Biostatistics Practice Questions

Q: In a population of 10,000, 20% have a particular disease. A screening test for this disease has a sensitivity of 95% and a specificity of 80%. What is the positive predictive value (PPV) of this test?

54.3%. ### Explanation To calculate the **Positive Predictive Value (PPV)**, we must determine the probability that a person with a positive test result actually has the disease. This is best solved using a 2x2 contingency table based on the provided data: * **Total Population:** 10,000 * **Prevalence (20%):** Disease Present = 2,000; Disease Absent = 8,000 * **Sensitivity (95%):** True Positives (TP) = 95% of 2,000 = **1,900** * **Specificity (80%):** True Negatives (TN) = 80% of 8,000 = 6,400 * **False Positives (FP):** Total Healthy - TN = 8,000 - 6,400 = **1,600** **Calculation:** $$PPV = \frac{TP}{TP + FP} \times 100$$ $$PPV = \frac{1,900}{1,900 + 1,600} \times 100 = \frac{1,900}{3,500} \times 100 = \mathbf{54.28\% \approx 54.3\%}$$ --- ### Analysis of Options: * **A (54.3%):** Correct. This represents the proportion of true positives among all those who tested positive. * **B (98.5%):** Incorrect. This might be mistaken for Negative Predictive Value (NPV) or a calculation error ignoring the high number of false positives. * **C (47.5%):** Incorrect. This is a common distractor resulting from miscalculating the denominator. * **D (20%):** Incorrect. This is the **Prevalence** (Pre-test probability) of the disease, not the post-test probability (PPV). --- ### NEET-PG High-Yield Pearls: 1. **Relationship with Prevalence:** PPV is **directly proportional** to the prevalence of the disease in the population. If prevalence increases, PPV increases. 2. **NPV vs. Prevalence:** Negative Predictive Value is **inversely proportional** to prevalence. 3. **Sensitivity/Specificity:** These are inherent properties of the test and do not change with disease prevalence, whereas PPV and NPV are population-dependent. 4. **Screening Strategy:** In clinical practice, a test with high sensitivity is used for **screening** (to rule out disease - SnNout), while a test with high specificity is used for **confirmation** (to rule in disease - SpPin).

Q: Which of the following is NOT a benefit of randomization in a study?

Increases external validity of the study. ### Explanation **Randomization** is the "heart" of a Randomized Controlled Trial (RCT). Its primary purpose is to eliminate **selection bias** by ensuring that every participant has an equal chance of being assigned to either the study or control group. #### Why Option D is the Correct Answer **External validity** (Generalizability) refers to the extent to which study results can be applied to the general population. This depends on the **sampling method** (how participants are chosen from the universe), not randomization. Randomization ensures **Internal Validity** by ensuring that the observed differences between groups are due to the intervention and not confounding factors. It does not guarantee that the study sample represents the wider population. #### Why the Other Options are Incorrect * **A. Reduction of bias:** Randomization eliminates selection bias and investigator bias in allocating participants. * **B. Ensures comparability:** It balances both **known and unknown confounders** (e.g., age, genetics, lifestyle) between the two groups, making them comparable at baseline. * **C. Facilitates blinding:** Randomization creates the unpredictable assignment necessary for successful blinding (masking), which further reduces performance and detection bias. --- ### High-Yield Clinical Pearls for NEET-PG * **Gold Standard:** The RCT is the gold standard design for evaluating the efficacy of a new drug or intervention. * **Randomization vs. Random Sampling:** * *Randomization* $\rightarrow$ Internal Validity (Assigning to groups). * *Random Sampling* $\rightarrow$ External Validity (Selecting from population). * **Unique Strength:** Randomization is the **only** method that can control for **unknown confounders**. * **Types of Randomization:** Simple (toss of a coin), Block (ensures equal group sizes), and Stratified (balances specific prognostic factors like gender).

Q: A study found the relative risk of passive smoking to have depression to be 1.05. What is the interpretation?

