Biostatistics — MCQs

A researcher wants to study a new antidepressant in patients with severe depression. Standard antidepressants are available and effective. The pharmaceutical company insists on a placebo-controlled design, arguing it provides the clearest evidence of efficacy. What is the most appropriate study design?

Q780

A surgeon notices that their complication rates are higher than expected. Hospital administration suggests this might be due to taking more complex cases. Analyze the statistical concept that explains this phenomenon.

Biostatistics Indian Medical PG Practice Questions and MCQs

Question 771: In the estimation of statistical probability, Z score is applicable to:

A. Poisson distribution
B. Normal distribution (Correct Answer)
C. Skewed distribution
D. Binomial distribution

Explanation: ***Normal distribution*** - The **Z-score** (or standard score) is a measure of how many **standard deviations** an element is from the mean. It is specifically used when working with **normally distributed data**. - It allows for the comparison of scores from different normal distributions by standardizing them to a common scale. *Poisson distribution* - This distribution deals with the **number of events** occurring in a fixed interval of time or space, given a known average rate, and is not typically used with Z-scores directly. - It is a **discrete probability distribution**, unlike the continuous nature required for direct Z-score application. *Skewed distribution* - A skewed distribution has an **asymmetrical shape**, where points cluster more on one side of the mean. - Z-scores can be calculated for skewed distributions, but their interpretation as probabilities (e.g., using a standard normal table) is **not valid** because the data do not follow a bell-shaped curve. *Binomial distribution* - This distribution describes the **number of successes** in a fixed number of independent Bernoulli trials. - It is a **discrete probability distribution** and generally, Z-scores are not directly applied to it, although for a large number of trials, it can be approximated by a normal distribution.

Question 772: The two important values necessary for describing the variation in a series of observations are:

A. Median and standard deviation
B. Mean and range
C. Mean and standard deviation (Correct Answer)
D. Median and range

Explanation: ***Mean and standard deviation*** - The **mean** provides a measure of the **central tendency**, representing the average value in the dataset. - The **standard deviation** quantifies the **dispersion** or spread of the data points around the mean, indicating the variability. *Median and standard deviation* - The **median** is a measure of **central tendency**, specifically the middle value, but it doesn't directly pair with standard deviation for describing overall variation in the most common statistical contexts. - While standard deviation describes spread, using the median for central tendency often leads to other measures of spread like **interquartile range (IQR)** for a more consistent representation of non-normally distributed data. *Mean and range* - The **mean** indicates the central point of the data, but the **range** (difference between maximum and minimum values) is a less robust measure of variation. - **Range** is highly susceptible to outliers and does not provide information about the distribution of data points within the entire set. *Median and range* - The **median** describes the **center** of the data, particularly useful for skewed distributions or data with outliers. - The **range** is a simple measure of spread, but it's very sensitive to extreme values and does not give a comprehensive picture of data variability.

Question 773: Which one of the following tests should be applied to compare mean haemoglobin level of two groups of antenatal mothers?

A. Analysis of variance
B. Chi-square test
C. Unpaired t-test (Correct Answer)
D. Paired t-test

Explanation: ***Unpaired t-Test*** - The **unpaired t-test** is used to compare the means of **two independent groups** on a continuous variable, such as hemoglobin levels. - Antenatal mothers in two distinct groups are independent, and **hemoglobin level is a continuous variable**, making this the appropriate choice. *Analysis of variance* - **ANOVA** (Analysis of Variance) is used to compare the means of **three or more independent groups**. - Since there are only **two groups** being compared, ANOVA is not the most efficient or appropriate test. *Chi-square test* - The **Chi-square test** is used to analyze the association between **two categorical variables**. - Hemoglobin level is a **continuous variable**, not categorical, so this test is not suitable for comparing means. *Paired t-test* - The **paired t-test** is used to compare the means of **two related groups** or the same group measured at two different times (e.g., before and after an intervention). - The two groups of antenatal mothers are **independent**, not paired or related.

Question 774: What is the specificity of sputum microscopy in detection of Pulmonary Tuberculosis (PTB) as per the information given below?

A. 94 %
B. 10 %
C. 90 % (Correct Answer)
D. 36 %

Explanation: ***90 %*** - Specificity is calculated as the number of **true negatives** divided by the sum of true negatives and **false positives**. - From the table: True Negatives = 180 (PTB Absent, Sputum Negative) and False Positives = 20 (PTB Absent, Sputum Positive). - Specificity = (180 / (180 + 20)) × 100 = (180 / 200) × 100 = **90%**. - This represents the ability of the test to correctly identify those **without the disease**. *36 %* - This value does not correspond to any standard diagnostic test metric such as sensitivity, specificity, positive predictive value, or negative predictive value based on the provided data. - It might be a miscalculation or a different ratio not typically used in this context. *94 %* - This value does not match any standard calculation from the given 2×2 table. - It may represent a misinterpretation of the data or an incorrect calculation. *10 %* - This value represents the **false positive rate** (1 - specificity). - Calculated as: False Positives / Total without disease = 20 / 200 = 10%. - It is the complement of specificity, not specificity itself.

