Confidence intervals for NNT/NNH US Medical PG Practice Questions and MCQs
Practice US Medical PG questions for Confidence intervals for NNT/NNH. These multiple choice questions (MCQs) cover important concepts and help you prepare for your exams.
Confidence intervals for NNT/NNH US Medical PG 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)
Confidence intervals for NNT/NNH 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.
Confidence intervals for NNT/NNH US Medical PG 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%
Confidence intervals for NNT/NNH 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.
Confidence intervals for NNT/NNH US Medical PG 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.
Confidence intervals for NNT/NNH 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.
Confidence intervals for NNT/NNH US Medical PG Question 4: 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
Confidence intervals for NNT/NNH 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.
Confidence intervals for NNT/NNH US Medical PG Question 5: 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.
Confidence intervals for NNT/NNH 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.
Confidence intervals for NNT/NNH US Medical PG Question 6: A survey was conducted in a US midwestern town in an effort to assess maternal mortality over the past year. The data from the survey are given in the table below:
Women of childbearing age 250,000
Maternal deaths 2,500
Number of live births 100, 000
Number of deaths of women of childbearing age 7,500
Maternal death is defined as the death of a woman while pregnant or within 42 days of termination of pregnancy from any cause related to or aggravated by, the pregnancy. Which of the following is the maternal mortality rate in this midwestern town?
- A. 1,000 per 100,000 live births
- B. 33 per 100,000 live births
- C. 3,000 per 100,000 live births
- D. 33,300 per 100,000 live births
- E. 2,500 per 100,000 live births (Correct Answer)
Confidence intervals for NNT/NNH Explanation: ***2,500 per 100,000 live births***
- The maternal mortality rate is calculated as the number of **maternal deaths** per 100,000 **live births**. The given data directly provide these values.
- Calculation: (2,500 maternal deaths / 100,000 live births) × 100,000 = **2,500 per 100,000 live births**.
*1,000 per 100,000 live births*
- This value is incorrect as it does not align with the provided numbers for maternal deaths and live births in the calculation.
- It might result from a miscalculation or using incorrect numerator/denominator values from the dataset.
*33 per 100,000 live births*
- This value is significantly lower than the correct rate and suggests a substantial error in calculation or an incorrect understanding of how the maternal mortality rate is derived.
- It could potentially result from dividing the number of live births by maternal deaths, which is the inverse of the correct formula.
*3,000 per 100,000 live births*
- This option is close to the correct answer but slightly higher, indicating a possible calculation error, for instance, including non-maternal deaths or other causes of deaths in the numerator.
- The definition of maternal death is specific to pregnancy-related or aggravated causes, so extraneous deaths would inflate the rate.
*33,300 per 100,000 live births*
- This figure results from incorrectly calculating the proportion of maternal deaths among all deaths of women of childbearing age: (2,500 / 7,500) × 100,000 = 33,333.
- This is a conceptual error as the maternal mortality rate should use live births as the denominator, not total deaths of women of childbearing age.
Confidence intervals for NNT/NNH US Medical PG Question 7: You are reviewing raw data from a research study performed at your medical center examining the effectiveness of a novel AIDS screening examination. The study enrolled 250 patients with confirmed AIDS, and 240 of these patients demonstrated a positive screening examination. The control arm of the study enrolled 250 patients who do not have AIDS, and only 5 of these patients tested positive on the novel screening examination. What is the NPV of this novel test?
- A. 240 / (240 + 15)
- B. 240 / (240 + 5)
- C. 240 / (240 + 10)
- D. 245 / (245 + 10) (Correct Answer)
- E. 245 / (245 + 5)
Confidence intervals for NNT/NNH Explanation: ***245 / (245 + 10)***
- The **negative predictive value (NPV)** is calculated as **true negatives (TN)** divided by the sum of **true negatives (TN)** and **false negatives (FN)**.
- In this study, there are 250 patients with AIDS; 240 tested positive (true positives, TP), meaning 10 tested negative (false negatives, FN = 250 - 240). There are 250 patients without AIDS; 5 tested positive (false positives, FP), meaning 245 tested negative (true negatives, TN = 250 - 5). Therefore, NPV = 245 / (245 + 10).
*240 / (240 + 15)*
- This calculation incorrectly uses the number of **true positives** (240) in the numerator and denominator, which is relevant for **positive predictive value (PPV)**, not NPV.
- The denominator `(240 + 15)` does not correspond to a valid sum for calculating NPV from the given data.
*240 / (240 + 5)*
- This calculation incorrectly uses **true positives** (240) in the numerator, which is not part of the NPV formula.
- The denominator `(240 + 5)` mixes true positives and false positives, which is incorrect for NPV.
*240 / (240 + 10)*
- This incorrectly places **true positives** (240) in the numerator instead of **true negatives**.
