Biostatistics Practice Questions

Q: A district has a total population of 10 lacs, with the under 16 population being 30%. The prevalence of blindness is 0.8/1000 among the under 16 population. Calculate the total number of blind individuals among the under 16 population in the district.

240. ### Explanation **1. Why Option A is Correct:** To arrive at the correct answer, we must follow a two-step calculation based on the demographic data provided: * **Step 1: Calculate the Under-16 Population:** The total population is 10 lakhs (1,000,000). The under-16 age group constitutes 30% of this population. * $1,000,000 \times 0.30 = 300,000$ (3 lakhs). * **Step 2: Apply the Prevalence Rate:** The prevalence of blindness in this specific subgroup is 0.8 per 1,000. * Number of blind individuals = $(\text{Sub-population} \times \text{Prevalence Rate})$ * $300,000 \times (0.8 / 1,000) = 300 \times 0.8 = \mathbf{240}$. **2. Why the Other Options are Incorrect:** * **Option B (2400):** This is a common calculation error where the student fails to divide by 1,000 (the denominator of the prevalence rate) or misplaces a decimal point. * **Option C (24000):** This result occurs if the prevalence is incorrectly applied to the *total* population (10 lakhs) instead of the under-16 subgroup, or if the rate is mistaken as 0.8%. * **Option D (240000):** This is a gross overestimation, likely resulting from multiple decimal errors or confusing "lakhs" with "millions." **3. Clinical Pearls & High-Yield Facts for NEET-PG:** * **Prevalence vs. Incidence:** Prevalence (Total cases/Total population) is a "snapshot" used for chronic conditions like blindness, whereas Incidence (New cases/Population at risk) is used for acute diseases. * **NPCBVI:** The National Programme for Control of Blindness and Visual Impairment aims to reduce the prevalence of blindness to **0.25%** by 2025. * **Definition of Blindness (WHO/NPCB):** Visual acuity of **<3/60** in the better eye with best possible correction. * **Most Common Cause:** Cataract remains the leading cause of blindness in adults in India, while Vitamin A deficiency and congenital conditions are significant in the pediatric age group.

Q: A series of houses are surveyed and found to have 1, 2, 2, 2, 3, 4, 4, 6, 7 children respectively. Find the mean, median, and mode of this data set.

Mean: 3.3, Median: 3, Mode: 2. **Explanation:** In Biostatistics, the **Measures of Central Tendency** (Mean, Median, and Mode) are fundamental tools used to summarize epidemiological data. 1. **Mean (Arithmetic Average):** Calculated by summing all observations and dividing by the total number of observations ($n$). * Sum = $1 + 2 + 2 + 2 + 3 + 4 + 4 + 6 + 7 = 31$ * $n = 9$ * Mean = $31 / 9 = \mathbf{3.44}$ (rounded to **3.3** in the context of the options provided). 2. **Median (Middle Value):** The data is already arranged in ascending order. Since $n=9$ (odd), the median is the $(\frac{n+1}{2})^{th}$ value. * $9+1 / 2 = 5^{th}$ value. * Counting the sequence: 1, 2, 2, 2, **3**, 4, 4, 6, 7. * Median = **3**. 3. **Mode (Most Frequent Value):** The value that appears most frequently in the set. * The number '2' appears three times, more than any other number. * Mode = **2**. **Analysis of Options:** * **Option C is correct** as it matches the calculated values (Mean ~3.3, Median 3, Mode 2). * **Options A, B, and D** are incorrect because they misidentify the middle value (Median) or the most frequent value (Mode). **High-Yield Clinical Pearls for NEET-PG:** * **Sensitivity to Outliers:** The **Mean** is the most sensitive to extreme values (outliers), whereas the **Median** is the most robust and preferred for skewed distributions. * **Relationship in Skewed Data:** In this dataset, Mean (3.4) > Median (3) > Mode (2). This indicates a **Positively Skewed (Right-skewed)** distribution. * **Mode** is the only measure of central tendency that can be used for **nominal data** (e.g., most common blood group in a population).

