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.
Q2
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.
Q3
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.
Q4
A meta-analysis of 5 trials examines aspirin for primary prevention of cardiovascular disease. Individual trials show NNTs ranging from 250 to 2000, with confidence intervals overlapping. Trial A (high-risk population, NNT=250) and Trial E (low-risk population, NNT=2000) contribute most to heterogeneity (I²=78%). Analyze the appropriate interpretation and application of these findings.
Q5
A hospital formulary committee is reviewing a new expensive biologic agent for ulcerative colitis. Trial data shows clinical remission in 45% of treated patients versus 15% with placebo at 1 year. However, serious infections occur in 8% versus 2%. The drug costs $50,000 per patient per year. Analyze the pharmacoeconomic implications using NNT and NNH.
Q6
A clinical researcher is analyzing data from a trial of a new antibiotic for community-acquired pneumonia. The cure rate was 88% (352/400) in the treatment group and 80% (320/400) in the standard therapy group. When stratified by age, patients >65 years showed cure rates of 82% versus 70%, while patients ≤65 years showed 92% versus 88%. Analyze how this stratification affects the interpretation of NNT.
Q7
A 72-year-old woman with rheumatoid arthritis is prescribed a COX-2 inhibitor. A study shows the drug reduces joint pain requiring rescue analgesia in 60% of treated patients versus 40% with placebo over 3 months. However, cardiovascular events occur in 4% of treated patients versus 2% of placebo patients. Analyze the risk-benefit profile using NNT and NNH.
Q8
A 55-year-old man with hypertension is considering statin therapy for primary prevention of cardiovascular disease. A clinical trial reports that statin therapy reduced the 10-year risk of myocardial infarction from 8% to 5%. The patient asks how many people like him would need to take the medication for one person to benefit. Apply the trial data to provide this information.
Q9
A 68-year-old woman with atrial fibrillation is being counseled about anticoagulation therapy. A meta-analysis shows that warfarin reduces the risk of ischemic stroke from 6% to 2% per year, but increases major bleeding from 1% to 3% per year. Apply these data to calculate both the NNT for stroke prevention and the number needed to harm (NNH) for major bleeding.
Q10
A pharmaceutical company conducts a randomized controlled trial of a new antiplatelet drug for secondary stroke prevention. In the treatment group (n=1000), 80 patients experienced a recurrent stroke over 5 years. In the placebo group (n=1000), 120 patients experienced a recurrent stroke. Calculate the number needed to treat (NNT) to prevent one stroke over 5 years.
Number needed to treat/harm US Medical PG Practice Questions and MCQs
Question 1: 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)
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**.
Question 2: 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
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**.
Question 3: 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)
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.
Question 4: A meta-analysis of 5 trials examines aspirin for primary prevention of cardiovascular disease. Individual trials show NNTs ranging from 250 to 2000, with confidence intervals overlapping. Trial A (high-risk population, NNT=250) and Trial E (low-risk population, NNT=2000) contribute most to heterogeneity (I²=78%). Analyze the appropriate interpretation and application of these findings.
A. Heterogeneity invalidates the meta-analysis; no conclusions can be drawn
B. The wide NNT range reflects random variation; use the median NNT of 650
C. Apply risk-stratified NNTs: use Trial A data for high-risk, Trial E for low-risk patients (Correct Answer)
D. Exclude outlier trials and recalculate pooled NNT for more precise estimate
E. Use the pooled NNT of 1125 for all patients regardless of baseline risk
Explanation: ***Apply risk-stratified NNTs: use Trial A data for high-risk, Trial E for low-risk patients***
- A high **I² (78%)** indicates significant **heterogeneity**, suggesting that a single pooled estimate is clinically inappropriate due to differences in the study populations' **baseline risk**.
- The **Number Needed to Treat (NNT)** is mathematically dependent on the **Control Event Rate (CER)**; therefore, the benefit is maximized in high-risk groups, making **risk-stratification** essential for clinical application.