- The denominator `(240+10)` represents **true positives + false negatives**, which is related to sensitivity, not NPV.
*245 / (245 + 5)*
- This calculation correctly identifies **true negatives** (245) in the numerator but incorrectly uses **false positives** (5) in the denominator instead of **false negatives**.
- The denominator for NPV should be **true negatives + false negatives**, which is 245 + 10.
Confidence intervals for NNT/NNH US Medical PG Question 8: A pharmaceutical company reports a new antihypertensive drug reduces cardiovascular events with an NNT of 50 over 5 years based on a trial of 10,000 patients. An independent analysis reveals the benefit was driven entirely by a subgroup with resistant hypertension (20% of participants, NNT=15), while the remaining 80% showed no benefit over standard therapy (NNT approaching infinity). Evaluate the ethical and regulatory implications of reporting the overall NNT.
- A. Conduct a new trial in the general hypertensive population to validate efficacy before broader approval
- B. The subgroup analysis represents data dredging; only the overall NNT should be used for clinical decisions
- C. The overall NNT of 50 is statistically valid and appropriate for regulatory approval and marketing
- D. Report both overall and subgroup NNTs; allow clinicians to determine appropriate use based on patient characteristics
- E. The overall NNT is misleading; approval should be restricted to resistant hypertension population where benefit is demonstrated (Correct Answer)
Confidence intervals for NNT/NNH Explanation: ***The overall NNT is misleading; approval should be restricted to resistant hypertension population where benefit is demonstrated***
- Reporting an **aggregate NNT** when the clinical benefit is confined to a specific **subgroup** obscures the fact that the drug is ineffective for 80% of the study population.
- Regulatory and ethical standards dictate that **indication for use** must be limited to populations where a **favorable benefit-risk ratio** has been proven, preventing unnecessary exposure to side effects in non-responders.
*The overall NNT of 50 is statistically valid and appropriate for regulatory approval and marketing*
- While the math is accurate for the trial population as a whole, it ignores **heterogeneity of treatment effect**, which is critical for making safe **clinical recommendations**.
- Marketing a drug based on an **averaged NNT** when the majority of patients derive zero benefit is considered **clinically misleading** and ethically questionable.
*Report both overall and subgroup NNTs; allow clinicians to determine appropriate use based on patient characteristics*
- This approach puts the burden of identifying the correct population on the clinician rather than setting **clear regulatory boundaries** through specific labelling.
- Merely reporting the **overall NNT** may lead to **off-label use** in populations where the NNT is effectively **infinity**, representing a failure in evidence-based guidance.
*Conduct a new trial in the general hypertensive population to validate efficacy before broader approval*
- The existing data already demonstrates that the **general population** (the 80% non-resistant group) showed no benefit over standard therapy.
- Conducting a new trial for the general population would be **unethical and redundant**, as the lack of efficacy in that specific group has already been established by the **independent analysis**.
*The subgroup analysis represents data dredging; only the overall NNT should be used for clinical decisions*
- **Data dredging** refers to finding random patterns; however, identifying a lack of benefit in 80% of a population is a critical **safety and efficacy finding** that cannot be ignored.
- Dismissing the **subgroup effect** would result in potentially treating millions of patients with an **ineffective medication**, violating the principle of **non-maleficence**.
Confidence intervals for NNT/NNH US Medical PG Question 9: A public health agency must allocate a fixed budget between two interventions for diabetes prevention. Program A (intensive lifestyle modification): NNT=7, cost $3,500/person. Program B (metformin): NNT=14, cost $1,000/person. Both prevent one case of diabetes over 3 years. The budget allows treating 1,000 people with Program A or 3,500 people with Program B. Evaluate the optimal allocation strategy to maximize population health impact.
- A. Choose based on cost per case prevented: Program A ($24,500) vs Program B ($14,000), favoring Program B (Correct Answer)
- B. Choose Program B exclusively: higher population reach (3,500 vs 1,000) and lower cost per person treated maximizes prevention (250 cases) despite higher NNT
- C. Allocate budget equally between programs: provides both high-efficacy and broad-reach approaches
- D. Choose Program A for high-risk individuals and Program B for moderate-risk: risk-stratified approach optimizes NNT
- E. Choose Program A exclusively: lower NNT means superior efficacy, preventing 143 cases versus 250 with Program B
Confidence intervals for NNT/NNH Explanation: ***Choose based on cost per case prevented: Program A ($24,500) vs Program B ($14,000), favoring Program B***
- To maximize **population health impact** under a fixed budget, one must calculate the **cost per case prevented**, which is found by multiplying the **NNT** by the **cost per person** ($1,000 x 14 = $14,000 for Program B).
- Program B allows for a much higher total number of cases prevented (**250 cases**) compared to Program A (**142 cases**) because the **lower unit cost** outweighs the higher NNT.
