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?
Bias in clinical trials can be minimized by all of the following methods, EXCEPT:
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 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: 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 809: 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 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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