Biostatistics — MCQs
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In a vaccine trial, relative risk is 0.2. What is the vaccine efficacy?
Hardy-Weinberg equilibrium shows gene frequency p=0.7, q=0.3. What is frequency of heterozygotes?
Calculate the sensitivity of a screening test: True Positives=80, False Negatives=20, True Negatives=90, False Positives=10
What is the correlation coefficient if regression coefficient of X on Y is 0.8 and Y on X is 0.9?
The crude birth rate for a sub-center with a population of 1000 is 20. What is the estimated number of pregnant women registered in the sub-center during the year?
What is the sensitivity of a screening test that correctly identifies 90 out of 100 true positive cases?
A researcher is conducting a study to compare two treatment modalities for hypertension. The study finds a p-value of 0.02 and a 95% confidence interval for the difference in means that does not include zero. How should these results be interpreted?
A study comparing two antihypertensive drugs reports a p-value of 0.03 for the primary outcome. What is the correct interpretation of this result?
Bias in clinical trials can be minimized by all of the following methods, EXCEPT:
A study finds that a new diet reduces the risk of heart disease by 30%. What type of measure does this represent?
Biostatistics Indian Medical PG Practice Questions and MCQs
Question 801: In a vaccine trial, relative risk is 0.2. What is the vaccine efficacy?
- A. 90%
- B. 80% (Correct Answer)
- C. 95%
- D. 20%
Explanation: ***80%*** - Vaccine efficacy is calculated as **(1 - Relative Risk) x 100%**. Given a relative risk of 0.2, the efficacy is (1 - 0.2) x 100% = **80%**. - This value represents the **proportionate reduction** in disease incidence in the vaccinated group compared to an unvaccinated group. *90%* - This would imply a relative risk of 0.1, as **(1 - 0.1) x 100% = 90%**. - The given relative risk of **0.2** does not correspond to 90% efficacy. *95%* - This would imply a relative risk of 0.05, as **(1 - 0.05) x 100% = 95%**. - The given relative risk of **0.2** does not correspond to 95% efficacy. *20%* - This value directly represents the **Relative Risk (RR)** itself, or an efficacy calculated incorrectly as RR x 100%. - Vaccine efficacy is a measure of reduction from the unvaccinated state, hence it is **1 - RR**.
Question 802: Hardy-Weinberg equilibrium shows gene frequency p=0.7, q=0.3. What is frequency of heterozygotes?
- A. 0.09
- B. 0.49
- C. 0.42 (Correct Answer)
- D. 0.21
Explanation: ***0.42*** - In **Hardy-Weinberg equilibrium**, the frequency of heterozygotes is given by the formula **2pq**. - Given **p = 0.7** and **q = 0.3**, the frequency of heterozygotes is 2 * 0.7 * 0.3 = **0.42**. *0.09* - This value represents **q²**, which is the frequency of the **homozygous recessive genotype** (0.3 * 0.3 = 0.09). - It does not represent the frequency of heterozygous individuals. *0.49* - This value represents **p²**, which is the frequency of the **homozygous dominant genotype** (0.7 * 0.7 = 0.49). - It does not represent the frequency of heterozygous individuals. *0.21* - This value represents only **pq** (0.7 * 0.3 = 0.21), not the full frequency of heterozygotes which is **2pq**. - The coefficient of 2 is necessary because there are two ways to be heterozygous (one allele from each parent).
Question 803: Calculate the sensitivity of a screening test: True Positives=80, False Negatives=20, True Negatives=90, False Positives=10
- A. 90%
- B. 85%
- C. 80% (Correct Answer)
- D. 95%
Explanation: ***80%*** - Sensitivity is calculated as **True Positives / (True Positives + False Negatives)**. In this case, 80 / (80 + 20) = 80/100, which equals 0.8 or 80%. - This metric represents the proportion of **actual positive cases** that are correctly identified by the test. *90%* - This value might represent the **specificity** (True Negatives / (True Negatives + False Positives)) if calculated with the given numbers (90 / (90 + 10) = 90%). - However, the question specifically asks for **sensitivity**, which is a different measure. *85%* - This percentage would be obtained if the total number of true positives and false negatives was 94 (e.g., 80 / 94), which is not the case here. - It does not correspond to the correct formula for **sensitivity** using the provided data. *95%* - This result would occur if the test correctly identified 95 out of 100 actual positive cases (e.g., 95 TP and 5 FN). - The given data of **80 True Positives** and **20 False Negatives** leads to a lower sensitivity.
Question 804: What is the correlation coefficient if regression coefficient of X on Y is 0.8 and Y on X is 0.9?