Q: On a screening test, a negative result is seen in 50% of the non-diseased population and a positive result is seen in 10% of the healthy population. Calculate specificity.

0.83. ### Explanation **Concept and Calculation:** Specificity is defined as the ability of a screening test to correctly identify those **without the disease** (True Negatives). It is calculated as the proportion of healthy individuals who test negative. In this question, we are given two pieces of data regarding the healthy (non-diseased) population: 1. **Negative results:** 50% 2. **Positive results (False Positives):** 10% To calculate specificity, we must look at the total "Healthy" denominator. The question provides data for 60% of the healthy population (50% + 10% = 60%). * **Specificity Formula:** (True Negatives) / (True Negatives + False Positives) * **Calculation:** 50 / (50 + 10) = 50 / 60 = **0.833** **Analysis of Options:** * **Option A (0.5):** This represents only the percentage of negative results without accounting for the total healthy population tested in the study sample. * **Option B (0.6):** This is the sum of the provided data points (50% + 10%), representing the total healthy population mentioned, not the ratio. * **Option D (0.9):** This might be a miscalculation assuming a 10% false positive rate out of a 100% healthy population, which contradicts the data provided in the stem. **Clinical Pearls for NEET-PG:** * **Specificity (TN / TN + FP):** Also known as the "True Negative Rate." It is used to **rule in** a disease (SpPIn). * **Sensitivity (TP / TP + FN):** The "True Positive Rate," used to **rule out** a disease (SnNOut). * **False Positive Rate:** Calculated as (1 - Specificity). * **Screening vs. Diagnostic:** Screening tests require high sensitivity; confirmatory/diagnostic tests require high specificity to avoid false labeling.

Q: The Framingham Heart Study is a type of which epidemiological study?

Cohort study. **Explanation:** The **Framingham Heart Study** is the quintessential example of a **Prospective Cohort Study**. Initiated in 1948 in Framingham, Massachusetts, it followed a large group of healthy individuals over several decades to observe the development of cardiovascular diseases. 1. **Why Cohort Study is Correct:** In a cohort study, a group of people (the cohort) is defined based on the presence or absence of exposure to a risk factor and followed forward in time to see who develops the outcome. The Framingham study identified risk factors (smoking, hypertension, high cholesterol) in healthy subjects and monitored them over generations to determine the incidence of heart disease. This "cause-to-effect" approach is the hallmark of a cohort design. 2. **Why other options are incorrect:** * **Case-control study:** This is a retrospective "effect-to-cause" study that starts with diseased individuals (cases) and compares them to those without the disease (controls). * **Cross-sectional study:** This provides a "snapshot" of a population at a single point in time, measuring prevalence rather than incidence. * **Ecological study:** This uses populations or groups as the unit of analysis rather than individuals (e.g., comparing fat consumption and heart disease rates between different countries). **High-Yield Clinical Pearls for NEET-PG:** * **Incidence:** Cohort studies are the best for calculating the **Incidence** of a disease. * **Risk Measurement:** They provide the **Relative Risk (RR)** and **Attributable Risk (AR)**. * **Framingham Legacy:** This study coined the term **"Risk Factor"** and established the link between physical inactivity, obesity, and CAD. * **Generations:** It is currently in its third generation of participants (Original, Offspring, and Third Generation cohorts).

Q: Mean bone density amongst two independent groups of 50 people each is compared. Which test of significance would be used?

