nausea | |---|---|---|---| | Treatment group (%) | 20 | 30 | 50 | | Control group (%) | 35 | 35 | 30 | Which of the following statistical methods would be most appropriate to assess the statistical significance of these results?

A. Chi-square test (Correct Answer)
B. Pearson correlation coefficient
C. Multiple logistic regression
D. Unpaired t-test
E. Paired t-test

Explanation: **Chi-square test** - The **Chi-square test** is appropriate for comparing **categorical data** (mild, moderate, severe) between two or more independent groups (treatment vs. control). - It assesses whether there is a statistically significant association between the two categorical variables (treatment group and nausea severity). *Pearson correlation coefficient* - The **Pearson correlation coefficient** is used to measure the **linear relationship** between two **continuous variables**. - Nausea severity (mild, moderate, severe) is an **ordinal categorical variable**, not a continuous one. *Multiple logistic regression* - **Multiple logistic regression** is used to predict a **binary outcome** (e.g., presence or absence of nausea) based on one or more independent variables, which can be continuous or categorical. - The outcome here is **ordinal categorical** (mild, moderate, severe nausea), not binary. While logistic regression can be adapted for ordinal outcomes, a simpler Chi-square test is more direct for comparing distributions without prediction. *Unpaired t-test* - An **unpaired t-test** is used to compare the **means of two independent continuous variables**. - Nausea levels are categorical, and we are interested in comparing proportions within categories, not means. *Paired t-test* - A **paired t-test** is used to compare the **means of two related (paired) continuous variables**. - The study involves independent treatment and control groups, and the nausea data is categorical, making the paired t-test unsuitable.

Question 5: A biostatistician is processing data for a large clinical trial she is working on. The study is analyzing the use of a novel pharmaceutical compound for the treatment of anorexia after chemotherapy with the outcome of interest being the change in weight while taking the drug. While most participants remained about the same weight or continued to lose weight while on chemotherapy, there were smaller groups of individuals who responded very positively to the orexic agent. As a result, the data had a strong positive skew. The biostatistician wishes to report the measures of central tendency for this project. Just by understanding the skew in the data, which of the following can be expected for this data set?

A. Mean = median = mode
B. Mean < median < mode
C. Mean > median > mode (Correct Answer)
D. Mean > median = mode
E. Mean < median = mode

Explanation: ***Mean > median > mode*** - In a dataset with a **strong positive skew**, the tail of the distribution is on the right, pulled by a few **unusually large values**. - These extreme high values disproportionately influence the **mean**, pulling it to the right (higher value), while the **median** (middle value) is less affected, and the **mode** (most frequent value) is often located at the peak of the distribution towards the left. *Mean = median = mode* - This relationship between the measures of central tendency is characteristic of a **perfectly symmetrical distribution**, such as a **normal distribution**, where there is no skew. - In a symmetrical distribution, the mean, median, and mode are all located at the exact center of the data. *Mean < median < mode* - This order is typical for a dataset with a **negative skew**, where the tail is on the left due to a few **unusually small values**. - In a negatively skewed distribution, the mean is pulled to the left (lower value) by the small values, making it less than the median and mode. *Mean > median = mode* - This configuration is generally not characteristic of standard skewed distributions and would imply a specific, less common bimodal or complex distribution shape where the mode coincides with the median, but the mean is pulled higher. - While theoretically possible, it doesn't describe a typical positively skewed distribution where the mode is usually the lowest of the three. *Mean < median = mode* - This relationship would suggest a negatively skewed distribution where the median and mode are equal, but the mean is pulled to the left (lower value) by a leftward tail. - Again, this is a less typical representation of a standard negatively skewed distribution, which often follows the Mean < Median < Mode pattern.

Question 6: A resident in the department of obstetrics and gynecology is reading about a randomized clinical trial from the late 1990s that was conducted to compare breast cancer mortality risk, disease localization, and tumor size in women who were randomized to groups receiving either annual mammograms starting at age 40 or annual mammograms starting at age 50. One of the tables in the study compares the two experimental groups with regard to socioeconomic demographics (e.g., age, income), medical conditions at the time of recruitment, and family history of breast cancer. The purpose of this table is most likely to evaluate which of the following?