Question 775: A research study comparing two groups shows a statistically significant difference (p=0.04) but the confidence interval is very wide (0.5 to 4.2). How should this result be interpreted?

A. Additional statistical tests are needed
B. The result is statistically significant but imprecise (Correct Answer)
C. The result shows no meaningful difference between groups
D. The result is both statistically and clinically significant

Explanation: ***The result is statistically significant but imprecise*** - A **p-value of 0.04** indicates **statistical significance** at the conventional ɑ=0.05 level, meaning the observed difference is unlikely due to chance. - A **wide confidence interval (0.5 to 4.2)** suggests that while the true effect is likely positive, its magnitude is **highly uncertain** or **imprecise**, possibly due to a small sample size. *Additional statistical tests are needed* - While more analysis is often valuable, the current statistical outputs (p-value and CI) are sufficient to interpret the **significance** and **precision** of the original finding. - Simply adding more tests without addressing the underlying **imprecision** (e.g., through larger studies) would not fundamentally change the interpretation of the current result. *The result shows no meaningful difference between groups* - The **p-value of 0.04** suggests there *is* a statistically significant difference, so stating there's "no meaningful difference" is incorrect based on the statistical evidence. - However, the **precision of the effect** with the large confidence interval means the *clinical meaningfulness* is still very uncertain, as the effect could be anywhere from small to quite large. *The result is both statistically and clinically significant* - The result is **statistically significant** (p=0.04). - However, the **wide confidence interval (0.5 to 4.2)** means the **clinical significance** is unknown, as the true effect size could be small (0.5) or large (4.2); it is not definitively "clinically significant."

Question 776: A randomized controlled trial of a new diabetes medication is stopped early when interim analysis shows significant benefit. The trial enrolled only 60% of the planned participants. What is the most important consideration about this early termination?

A. The result may overestimate the true treatment effect (Correct Answer)
B. Early termination is always appropriate when benefit is shown
C. Early termination violates research protocols
D. Statistical significance justifies stopping the trial

Explanation: ***The result may overestimate the true treatment effect*** - Early termination of a trial due to a strong interim signal of benefit often leads to an **overestimation of the treatment effect** observed in the final results. This phenomenon is known as **"stopping early for benefit bias"** or **"truncation bias"**. - This occurs because trials are stopped when random fluctuations happen to show a particularly large effect, and if the trial continued, the effect might regress to the mean. - This is the **most important methodological concern** when trials are terminated early based on interim analyses. *Early termination is always appropriate when benefit is shown* - While showing benefit is a common reason for early termination, it is not "always appropriate" without careful consideration of the **magnitude of benefit**, **potential harms**, and the impact on **statistical inference**. - **Ethical considerations** to prevent exposing more patients to an inferior treatment must be balanced against the **scientific rigor** of completing the study as planned. *Early termination violates research protocols* - **Research protocols** often include pre-specified rules for early termination based on interim analyses, such as a **stopping boundary** for efficacy or harm (e.g., O'Brien-Fleming boundaries). - If a protocol includes such rules, termination is within the protocol, not a violation. However, if no such rules are in place and termination is ad hoc, it could be problematic. *Statistical significance justifies stopping the trial* - While **statistical significance** is necessary for early stopping, it is not the sole justification. - **Clinical significance**, the magnitude of the effect, ethical considerations, and the potential for **overestimation bias** are also crucial factors in the decision to stop early.

Question 777: A meta-analysis of 10 studies shows significant benefit from a new treatment (p=0.001), but there is high heterogeneity between studies (I² = 78%). Individual studies show conflicting results. How should this evidence be interpreted?

A. Evidence supports treatment in all patient populations
B. Statistical significance overrides heterogeneity concerns
C. Inconclusive evidence requiring additional studies (Correct Answer)
D. Treatment harmful due to conflicting individual results

Explanation: ***Inconclusive evidence requiring additional studies*** - High **heterogeneity (I² = 78%)** indicates that the studies are measuring different effects, making a combined statistical result unreliable even with a low p-value. - **Conflicting individual study results** despite a statistically significant meta-analysis result means that the overall conclusion might be misleading or only applicable to a specific, unidentifiable subgroup. *Evidence supports treatment in all patient populations* - **High heterogeneity** suggests that treatment effects vary significantly between studies, making it inappropriate to universally apply the findings to all patient populations. - The presence of **conflicting individual results** contradicts the idea of a universal benefit across all populations. *Statistical significance overrides heterogeneity concerns* - While a **low p-value (p=0.001)** indicates statistical significance for the overall effect, **high heterogeneity (I² = 78%)** fundamentally questions the validity of pooling such diverse results. - Ignoring significant heterogeneity can lead to **misleading conclusions** about the consistency and generalizability of the treatment effect. *Treatment harmful due to conflicting individual results* - While conflicting results do raise concerns about the consistency of the treatment effect, they do not automatically imply that the treatment is **harmful**. - The data merely indicates **inconsistency** rather than a detrimental effect, suggesting a need for further investigation to understand the variability.

Question 778: A clinical trial shows that a new cardiac medication reduces mortality from 20% to 15%. The relative risk is 0.75 and the number needed to treat is 20. How should the clinical significance be interpreted?