Positive association. ### Explanation **1. Why Option A is Correct:** Relative Risk (RR) is the ratio of the incidence of a disease among exposed individuals to the incidence among non-exposed individuals. The interpretation of RR is based on its value relative to **1.0**: * **RR > 1.0:** Indicates a **positive association** (the exposure increases the risk of the outcome). * In this case, RR = 1.05. Since 1.05 is greater than 1, it signifies that passive smokers have a 5% higher risk of developing depression compared to non-smokers. Even though the increase is small, it remains a positive association. **2. Why Other Options are Incorrect:** * **Option B (No association):** This would require an **RR = 1.0**, meaning the risk is identical in both groups. * **Option C (Negative association):** This would require an **RR < 1.0**, indicating a protective effect (the exposure reduces the risk of the outcome). * **Option D (Not significant):** Statistical significance is determined by the **p-value** or the **95% Confidence Interval (CI)**. Since neither is provided in the question, we cannot comment on significance. We can only interpret the direction of the association based on the numerical value of the RR. **3. High-Yield NEET-PG Pearls:** * **RR Formula:** $Incidence\ among\ exposed\ /\ Incidence\ among\ non-exposed$. * **Study Design:** RR is typically calculated in **Cohort Studies**. * **Odds Ratio (OR):** Used in Case-Control studies; interpreted similarly to RR (OR > 1 is positive association). * **Attributable Risk (AR):** Measures the impact of an exposure; calculated as $Incidence\ (exposed) - Incidence\ (non-exposed)$. * **Significance Rule:** If the 95% CI for RR includes 1.0 (e.g., 0.8 to 1.2), the result is **not** statistically significant. If it excludes 1.0 (e.g., 1.02 to 1.08), it is significant.

Q: If the coefficient of correlation between variables X and Y is 'r', what is the coefficient of correlation between 4X and 4Y?

r. ### Explanation **1. Why the Correct Answer (D) is Right:** The coefficient of correlation (Pearson’s ‘r’) measures the **strength and direction of a linear relationship** between two variables. A fundamental mathematical property of ‘r’ is that it is **independent of change of scale and change of origin.** In this question, both variables X and Y are multiplied by 4. This is a "change of scale." Since the correlation coefficient is a dimensionless index (standardized by the standard deviations of the variables), multiplying the variables by the same positive constant does not change the degree to which they vary together. Therefore, the correlation between 4X and 4Y remains exactly **'r'**. **2. Why the Incorrect Options are Wrong:** * **Options A, B, and C (4r, 3r, 2r):** These options suggest that the correlation increases proportionally with the scale of the variables. This is a common misconception. If 'r' were to increase, it could easily exceed the mathematical limit of +1 (e.g., if r = 0.5, then 4r would be 2.0, which is impossible). Correlation measures the *pattern* of the data, not the absolute magnitude of the values. **3. High-Yield Clinical Pearls for NEET-PG:** * **Range of 'r':** It always lies between **-1 and +1**. * **Change of Origin:** Adding or subtracting a constant from X or Y (e.g., X+10, Y-5) does **not** change 'r'. * **Change of Scale:** Multiplying or dividing by a **positive** constant does **not** change 'r'. * **Note on Signs:** If one variable is multiplied by a positive number and the other by a negative number, the magnitude of 'r' stays the same, but the **sign flips** (e.g., correlation between 4X and -4Y would be -r). * **Coefficient of Determination:** This is **r²**, which represents the proportion of variance in one variable explained by the other. Unlike 'r', it is always positive.

Q: Blood pressure readings of 210/110 mm Hg in elderly individuals are classified as severe hypertension. This type of data represents which of the following?