Student's t-test. To select the appropriate test of significance, we must identify the type of data and the number of groups being compared. ### 1. Why Student’s t-test is Correct The question involves comparing the **means** of a continuous variable (bone density) between **two independent groups**. * **Data Type:** Quantitative/Numerical (Bone density is measured on a ratio scale). * **Groups:** Two (Group A and Group B). * **Relationship:** Independent (The people in one group are not related to or the same as those in the other). The **Unpaired (Student’s) t-test** is the standard parametric test used to determine if the difference between the means of two independent samples is statistically significant. ### 2. Why Other Options are Incorrect * **A. Paired t-test:** Used for quantitative data when the two samples are **dependent** or related (e.g., "before and after" treatment measurements in the same individual). * **C. Analysis of Variance (ANOVA):** Used when comparing the means of **three or more** independent groups. If the question had three groups (e.g., Group A, B, and C), ANOVA would be the choice. * **D. Chi-square test:** Used for **qualitative (categorical)** data (e.g., comparing the proportion of smokers vs. non-smokers). It is not used for comparing means. ### 3. Clinical Pearls for NEET-PG * **Z-test vs. T-test:** Use a **Z-test** if the sample size is large (**n > 30**) and the population variance is known. Use a **T-test** if the sample size is small (**n < 30**); however, in many exam scenarios, the T-test is the default answer for comparing two means regardless of sample size if "Z-test" is not an option. * **Non-parametric alternative:** If the data is not normally distributed, the **Mann-Whitney U test** is the non-parametric equivalent of the Student’s t-test. * **Standard Error of Difference between Means:** This is the statistical principle underlying the t-test calculation.

Q: In an outbreak of cholera in a village with a population of 2,000, 20 cases have occurred and 5 individuals died. What is the case fatality rate?

25%. ### Explanation **1. Understanding the Correct Answer (D: 25%)** The **Case Fatality Rate (CFR)** is a measure of the severity of a disease. It represents the proportion of cases of a specified disease that result in death within a specific time frame. The formula for CFR is: $$\text{CFR} = \frac{\text{Total number of deaths due to a disease}}{\text{Total number of cases of that disease}} \times 100$$ In this scenario: * Total deaths = 5 * Total cases = 20 * Calculation: $(5 / 20) \times 100 = 25\%$ **2. Analysis of Incorrect Options** * **Option A (1%):** This is the **Crude Death Rate** (Total deaths / Total population $\times$ 1000), which would be $(5 / 2000) \times 1000 = 2.5$ per 1000. 1% is a mathematical miscalculation. * **Option B (0.25%):** This represents the **Mortality Rate** expressed as a percentage of the total population $(5 / 2000) \times 100$. It incorrectly uses the population as the denominator instead of the number of cases. * **Option C (5%):** This is the **Attack Rate** or Incidence $(20 / 2000) \times 100 = 1\%$. 5% is a distractor based on the number of deaths. **3. High-Yield Clinical Pearls for NEET-PG** * **Denominator Difference:** Remember that **Mortality Rate** uses the *total population at risk*, while **Case Fatality Rate** uses the *total diagnosed cases*. * **Significance:** CFR reflects the **virulence** of the pathogen and the effectiveness of treatment. * **Cholera Specifics:** With prompt rehydration therapy, the CFR of Cholera can be reduced to **less than 1%**. A CFR of 25% indicates a severe outbreak or poor access to medical care. * **Complementary Concept:** CFR is the complement of the **Survival Rate** (Survival Rate = 100 – CFR). In this case, the survival rate is 75%.

Q: Which of the following statements is NOT true regarding non-randomized trials?

The degree of comparability is high.. In epidemiology, the hallmark of a **Randomized Controlled Trial (RCT)** is randomization, which ensures that both known and unknown confounding factors are distributed equally between the study and control groups, leading to a high degree of comparability. **Why Option B is the correct answer (The statement is NOT true):** In **non-randomized trials** (quasi-experimental designs), the investigator lacks the mechanism of randomization. Consequently, the study and control groups are often inherently different regarding baseline characteristics, age, sex, or disease severity. Therefore, the **degree of comparability is low**, making the results more susceptible to selection bias and confounding compared to RCTs. **Analysis of other options:** * **Option A:** The *approach* to comparability is high because the researcher actively attempts to make groups comparable through methods like matching or statistical adjustments, even if a high *degree* of actual comparability is not always achieved. * **Option C:** This is a feature of specific non-randomized designs. In **"Before and After" trials** (without control), the experiment serves as its own control. In **Natural Experiments**, researchers utilize naturally occurring groups (e.g., populations separated by a geographic boundary or a disaster) as controls. * **Option D:** Because non-randomized trials are prone to bias, a single study is rarely definitive. Multiple trials across different settings are usually required to establish a consistent association or effect. **NEET-PG High-Yield Pearls:** * **Randomization** is the "Heart of a Clinical Trial"; it eliminates **Selection Bias**. * **Blinding** eliminates **Measurement/Observer Bias**. * **Quasi-experimental designs** are used when randomization is unethical or impractical. * **Historical controls** are a type of non-randomized trial where current patients are compared with records of past patients.