A. Not clinically meaningful despite statistical significance
B. Highly significant due to mortality reduction
C. Excellent result warranting immediate adoption
D. Modest benefit requiring individual risk-benefit assessment (Correct Answer)

Explanation: ***Modest benefit requiring individual risk-benefit assessment*** - A reduction in mortality from 20% to 15% represents an absolute risk reduction of 5% (20% - 15% = 5%). This corresponds to a **Number Needed to Treat (NNT)** of 20 (1/0.05 = 20), meaning 20 patients must be treated to prevent one additional death. - While any reduction in mortality is beneficial, an NNT of 20 suggests a **modest benefit** rather than a dramatic one, necessitating an assessment of potential side effects, cost, and patient preferences to determine the overall utility. *Not clinically meaningful despite statistical significance* - A 5% absolute reduction in mortality and an NNT of 20 for a life-threatening condition like heart disease is generally considered **clinically meaningful**, as it directly impacts patient survival. - The implication of "statistical significance" without clinical meaning usually applies when the effect size is very small, which is not the case here given the mortality outcome. *Highly significant due to mortality reduction* - Although the medication reduces mortality, a **5% absolute risk reduction** and an **NNT of 20** are not typically considered "highly significant" in the context of immediately revolutionizing clinical practice. - "Highly significant" would imply a much larger reduction in adverse outcomes or a much lower NNT (e.g., NNT of 2-5). *Excellent result warranting immediate adoption* - An "excellent result" would imply a more substantial impact (e.g., a significantly lower NNT or a much larger absolute risk reduction) that clearly outweighs potential harms and costs for most patients. - The need to treat 20 patients to save one life suggests that while beneficial, the medication may not be universally suitable without considering individual patient factors and potential side effects in comparison to its benefits.

Question 779: A researcher wants to study a new antidepressant in patients with severe depression. Standard antidepressants are available and effective. The pharmaceutical company insists on a placebo-controlled design, arguing it provides the clearest evidence of efficacy. What is the most appropriate study design?

A. Placebo-controlled trial as requested by the company
B. Crossover design with placebo and active drug periods
C. Observational study without intervention
D. Active-controlled trial comparing to standard antidepressant (Correct Answer)

Explanation: ***Active-controlled trial comparing to standard antidepressant*** - When an effective standard treatment exists for a severe condition, an **active-controlled trial** is ethically superior to a placebo-controlled trial. - This design ensures all participants receive an active treatment while allowing for direct comparison of the **new drug's efficacy** against an established therapy. - Follows the **Declaration of Helsinki** principles that require using the best proven intervention as a comparator when one exists. *Placebo-controlled trial as requested by the company* - Administering a **placebo** to patients with **severe depression** when effective treatments are available raises significant **ethical concerns**, as it may cause preventable suffering. - While placebo controls provide strong evidence of efficacy, their use is generally discouraged when withholding known effective treatment is not justifiable. *Crossover design with placebo and active drug periods* - A **crossover design** would still expose patients with severe depression to a **placebo period**, which is ethically problematic. - The severity of the condition makes it inappropriate to withhold active treatment, even for a limited time. *Observational study without intervention* - An **observational study** would track patient outcomes without actively administering an intervention, making it unsuitable for evaluating the **efficacy of a new drug**. - Such a design would not provide the controlled environment needed to isolate the effects of the new antidepressant.

Question 780: A surgeon notices that their complication rates are higher than expected. Hospital administration suggests this might be due to taking more complex cases. Analyze the statistical concept that explains this phenomenon.

A. Observer bias in outcome assessment
B. Selection bias in case assignment
C. Regression to the mean
D. Confounding by case complexity (Correct Answer)

Explanation: ***Confounding by case complexity*** - The higher complication rates are explained by the increased inherent risk associated with **more complex cases**, which the surgeon is undertaking. The complexity of cases is acting as a **confounding variable**, influencing both the surgeon's choice of cases and the complication rate. - To accurately assess the surgeon's performance, the analysis must account for the baseline risk disparities between patient groups, rather than simply comparing crude complication rates. *Observer bias in outcome assessment* - This bias occurs when the **observation or recording of outcomes** is systematically influenced by the observer's expectations or knowledge, not by the true characteristics of the cases themselves. - In this scenario, the issue is not how complications are observed, but rather the underlying patient population driving the observed rates. *Selection bias in case assignment* - Selection bias occurs when there are **systematic differences** between participant groups in a study that can distort the results. While the surgeon is "selecting" more complex cases, the term "selection bias" in statistical research typically refers to issues in forming comparative groups (e.g., in clinical trials). - Here, the issue is not a flaw in study design for comparison, but rather a characteristic of clinical practice where the surgeon's case mix inherently impacts outcomes. *Regression to the mean* - This statistical phenomenon describes the tendency for **extreme measurements** to be followed by less extreme measurements closer to the average. For example, an exceptionally high or low score is likely to be closer to the average on subsequent measurements. - While it explains why an unusually high measurement might decrease over time, it does not explain why consistently taking on more complex cases would lead to higher complication rates as a sustained trend.

Practice by Chapter

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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