A. Observer bias
B. Statistical power
C. Confounding
D. Randomization (Correct Answer)
E. Effect modification

Explanation: ***Randomization*** - In a randomized clinical trial, the purpose of comparing baseline characteristics between experimental groups is to assess if **randomization successfully distributed potential confounders** evenly. - An even distribution of baseline characteristics suggests that any observed differences in outcomes are more likely due to the intervention rather than **pre-existing differences** between the groups. *Observer bias* - **Observer bias** occurs when researchers' expectations influence their observations or interpretation of results, which is not evaluated by comparing baseline demographics. - This type of bias is typically mitigated through **blinding** of researchers or participants, rather than checking baseline characteristics. *Statistical power* - **Statistical power** refers to the probability of correctly rejecting a false null hypothesis and detecting a true effect. - It is determined by factors like sample size and effect size, not by the **balance of baseline characteristics** between groups. *Effect modification* - **Effect modification** occurs when the effect of an exposure on an outcome varies across different levels of a third variable. - This is an **analytical consideration** explored in later stages of data analysis, not a concern addressed by comparing baseline characteristics. *Confounding* - **Confounding** occurs when an extraneous variable is associated with both the exposure and the outcome, distorting the true relationship. - While the baseline table helps verify that potential confounders are evenly distributed, the primary purpose is to evaluate whether **randomization was successful**, not to directly assess confounding as an analysis concern.

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: A 28-year-old male presents to his primary care physician with complaints of intermittent abdominal pain and alternating bouts of constipation and diarrhea. His medical chart is not significant for any past medical problems or prior surgeries. He is not prescribed any current medications. Which of the following questions would be the most useful next question in eliciting further history from this patient?

A. "Does the diarrhea typically precede the constipation, or vice-versa?"
B. "Is the diarrhea foul-smelling?"
C. "Please rate your abdominal pain on a scale of 1-10, with 10 being the worst pain of your life"
D. "Are the symptoms worse in the morning or at night?"
E. "Can you tell me more about the symptoms you have been experiencing?" (Correct Answer)

Explanation: ***Can you tell me more about the symptoms you have been experiencing?*** - This **open-ended question** encourages the patient to provide a **comprehensive narrative** of their symptoms, including details about onset, frequency, duration, alleviating/aggravating factors, and associated symptoms, which is crucial for diagnosis. - In a patient presenting with vague, intermittent symptoms like alternating constipation and diarrhea, allowing them to elaborate freely can reveal important clues that might not be captured by more targeted questions. *Does the diarrhea typically precede the constipation, or vice-versa?* - While knowing the sequence of symptoms can be helpful in understanding the **pattern of bowel dysfunction**, it is a very specific question that might overlook other important aspects of the patient's experience. - It prematurely narrows the focus without first obtaining a broad understanding of the patient's overall symptomatic picture. *Is the diarrhea foul-smelling?* - Foul-smelling diarrhea can indicate **malabsorption** or **bacterial overgrowth**, which are important to consider in some gastrointestinal conditions. - However, this is a **specific symptom inquiry** that should follow a more general exploration of the patient's symptoms, as it may not be relevant if other crucial details are missed. *Please rate your abdominal pain on a scale of 1-10, with 10 being the worst pain of your life* - Quantifying pain intensity is useful for assessing the **severity of discomfort** and monitoring changes over time. - However, for a patient with intermittent rather than acute, severe pain, understanding the **character, location, and triggers** of the pain is often more diagnostically valuable than just a numerical rating initially. *Are the symptoms worse in the morning or at night?* - Diurnal variation can be relevant in certain conditions, such as inflammatory bowel diseases where nocturnal symptoms might be more concerning, or functional disorders whose symptoms might be stress-related. - This is another **specific question** that should come after gathering a more complete initial picture of the patient's symptoms to ensure no key information is overlooked.

Question 9: 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 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.

Want unlimited practice?

Get full access to all questions, explanations, and performance tracking.

Start For Free