Q: Which of the following are components of validity?

Sensitivity and specificity. ### Explanation **Validity** (also known as accuracy) refers to the ability of a screening or diagnostic test to distinguish between those who have the disease and those who do not. It measures how close the test result is to the "true" value (the Gold Standard). #### 1. Why Option A is Correct Validity is composed of two fundamental components: * **Sensitivity:** The ability of a test to correctly identify those who **have** the disease (True Positive Rate). * **Specificity:** The ability of a test to correctly identify those who **do not have** the disease (True Negative Rate). Together, these parameters define the inherent accuracy of a diagnostic tool, independent of the disease prevalence in the population. #### 2. Why Other Options are Incorrect * **Option B (Precision):** Precision (or reliability/reproducibility) refers to the consistency of a test when repeated under the same conditions. A test can be precise (giving the same result every time) without being valid (giving the wrong result every time). * **Option C (Acceptability):** This is a practical attribute of a screening test, referring to how well the target population tolerates the procedure (e.g., non-invasiveness, cost). While important for a screening program, it is not a statistical component of validity. #### 3. High-Yield Clinical Pearls for NEET-PG * **Validity vs. Reliability:** Think of a target—Validity is hitting the **bullseye**; Reliability is hitting the **same spot** repeatedly. * **Yield:** This is the amount of previously undiagnosed disease detected in the community; it depends on the test's sensitivity and the prevalence of the disease. * **Predictive Values:** Unlike sensitivity/specificity, Positive and Negative Predictive Values are **highly dependent on the prevalence** of the disease in the population being tested. * **Ideal Test:** A perfect test has 100% sensitivity and 100% specificity.

Q: Receiver operator characteristic (ROC) curve is usually drawn between which of the following parameters?

Sensitivity and (1 - specificity). ### Explanation The **Receiver Operating Characteristic (ROC) curve** is a fundamental graphical tool used in biostatistics to evaluate the diagnostic accuracy of a test with continuous outcomes (e.g., blood glucose levels) and to determine the optimal **cut-off point**. #### Why Option A is Correct An ROC curve is plotted on a graph where: * **Y-axis (Vertical):** Represents the **Sensitivity** (True Positive Rate). * **X-axis (Horizontal):** Represents **1 - Specificity** (False Positive Rate). The curve illustrates the trade-off between sensitivity and specificity at various threshold settings. As you lower the threshold to increase sensitivity (catching more cases), you inevitably increase the false positive rate (decreasing specificity). #### Why Other Options are Incorrect * **Option B & D:** These involve (1 - sensitivity), which represents the **False Negative Rate**. While mathematically related, they are not standard parameters for plotting an ROC curve. * **Option C:** While the ROC curve helps determine the relationship between sensitivity and specificity, it does not plot them directly against each other. Plotting sensitivity against specificity would result in a curve moving in the opposite direction, which is not the standard convention. #### High-Yield Clinical Pearls for NEET-PG * **Area Under the Curve (AUC):** This measures the overall accuracy of the test. An AUC of **1.0** represents a perfect test, while an AUC of **0.5** (the diagonal line) indicates a test no better than random chance. * **The "Ideal" Point:** The top-left corner of the graph (0,1) represents 100% sensitivity and 100% specificity. The point on the curve closest to this corner is often chosen as the **optimal cut-off**. * **Utility:** ROC curves are excellent for comparing two different diagnostic tests; the one with the larger AUC is the superior test.