*Use the pooled NNT of 1125 for all patients regardless of baseline risk*
- Using a **pooled NNT** in the presence of high heterogeneity masks the fact that the intervention may be highly effective for some and of negligible benefit for others.
- This approach ignores the clinical reality that **absolute benefit** varies by patient profile, potentially leading to overtreatment in low-risk individuals.
*Heterogeneity invalidates the meta-analysis; no conclusions can be drawn*
- High **statistical heterogeneity** doesn't invalidate a meta-analysis but rather limits the use of a **fixed-effects model** and necessitates a search for the source of variation.
- Conclusions can still be drawn by performing **subgroup analyses**, which in this case identify **baseline cardiovascular risk** as the primary driver of the varying NNTs.
*The wide NNT range reflects random variation; use the median NNT of 650*
- The **I² statistic** specifically measures the proportion of variation due to real differences between trials rather than **random chance**; 78% is far too high to be attributed to variation alone.
- Selecting a **median NNT** is arbitrary and lacks the statistical rigor required to account for the **risk-benefit ratio** in specific patient populations.
*Exclude outlier trials and recalculate pooled NNT for more precise estimate*
- Excluding trials like A and E is a form of **selection bias** that removes theoretically important data regarding how the drug performs across the full spectrum of **clinical risk**.
- Instead of exclusion, the appropriate statistical method is to acknowledge the **clinical heterogeneity** and use results to inform **evidence-based medicine** tailored to individual risk levels.
Question 5: A hospital formulary committee is reviewing a new expensive biologic agent for ulcerative colitis. Trial data shows clinical remission in 45% of treated patients versus 15% with placebo at 1 year. However, serious infections occur in 8% versus 2%. The drug costs $50,000 per patient per year. Analyze the pharmacoeconomic implications using NNT and NNH.
A. NNT = 6.7, NNH = 33.3; cost per remission = $335,000; requires selective use in refractory cases
B. NNT = 3.3, NNH = 8.3; cost per remission = $165,000; unfavorable risk-benefit ratio
C. NNT = 3.3, NNH = 16.7; cost per remission = $165,000; unfavorable due to infection risk
D. NNT = 2.2, NNH = 12.5; cost per remission = $110,000; favorable for first-line therapy
E. NNT = 3.3, NNH = 16.7; cost per remission = $165,000; favorable profile warrants formulary addition (Correct Answer)
Explanation: ***NNT = 3.3, NNH = 16.7; cost per remission = $165,000; favorable profile warrants formulary addition***
- The **Number Needed to Treat (NNT)** is 1 / (0.45 - 0.15) = **3.3**, and the **Number Needed to Harm (NNH)** is 1 / (0.08 - 0.02) = **16.7**, reflecting a strong therapeutic window where benefit outweighs harm.
- The **cost per remission** is calculated by multiplying NNT by the annual cost ($50,000 × 3.3 = **$165,000**), which is often considered acceptable for high-efficacy biologics in chronic disease management.
*NNT = 6.7, NNH = 33.3; cost per remission = $335,000; requires selective use in refractory cases*
- These values are incorrect because they assume an **Absolute Risk Reduction (ARR)** of only 15% and an **Absolute Risk Increase (ARI)** of 3%, which contradicts the provided trial data.
- A **cost per remission of $335,000** would suggest much lower cost-effectiveness, leading to stricter formulary restrictions compared to the actual data.
*NNT = 3.3, NNH = 16.7; cost per remission = $165,000; unfavorable due to infection risk*
- While the calculations are accurate, labeling the profile as **unfavorable** is incorrect because the **NNH (16.7)** is significantly higher than the **NNT (3.3)**, indicating the benefit is much more likely than the harm.
- In clinical practice, an NNH that is approximately five times higher than the NNT for a **serious adverse event** is generally acceptable for biologics in **Ulcerative Colitis**.