Categorical data. In biostatistics, the classification of data depends on how the information is being used rather than the raw measurement itself. **Why "Categorical Data" is correct:** While blood pressure is measured as a numerical value (210/110 mm Hg), the question states that these readings are **"classified as severe hypertension."** Once a numerical value is placed into a descriptive group or "category" (e.g., Normal, Pre-hypertension, Stage 1, or Severe Hypertension), it loses its quantitative property and becomes **Categorical (specifically, Ordinal) data**. The focus here is on the label "Severe Hypertension," not the mathematical difference between the numbers. **Why the other options are incorrect:** * **B. Numerical data:** This refers to data expressed in numbers where the numbers have mathematical meaning. While 210/110 is a number, the act of *classifying* it transforms it into a category. * **C. Quantitative data:** This is a synonym for numerical data. It represents "how much" of something exists. * **D. Continuous data:** This is a sub-type of quantitative data that can take any value within a range (including decimals). Raw BP readings are continuous, but the *classification* of those readings is discrete and categorical. **High-Yield Clinical Pearls for NEET-PG:** * **Nominal Data:** Categories with no inherent order (e.g., Gender, Blood Group). * **Ordinal Data:** Categories with a logical rank or order (e.g., Stages of Cancer, Socio-economic status, Severity of Hypertension). * **Discrete Data:** Numerical data with whole integers (e.g., Number of hospital beds). * **Rule of Thumb:** If the question mentions "classification," "grading," or "staging," always look for **Categorical/Ordinal** as the answer.

Q: Which type of blinding is when both the subject and the investigator are unaware of the treatment being administered?

Double blinding. ### Explanation **Concept Overview:** Blinding (or masking) is a crucial methodological tool used in Randomized Controlled Trials (RCTs) to eliminate **bias**. It ensures that the participants and/or the researchers do not know which group (intervention or control) a subject belongs to, preventing preconceived notions from influencing the study results. **Why Double Blinding is Correct:** In **Double blinding**, two parties are kept unaware of the treatment allocation: 1. **The Subject:** To prevent the "Hawthorne Effect" or psychological placebo responses. 2. **The Investigator:** To prevent "Observer Bias" (where the researcher might unintentionally interpret results or treat patients differently based on their group). Since the question specifies that both the subject and investigator are unaware, double blinding is the correct answer. **Analysis of Incorrect Options:** * **A. Single blinding:** Only the **subject** is unaware. The investigator knows the treatment allocation. This is common in surgical trials where the surgeon cannot be blinded. * **C. Triple blinding:** In addition to the subject and investigator, the **data analyst** (statistician) is also unaware of which group is which. This is the most robust method to prevent "Analysis Bias." * **D. No blinding:** Also called an **Open-label trial**. Both parties know the treatment. This is often used in pilot studies or when blinding is ethically or practically impossible. **High-Yield Clinical Pearls for NEET-PG:** * **Primary Purpose:** Blinding is primarily used to eliminate **Bias**, whereas Randomization is used to eliminate **Confounding**. * **Gold Standard:** The "Double-blind RCT" is considered the gold standard for evaluating the efficacy of a new drug. * **Allocation Concealment:** This happens *before* the trial begins (to prevent selection bias), whereas **Blinding** happens *during* the trial (to prevent measurement/observer bias).

Q: What is the confidence limit when S.D. is 1.96?

95%. ### Explanation This question tests the fundamental concept of the **Normal Distribution (Gaussian Curve)** and its relationship with Standard Deviation (S.D.) and Confidence Intervals (C.I.). **1. Why 95% is Correct:** In a normal distribution, the area under the curve represents the probability of data points falling within a certain range. The standard mathematical relationship dictates that: * **Mean ± 1 S.D.** covers approximately **68%** of the values. * **Mean ± 1.96 S.D.** (often rounded to 2 S.D.) covers exactly **95%** of the values. * **Mean ± 2.58 S.D.** (often rounded to 3 S.D.) covers **99%** of the values. Therefore, if the S.D. multiplier (Z-score) is 1.96, the confidence limit is 95%. This means there is a 95% probability that the true population parameter lies within this range, and only a 5% chance (p < 0.05) that the result occurred by random chance. **2. Why Other Options are Incorrect:** * **A & B (63.60% & 66.60%):** These values do not correspond to standard confidence intervals used in biostatistics. 1 S.D. covers 68.2%, not 63% or 66%. * **D (99%):** This confidence limit corresponds to **2.58 S.D.** It is used when a higher degree of certainty is required, reducing the significance level (alpha) to 1%. **3. High-Yield Clinical Pearls for NEET-PG:** * **Standard Error (S.E.):** Remember that Confidence Intervals are calculated using S.E., not just S.D. Formula: $C.I. = Mean \pm (1.96 \times S.E.)$. * **Z-score values to memorize:** * 90% C.I. = 1.64 S.D. * 95% C.I. = 1.96 S.D. * 99% C.I. = 2.58 S.D. * **Precision:** A narrower confidence interval (e.g., 95% vs 99%) indicates greater precision but less certainty that the range contains the true mean.