- A. 0.95
- B. 0.85 (Correct Answer)
- C. 0.81
- D. 0.72
Explanation: ***Correct: 0.85*** - The correlation coefficient (r) is the **geometric mean** of the two regression coefficients - Formula: r = √(b_xy × b_yx), where b_xy is the regression coefficient of X on Y and b_yx is the regression coefficient of Y on X - Calculation: r = √(0.8 × 0.9) = √0.72 ≈ **0.8485**, which rounds to **0.85** - Since both regression coefficients are positive, the correlation is positive *Incorrect: 0.95* - This would be obtained by taking the **arithmetic mean** [(0.8 + 0.9)/2 = 0.85... wait, that's not 0.95] - Actually, this value is too high and doesn't result from any standard calculation with these regression coefficients - The correct method requires the **geometric mean** (square root of the product), not any simple average *Incorrect: 0.81* - This appears to be the square of one regression coefficient (0.9² = 0.81) - However, the correlation coefficient requires the **square root of the product** of both coefficients, not squaring a single coefficient - This is a common error in calculation *Incorrect: 0.72* - This is the **product** of the two regression coefficients (0.8 × 0.9 = 0.72) - This is an intermediate step in the calculation, but not the final answer - The correlation coefficient requires taking the **square root** of this product: √0.72 ≈ 0.85
Question 805: The crude birth rate for a sub-center with a population of 1000 is 20. What is the estimated number of pregnant women registered in the sub-center during the year?
- A. 110
- B. 80
- C. 60 (Correct Answer)
- D. 100
Explanation: ***60*** - The **crude birth rate** of 20 means 20 live births per 1,000 population. For a population of 1,000 people, this means there were **20 live births** in that year. - Using the standard epidemiological formula: **Estimated pregnancies = Live births × 3** - This multiplier of 3 accounts for stillbirths, abortions, miscarriages, and ongoing pregnancies that are registered but may not result in live births. - Therefore: **20 live births × 3 = 60 registered pregnant women** ✓ *110* - This value would require a multiplier of 5.5 (110/20), which is significantly higher than the standard epidemiological estimation. - It overestimates the pregnancy-to-live-birth ratio and does not align with established public health calculations. *80* - This implies a multiplier of 4 (80/20), which exceeds the standard ratio of 3 used in community medicine. - While some regions may have higher pregnancy wastage, this is not the standard calculation method. *100* - This suggests a multiplier of 5 (100/20), which greatly overestimates registered pregnancies relative to live births. - This does not correspond to the accepted formula used in Indian public health programs and NEET PG examinations.
Question 806: What is the sensitivity of a screening test that correctly identifies 90 out of 100 true positive cases?
- A. 90% (Correct Answer)
- B. 100%
- C. 80%
- D. 85%
Explanation: **90%** - **Sensitivity** is calculated as the number of **true positives** divided by the sum of true positives and **false negatives**. - In this case, 90 true positive cases out of 100 total true cases (90 true positives + 10 false negatives) equals 90/100, or **90%**. *100%* - A sensitivity of **100%** would mean that the test correctly identified all 100 true positive cases. - This value indicates that there were **no false negatives**, which is not the case here. *80%* - An **80%** sensitivity would mean that only 80 out of 100 true positive cases were correctly identified. - This would imply **20 false negatives**, which is less accurate than the given scenario. *85%* - An **85%** sensitivity would mean that 85 out of 100 true positive cases were correctly identified. - This implies **15 false negatives**, which is also less accurate than the given scenario of 90 true positives.
Question 807: A researcher is conducting a study to compare two treatment modalities for hypertension. The study finds a p-value of 0.02 and a 95% confidence interval for the difference in means that does not include zero. How should these results be interpreted?
- A. There is no significant difference between the two treatments.
- B. The p-value indicates that the results are not significant.
- C. The confidence interval suggests that the study has low power.
- D. The results are statistically significant, indicating that the null hypothesis can be rejected. (Correct Answer)
Explanation: ***The results are statistically significant, indicating that the null hypothesis can be rejected.*** - A **p-value of 0.02** is less than the conventional significance level of 0.05, meaning the observed difference is unlikely due to **random chance**. - A **95% confidence interval** for the difference in means that does not include **zero** further reinforces that there is a statistically significant difference between the two treatments. *There is no significant difference between the two treatments.* - A **p-value of 0.02** indicates a statistically significant difference, not an absence of difference. - The **confidence interval not including zero** explicitly shows a significant difference between the treatment effects. *The p-value indicates that the results are not significant.* - A **p-value of 0.02** is typically considered **statistically significant** within a 95% confidence threshold (alpha = 0.05). - A p-value **less than 0.05** allows for the rejection of the null hypothesis. *The confidence interval suggests that the study has low power.* - The **width of the confidence interval** is related to the precision of the estimate and sample size, but not directly to the statistical significance or power in this context. - A **confidence interval that does not include zero** indicates a significant finding, which typically implies adequate power to detect that specific difference, not low power.