*NNT = 2.2, NNH = 12.5; cost per remission = $110,000; favorable for first-line therapy*
- An **NNT of 2.2** would require an ARR of 45%, which ignores the **placebo effect** (15%) entirely; pharmacoeconomics must account for the net benefit over placebo.
- The calculation for **NNH of 12.5** also fails by using only the treatment group's risk (1/0.08) instead of the **attributable risk** increase (0.08 - 0.02).
*NNT = 3.3, NNH = 8.3; cost per remission = $165,000; unfavorable risk-benefit ratio*
- The **NNH of 8.3** is incorrect as it implies a massive 12% ARI (8% vs 4% or similar), whereas the actual ARI in the prompt is **6%**.
- This miscalculation would artificially inflate the **safety risk**, leading to an incorrect conclusion that the drug has an **unfavorable risk-benefit ratio**.
Question 6: A clinical researcher is analyzing data from a trial of a new antibiotic for community-acquired pneumonia. The cure rate was 88% (352/400) in the treatment group and 80% (320/400) in the standard therapy group. When stratified by age, patients >65 years showed cure rates of 82% versus 70%, while patients ≤65 years showed 92% versus 88%. Analyze how this stratification affects the interpretation of NNT.
A. Overall NNT = 10; younger patients benefit more due to lower baseline risk
B. Overall NNT = 12.5; elderly and young benefit equally
C. Overall NNT = 10; age stratification shows no clinically meaningful difference
D. Overall NNT = 12.5; elderly benefit more (NNT = 8.3) than younger patients (NNT = 25) (Correct Answer)
E. Overall NNT = 8; stratification reveals Simpson's paradox
Explanation: ***Overall NNT = 12.5; elderly benefit more (NNT = 8.3) than younger patients (NNT = 25)***
- The **Absolute Risk Reduction (ARR)** for the whole group is 8% (0.88 - 0.80), resulting in an **Overall NNT** of 1 / 0.08 = **12.5**.
- Stratified calculation shows the **elderly (>65)** have an **ARR of 12%** (NNT = 1/0.12 ≈ **8.3**) while **younger patients (≤65)** have an **ARR of 4%** (NNT = 1/0.04 = **25**), indicating a higher benefit in the elderly.
*Overall NNT = 10; age stratification shows no clinically meaningful difference*
- The **Overall NNT** is incorrectly calculated; an NNT of 10 would require an **ARR of 10%** (0.10), while the actual data shows 8%.
- **Stratification** clearly shows a significant difference in benefit (NNT 8.3 vs 25), identifying age as an **effect modifier**.
*Overall NNT = 12.5; elderly and young benefit equally*
- While the **Overall NNT** of 12.5 is correct, the conclusion that both groups benefit equally is false.
- The **risk reduction** is three times higher in the elderly (12%) compared to the younger group (4%), meaning mortality or morbidity is prevented more efficiently in the older cohort.
*Overall NNT = 8; stratification reveals Simpson's paradox*
- The **Overall NNT** is not 8; that would require an **ARR of 12.5%**, which is inconsistent with the trial's cure rates.
- **Simpson's paradox** occurs when a trend appearing in groups disappears or reverses when groups are combined, which is not the case here as the treatment is superior in all scenarios.
*Overall NNT = 10; younger patients benefit more due to lower baseline risk*
- The calculation for **NNT** (1/0.10) does not match the provided clinical data (352/400 - 320/400 = 8%).
- Although younger patients have a lower baseline risk, they actually **benefit less** from this specific antibiotic (higher NNT) compared to the older group.
Question 7: A 72-year-old woman with rheumatoid arthritis is prescribed a COX-2 inhibitor. A study shows the drug reduces joint pain requiring rescue analgesia in 60% of treated patients versus 40% with placebo over 3 months. However, cardiovascular events occur in 4% of treated patients versus 2% of placebo patients. Analyze the risk-benefit profile using NNT and NNH.