Q: A woman is a carrier for an X-linked disease. The disease frequency in the population is 1 in 2,000. What fraction of women in this population are carriers for this particular disease?

1 in 1,000. ### Explanation This question tests the application of the **Hardy-Weinberg Principle** in the context of X-linked recessive disorders. **1. Why the Correct Answer is Right:** In X-linked recessive diseases, the frequency of the disease in the population is equal to the frequency of the disease-causing allele (**q**) because males have only one X chromosome. * Given: Disease frequency ($q$) = $1/2,000$. * The frequency of female carriers (heterozygotes) is represented by **$2pq$**. * Since $q$ is very small ($1/2,000$), $p$ (the normal allele frequency) is approximately **1**. * Calculation: Carrier frequency = $2 \times 1 \times (1/2,000) = 2/2,000 = \mathbf{1/1,000}$. **2. Why the Incorrect Options are Wrong:** * **Option A (1 in 500):** This would be the carrier frequency if the disease frequency ($q$) were $1/1,000$. * **Option C (1 in 1,500):** This value does not align with the $2pq$ calculation based on the provided $q$. * **Option D (1 in 2,000):** This is the frequency of the disease in males ($q$). It fails to account for the fact that carriers are $2pq$. **3. Clinical Pearls & High-Yield Facts:** * **Rule of Thumb:** For rare X-linked recessive traits, the carrier frequency in females is approximately **twice** the disease frequency in males ($2q$). * **Hardy-Weinberg Equation:** $p^2 + 2pq + q^2 = 1$. * **Male vs. Female Frequency:** In X-linked conditions, males are either $p$ (normal) or $q$ (affected). Females can be $p^2$ (normal), $2pq$ (carrier), or $q^2$ (affected). * **Common Examples:** Hemophilia A/B, Duchenne Muscular Dystrophy, and Color Blindness follow this inheritance pattern.

Q: Which sampling method is best for an inhomogeneous population?

Stratified random sampling. **Explanation:** **1. Why Stratified Random Sampling is Correct:** In an **inhomogeneous (heterogeneous) population**, individuals possess diverse characteristics (e.g., different age groups, socio-economic statuses, or disease severities) that may influence the study outcome. Stratified random sampling is the gold standard here because it involves dividing the population into homogenous subgroups called **"strata"** based on these characteristics. A random sample is then drawn from each stratum. This ensures that even small subgroups are represented proportionately, reducing sampling error and increasing the precision of the results compared to simple random sampling. **2. Why Other Options are Incorrect:** * **Simple Random Sampling:** Best suited for small, **homogeneous** populations where every individual has an equal chance of being selected. In an inhomogeneous population, it risks omitting smaller but important subgroups. * **Systematic Random Sampling:** Involves picking every $n^{th}$ individual from a list. While easy to implement, it assumes the sampling frame is randomly ordered. If there is a hidden periodicity in the population, it introduces bias. * **Cluster Sampling:** Used when the population is large and widely scattered (e.g., a whole city). It involves sampling intact groups (clusters) rather than individuals. While administratively convenient, it is actually **less precise** for inhomogeneous populations because individuals within a cluster tend to be similar to each other. **3. High-Yield Pearls for NEET-PG:** * **Stratified Sampling:** Think "Inhomogeneous population" or "Subgroup representation." * **Cluster Sampling:** Think "Large geographical area" or "WHO EPI coverage surveys" (30 x 7 cluster technique). * **Systematic Sampling:** Think "Linear pattern" or "Sampling interval ($K = N/n$)." * **Snowball Sampling:** Best for "Hidden populations" (e.g., IV drug users, commercial sex workers).

Q: A chest physician observed that the distribution of forced expiratory volume (FEV) in 300 smokers had a median value of 2.5 litres with the first and third quartiles being 1.5 and 4.5 litres respectively. Based on this data, how many persons in the sample are expected to have an FEV between 1.5 and 4.5 litres?