Question 808: A study comparing two antihypertensive drugs reports a p-value of 0.03 for the primary outcome. What is the correct interpretation of this result?
- A. The probability of making a Type I error is 3%.
- B. The study has a 97% chance of detecting a true difference if it exists.
- C. There is a 3% chance that the null hypothesis is false.
- D. There is a 3% chance that the observed difference occurred by chance if the null hypothesis is true. (Correct Answer)
Explanation: ***There is a 3% chance that the observed difference occurred by chance if the null hypothesis is true*** - A **p-value** of 0.03 means that if there were truly no difference between the drugs (the null hypothesis is true), there would be only a **3% probability** of observing a difference as large as or larger than the one found in the study. - This indicates statistical significance, suggesting that the observed difference is unlikely to be due to **random chance** alone. *The probability of making a Type I error is 3%.* - The probability of making a **Type I error** (alpha level) is typically set *before* the study, often at 0.05. The p-value is the *observed* significance level, not the pre-determined alpha. - While a low p-value *increases the risk* of falsely rejecting the null hypothesis if the null is true, the probability of a Type I error is the chosen alpha level, not the p-value itself. *The study has a 97% chance of detecting a true difference if it exists.* - The 97% figure here refers to **statistical power** (1 - beta), which is the probability of correctly rejecting a false null hypothesis. The p-value does not directly represent the power of the study. - A p-value of 0.03 indicates the probability of observed results under the null hypothesis, not the study's power to detect an effect. *There is a 3% chance that the null hypothesis is false.* - The p-value does not tell us the probability that the **null hypothesis is false** or that the alternative hypothesis is true. - It only quantifies the likelihood of observing the data given that the null hypothesis is true, without making a statement about the truthfulness of the null hypothesis itself.
Question 809: Bias in clinical trials can be minimized by all of the following methods, EXCEPT:
- A. Multivariate analysis (Correct Answer)
- B. Matching
- C. Randomization
- D. Blinding
Explanation: ***Multivariate analysis*** - **Multivariate analysis** is a statistical tool used to analyze data with multiple variables, but it cannot prevent bias during the design or execution phases of a clinical trial. - While it can help control for confounding variables during data analysis, it is applied *after* data collection and does not eliminate sources of bias related to participant selection, intervention assignment, or outcome assessment. *Matching* - **Matching** involves selecting control group participants who share similar characteristics (e.g., age, sex, comorbidities) with the intervention group, thereby reducing confounding by known variables. - This method helps to ensure that groups are comparable at baseline, minimizing **selection bias** and making observed differences more attributable to the intervention. *Blinding* - **Blinding** involves concealing the treatment assignment from participants, researchers, or both (single- or double-blinding) to prevent their expectations or preconceptions from influencing outcomes or assessments. - This method effectively minimizes various forms of **performance bias** (e.g., in participant behavior or co-interventions) and **detection bias** (e.g., in outcome assessment). *Randomization* - **Randomization** is the process of assigning participants to intervention or control groups purely by chance, which helps ensure that known and unknown confounding factors are evenly distributed between groups. - This method is crucial for minimizing **selection bias**, making the groups comparable and increasing the likelihood that any observed differences are due to the intervention rather than pre-existing differences.
Question 810: A study finds that a new diet reduces the risk of heart disease by 30%. What type of measure does this represent?
- A. Relative risk reduction (Correct Answer)
- B. Absolute risk reduction
- C. Odds ratio
- D. Number needed to treat
Explanation: ***Relative risk reduction*** - **Relative risk reduction (RRR)** is the percentage reduction in risk in the exposed group compared to the unexposed group. - A 30% reduction in risk specifically indicates RRR, calculated as: **(risk in unexposed - risk in exposed) / risk in unexposed × 100%**. *Absolute risk reduction* - **Absolute risk reduction (ARR)** is the difference in risk between the exposed and unexposed groups. - It is expressed as a **percentage point difference**, not a percentage *reduction* of the original risk. *Odds ratio* - The **odds ratio (OR)** quantifies the odds of an event occurring in one group compared to the odds of it occurring in another group. - It is typically used in **case-control studies** and does not directly express a reduction in risk. *Number needed to treat* - **Number needed to treat (NNT)** is the number of patients who need to be treated to prevent one additional adverse outcome. - It is calculated as the **reciprocal of the absolute risk reduction (1/ARR)**.
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Collection and Presentation of Data
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Measures of Central Tendency
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Measures of Dispersion
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Normal Distribution
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Sampling Methods
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Sample Size Calculation
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Hypothesis Testing
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Tests of Significance
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Correlation and Regression
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Survival Analysis
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Multivariate Analysis
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Statistical Software in Research
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