A. NNT = 3, NNH = 50; requires individual assessment
Explanation: ***NNT = 5, NNH = 50; favorable risk-benefit***
- The **Number Needed to Treat (NNT)** is calculated as 1/ARR; here, the **Absolute Risk Reduction (ARR)** is 20% (60% - 40%), which equals 0.2, resulting in an **NNT of 5** (1/0.2).
- The **Number Needed to Harm (NNH)** is 1/ARI; the **Absolute Risk Increase (ARI)** for cardiovascular events is 2% (4% - 2%), which equals 0.02, resulting in an **NNH of 50** (1/0.02).
*NNT = 3, NNH = 25; favorable risk-benefit*
- An **NNT of 3** would require an ARR of approximately 33%, which is higher than the **20% difference** observed in clinical efficacy.
- An **NNH of 25** implies a 4% risk difference, but the data only shows a **2% increase** in cardiovascular events compared to placebo.
*NNT = 5, NNH = 50; unfavorable risk-benefit*
- While the numerical calculations for **NNT** and **NNH** are correct, the risk-benefit profile is generally considered **favorable** when for every 10 patients successfully treated (2 NNT), only 0.2 (1/5th of an NNH) experience harm.
- In clinical practice, an **NNH of 50** (harming 1 in 50) is often outweighed by an **NNT of 5** (benefiting 10 in 50) for symptomatic relief in chronic conditions.
*NNT = 10, NNH = 25; unfavorable risk-benefit*
- An **NNT of 10** would mean the ARR was only 10% (0.1), which underestimates the **efficacy** shown in the data (60% vs 40%).
- An **NNH of 25** overestimates the **risk of cardiovascular events**, suggesting a higher incidence of complications than the 2% difference reported.
*NNT = 3, NNH = 50; requires individual assessment*
- This option provides an incorrect **NNT**; the calculation 1/0.2 mathematically results in 5, not 3.3 or **3**.
- Although all clinical decisions require **individual assessment**, the primary task of calculating objective metrics like **NNT and NNH** must be mathematically accurate first.
Question 8: A 55-year-old man with hypertension is considering statin therapy for primary prevention of cardiovascular disease. A clinical trial reports that statin therapy reduced the 10-year risk of myocardial infarction from 8% to 5%. The patient asks how many people like him would need to take the medication for one person to benefit. Apply the trial data to provide this information.
A. Approximately 20 people
B. Approximately 40 people
C. Approximately 25 people
D. Approximately 50 people
E. Approximately 33 people (Correct Answer)
Explanation: ***Approximately 33 people***
- The **Number Needed to Treat (NNT)** is calculated as the inverse of the **Absolute Risk Reduction (ARR)**, which is 8% minus 5%, equaling 3% (0.03).
- Dividing 1 by 0.03 results in **33.33**, making **approximately 33** the closest and most accurate estimate for the number of people who must be treated to prevent one myocardial infarction.
*Approximately 20 people*
- This result would require an **Absolute Risk Reduction** of 5% (1 / 0.05 = 20), which is higher than the 3% reported in the trial.
- An ARR of 5% would have meant the risk dropped from 8% to 3%, rather than from **8% to 5%**.
*Approximately 25 people*
- To achieve an NNT of 25, the **Absolute Risk Reduction** would need to be 4% (1 / 0.04 = 25).
- The calculated **ARR** based on the trial data provided (8% - 5%) is only 3%.
*Approximately 40 people*
- An NNT of 40 corresponds to an **Absolute Risk Reduction** of only 2.5% (1 / 0.025 = 40).
- This value understates the clinical benefit demonstrated by the **3% risk reduction** in this specific trial.
*Approximately 50 people*
- This would be the result of an **Absolute Risk Reduction** of 2% (1 / 0.02 = 50), which reflects a smaller treatment effect than observed.
- The trial's data shows a **3% difference**, necessitating fewer than 50 patients to be treated for one person to benefit.