150. ### Explanation **Concept: Understanding Quartiles and Interquartile Range** In biostatistics, quartiles divide a frequency distribution into four equal parts, each containing 25% of the total observations. * **First Quartile (Q1):** 25th percentile (25% of values lie below this). * **Second Quartile (Q2):** 50th percentile or **Median**. * **Third Quartile (Q3):** 75th percentile (75% of values lie below this). The range between the first quartile (1.5L) and the third quartile (4.5L) is known as the **Interquartile Range (IQR)**. By definition, the IQR contains the middle **50%** of the total sample population. **Calculation:** * Total sample size (n) = 300 * Percentage of people between Q1 and Q3 = 50% * Expected number of persons = 50% of 300 = **150**. --- ### Analysis of Options * **Option A (75):** This represents 25% of the sample. This would be the number of people falling *below* Q1 or *above* Q3, but not the total between them. * **Option B (150):** **Correct.** This represents the middle 50% of the distribution (from the 25th to the 75th percentile). * **Option C (225):** This represents 75% of the sample. This would be the number of people whose FEV is *below* the third quartile (4.5L). * **Option D (300):** This represents 100% of the sample, which is impossible given the specific range provided. --- ### High-Yield Clinical Pearls for NEET-PG 1. **Skewness:** When the distance between Q1 and Median is not equal to the distance between Median and Q3 (as seen here: 1.0 vs 2.0), the distribution is **skewed** (non-normal). 2. **Best Measure of Central Tendency:** For skewed data (like FEV in smokers), the **Median** is preferred over the Mean. 3. **Best Measure of Dispersion:** For skewed data, the **Interquartile Range** is preferred over Standard Deviation. 4. **Box-and-Whisker Plot:** This is the graphical representation used to display the median and quartiles of a dataset.

Question 1

In a population of 10,000, 20% have a particular disease. A screening test for this disease has a sensitivity of 95% and a specificity of 80%. What is the positive predictive value (PPV) of this test?

Accepted Answer

54.3%

Answer

98.50%

Answer

47.50%

Answer

20%

Question 2

Which of the following is NOT a benefit of randomization in a study?

Accepted Answer

Increases external validity of the study

Answer

Reduction of bias in the selection of groups

Answer

Ensures comparability of both groups

Answer

Facilitates blinding of treatment

Question 3

A study found the relative risk of passive smoking to have depression to be 1.05. What is the interpretation?

Accepted Answer

Positive association

Answer

No association

Answer

Negative association

Answer

Not significant

Question 4

If the coefficient of correlation between variables X and Y is 'r', what is the coefficient of correlation between 4X and 4Y?

Accepted Answer

r

Answer

4r

Answer

3r

Answer

2r

Question 5

Blood pressure readings of 210/110 mm Hg in elderly individuals are classified as severe hypertension. This type of data represents which of the following?

Accepted Answer

Categorical data

Answer

Numerical data

Answer

Quantitative data

Answer

Continuous data

Question 6

Which type of blinding is when both the subject and the investigator are unaware of the treatment being administered?

Accepted Answer

Double blinding

Answer

Single blinding

Answer

Triple blinding

Answer

No blinding

Question 7

What is the confidence limit when S.D. is 1.96?

Accepted Answer

95%

Answer

63.60%

Answer

66.60%

Answer

99%

Question 8

A woman is a carrier for an X-linked disease. The disease frequency in the population is 1 in 2,000. What fraction of women in this population are carriers for this particular disease?

Accepted Answer

1 in 1,000

Answer

1 in 500

Answer

1 in 1,500

Answer

1 in 2,000

Question 9

Which sampling method is best for an inhomogeneous population?

Accepted Answer

Stratified random sampling

Answer

Cluster Sampling

Answer

Systematic random sampling

Answer

Simple random sampling

Question 10

A chest physician observed that the distribution of forced expiratory volume (FEV) in 300 smokers had a median value of 2.5 litres with the first and third quartiles being 1.5 and 4.5 litres respectively. Based on this data, how many persons in the sample are expected to have an FEV between 1.5 and 4.5 litres?

Accepted Answer

150

Answer

75

Answer

225

Answer

300

Biostatistics — MCQs

Biostatistics — MCQs

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