*Choose Program A exclusively: lower NNT means superior efficacy, preventing 143 cases versus 250 with Program B*
- While Program A has a **lower NNT**, indicating it is more effective for an individual, it is significantly less **cost-effective** for a population due to its high cost.
- Exclusive use of Program A would result in fewer total cases prevented (142) compared to the 250 cases prevented by Program B, wasting **allocated resources**.
*Choose Program B exclusively: higher population reach (3,500 vs 1,000) and lower cost per person treated maximizes prevention (250 cases) despite higher NNT*
- This option correctly identifies the outcome but lacks the precise **economic justification** (cost per outcome) required for optimal health allocation decisions.
- Public health decisions are fundamentally based on **incremental cost-effectiveness ratios** or cost per case prevented rather than reach alone.
*Allocate budget equally between programs: provides both high-efficacy and broad-reach approaches*
- Managing a fixed budget by splitting it equally results in **196 total cases prevented**, which is mathematically inferior to the 250 cases prevented by prioritizing the more cost-efficient program.
- This approach fails to address the **opportunity cost** of not spending the entire budget on the more efficient intervention.
*Choose Program A for high-risk individuals and Program B for moderate-risk: risk-stratified approach optimizes NNT*
- While **risk stratification** is clinically sound, the prompt asks to maximize impact based on the provided fixed costs and NNTs for the general intervention group.
- Adding complexity to the delivery model can further increase **administrative costs**, which are not accounted for in this basic **cost-effectiveness analysis**.
Confidence intervals for NNT/NNH US Medical PG Question 10: A 45-year-old woman with a strong family history of breast cancer (lifetime risk 25%) is considering chemoprevention with tamoxifen. A trial shows tamoxifen reduces breast cancer incidence from 5% to 3% over 5 years in high-risk women, but increases endometrial cancer from 0.2% to 0.6% and thromboembolic events from 0.5% to 1.5%. Evaluate whether she should be recommended this therapy based on comprehensive risk-benefit analysis.
- A. Recommend alternative screening strategies as chemoprevention shows no net benefit when all outcomes are considered
- B. Recommend tamoxifen only if patient values breast cancer prevention significantly more than other risks, given similar absolute risk magnitudes (Correct Answer)
- C. Recommend tamoxifen: NNT=50 for breast cancer prevention outweighs combined NNH=250 for endometrial cancer and NNH=100 for thromboembolism
- D. Insufficient data to make recommendation without knowing patient's personal values and quality-of-life preferences
- E. Recommend against tamoxifen: The harms (2 complications per 100 treated) outweigh benefits (2 cancers prevented per 100 treated)
Confidence intervals for NNT/NNH Explanation: ***Recommend tamoxifen only if patient values breast cancer prevention significantly more than other risks, given similar absolute risk magnitudes***
- The **Absolute Risk Reduction (ARR)** for breast cancer is 2% (5% minus 3%), while the cumulative **Absolute Risk Increase (ARI)** for major harms is 1.4% (0.4% for endometrial cancer and 1.0% for thromboembolism).
- Because the magnitude of benefit (2 preventable cancers) is narrowly balanced against the magnitude of harm (1.4 serious complications), the decision relies on **patient preferences** and how they weigh the severity of different health outcomes.
*Recommend tamoxifen: NNT=50 for breast cancer prevention outweighs combined NNH=250 for endometrial cancer and NNH=100 for thromboembolism*
- While the **Number Needed to Treat (NNT)** is indeed 50 (1/0.02), the combined **Number Needed to Harm (NNH)** for any serious complication is approximately 71 (1/0.014), not 250 or 100 individually.
- This option oversimplifies the trade-off by suggesting a clear-cut advantage that does not exist when both serious adverse events are aggregated.
*Recommend against tamoxifen: The harms (2 complications per 100 treated) outweigh benefits (2 cancers prevented per 100 treated)*
- The calculation of harms is slightly inaccurate as the **ARI** is 1.4 per 100, which is numerically lower than the benefit of 2 cancers prevented per 100.
- A blanket recommendation against therapy ignores that a **2% ARR** in breast cancer may be clinically significant for a high-risk patient willing to accept the side-effect profile.
*Insufficient data to make recommendation without knowing patient's personal values and quality-of-life preferences*
- While patient values are crucial, the **clinical data** provided is sufficient to form a recommendation framework based on the **risk-benefit ratio**.
- The objective is to evaluate the therapy within the context of **evidence-based medicine**, which allows for a conditional recommendation rather than a claim of "insufficient data."
*Recommend alternative screening strategies as chemoprevention shows no net benefit when all outcomes are considered*
- This is incorrect because **chemoprevention** is a distinct primary prevention strategy that can be used in conjunction with, not just as a replacement for, high-risk screening.
- The data shows a **net numerical benefit** (2.0% reduction vs 1.4% increase), meaning it cannot be claimed there is "no net benefit" across all outcomes.
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