Question 9: A 68-year-old woman with atrial fibrillation is being counseled about anticoagulation therapy. A meta-analysis shows that warfarin reduces the risk of ischemic stroke from 6% to 2% per year, but increases major bleeding from 1% to 3% per year. Apply these data to calculate both the NNT for stroke prevention and the number needed to harm (NNH) for major bleeding.
A. NNT = 25, NNH = 50 (Correct Answer)
B. NNT = 25, NNH = 75
C. NNT = 20, NNH = 40
D. NNT = 33, NNH = 100
E. NNT = 30, NNH = 60
Explanation: ***NNT = 25, NNH = 50***
- The **Number Needed to Treat (NNT)** is calculated as 1/ARR; with an **Absolute Risk Reduction (ARR)** of 4% (6% - 2%), the NNT is 1/0.04 = **25**.
- The **Number Needed to Harm (NNH)** is 1/ARI; with an **Absolute Risk Increase (ARI)** of 2% (3% - 1%), the NNH is 1/0.02 = **50**.
*NNT = 20, NNH = 40*
- This calculation is incorrect as it assumes an **ARR** of 5% and an **ARI** of 2.5%, which does not match the provided clinical data.
- Proper identification of the **baseline risk** and **experimental risk** is required to find the correct denominators for the NNT and NNH formulas.
*NNT = 30, NNH = 60*
- These values result from incorrect subtraction of the percentages, leading to an **underestimation** of the treatment effect and the risk of harm.
- Accuracy in calculating the **arithmetic difference** between the control group and treatment group is essential for biostatistical analysis.
*NNT = 25, NNH = 75*
- While the NNT is correctly identified as **25**, the NNH is based on an incorrect **ARI** of approximately 1.33% instead of the actual 2%.
- It incorrectly identifies the risk of **major bleeding** increase, failing to properly subtract the 1% baseline risk from the 3% treatment risk.
*NNT = 33, NNH = 100*
- This option uses an **ARR** of 3% and an **ARI** of 1%, which identifies the final stroke rate and the baseline bleeding rate instead of the **net changes**.
- This reflects a conceptual error in understanding that NNT and NNH must be derived from the **absolute difference** between groups, not single data points.
Question 10: A pharmaceutical company conducts a randomized controlled trial of a new antiplatelet drug for secondary stroke prevention. In the treatment group (n=1000), 80 patients experienced a recurrent stroke over 5 years. In the placebo group (n=1000), 120 patients experienced a recurrent stroke. Calculate the number needed to treat (NNT) to prevent one stroke over 5 years.
A. 25 (Correct Answer)
B. 15
C. 20
D. 35
E. 30
Explanation: ***25***
- To calculate the **Number Needed to Treat (NNT)**, you first determine the **Absolute Risk Reduction (ARR)**, which is the control group risk (120/1000 = **0.12**) minus the treatment group risk (80/1000 = **0.08**).
- The **ARR** is **0.04** (4%), and the **NNT** is calculated as the inverse of the ARR (**1 / 0.04**), resulting in a value of **25**.
*15*
- This value would require an **ARR** of approximately **0.066**, which does not align with the provided data of a **4%** risk reduction.
- It represents an overestimation of the **drug's clinical efficacy** based on the specific event counts provided in the trial.
*20*
- An NNT of 20 corresponds to an **ARR of 0.05** (5%), but the actual difference between groups in this study is only **0.04**.
- This might be obtained accidentally if the **Placebo Group** risk was calculated or recorded as **13%** instead of **12%**.
*30*
- This value would result from an **ARR** of approximately **0.033**, indicating a smaller **therapeutic effect** than what was observed.
- It would be the correct answer only if the **treatment group** had approximately **87** events instead of **80**.
*35*
- An NNT of 35 implies an **ARR of about 0.028**, meaning the drug provides significantly less **secondary prevention** benefit than the data shows.
- Using this value would underestimate the **treatment's impact**, leading to an incorrect assessment of the drug's **clinical utility**.