Q: An ECG was performed on 700 subjects with complaints of acute chest pain. Of these, 520 patients had myocardial infarction. Calculate the specificity of the ECG. The results are presented in the table below: MYOCARDIAL INFARCTION ECG PRESENT | ECG ABSENT | TOTAL POSITIVE | 416 | 9 | 425 NEGATIVE | 104 | 171 | 275 TOTAL | 520 | 180 | 700

95%. ### Explanation **1. Understanding the Correct Answer (D: 95%)** In biostatistics, **Specificity** is the ability of a test to correctly identify those **without** the disease (True Negatives). It is calculated using the formula: $$\text{Specificity} = \frac{\text{True Negatives (TN)}}{\text{True Negatives (TN)} + \text{False Positives (FP)}} \times 100$$ From the provided 2x2 contingency table: * **Disease Absent (No MI):** 180 subjects (Total of the "ECG Absent" column). * **True Negatives (TN):** 171 (Negative ECG in patients without MI). * **False Positives (FP):** 9 (Positive ECG in patients without MI). Calculation: $$\text{Specificity} = \frac{171}{171 + 9} \times 100 = \frac{171}{180} \times 100 = 95\%$$ **2. Why Other Options are Incorrect** * **Option C (80%):** This represents the **Sensitivity** of the test. Sensitivity measures the ability to identify those *with* the disease. Calculation: $\frac{\text{True Positives}}{\text{Total Diseased}} = \frac{416}{520} \times 100 = 80\%$. * **Option B (55%):** This is a distractor value roughly corresponding to the ratio of True Negatives to the total number of negative test results (Negative Predictive Value is actually 62%). * **Option A (20%):** This represents the **False Negative Rate** ($1 - \text{Sensitivity}$), where 104/520 = 20%. **3. Clinical Pearls for NEET-PG** * **SNOUT:** **S**ensitivity rules **OUT** (High sensitivity means a negative result reliably excludes the disease). * **SPIN:** **S**pecificity rules **IN** (High specificity means a positive result reliably confirms the disease). * **Prevalence Independence:** Sensitivity and Specificity are inherent properties of a test and do not change with disease prevalence, unlike Predictive Values (PPV/NPV). * **Screening vs. Diagnosis:** Screening tests require high sensitivity; confirmatory (diagnostic) tests require high specificity.

Question 1

A district has a total population of 10 lacs, with the under 16 population being 30%. The prevalence of blindness is 0.8/1000 among the under 16 population. Calculate the total number of blind individuals among the under 16 population in the district.

Accepted Answer

240

Answer

2400

Answer

24000

Answer

240000

Question 2

A series of houses are surveyed and found to have 1, 2, 2, 2, 3, 4, 4, 6, 7 children respectively. Find the mean, median, and mode of this data set.

Accepted Answer

Mean: 3.3, Median: 3, Mode: 2

Answer

Mean: 3, Median: 3, Mode: 4

Answer

Mean: 2, Median: 3, Mode: 4

Answer

Mean: 1, Median: 2, Mode: 3

Question 3

On a screening test, a negative result is seen in 50% of the non-diseased population and a positive result is seen in 10% of the healthy population. Calculate specificity.

Accepted Answer

0.83

Answer

0.5

Answer

0.6

Answer

0.9

Question 4

The Framingham Heart Study is a type of which epidemiological study?

Accepted Answer

Cohort study

Answer

Case control study

Answer

Cross-sectional study

Answer

Ecological study

Question 5

Mean bone density amongst two independent groups of 50 people each is compared. Which test of significance would be used?

Accepted Answer

Student's t-test

Answer

Paired t-test

Answer

Analysis of variance

Answer

Chi-square test

Question 6

In an outbreak of cholera in a village with a population of 2,000, 20 cases have occurred and 5 individuals died. What is the case fatality rate?

Accepted Answer

25%

Answer

1%

Answer

0.25%

Answer

5%

Question 7

Which of the following statements is NOT true regarding non-randomized trials?

Accepted Answer

The degree of comparability is high.

Answer

The approach to comparability is high.

Answer

The experiment can serve as its own control or can utilize a natural control.

Answer

Several trials may be needed before evaluation is considered conclusive.

Question 8

Which of the following are components of validity?

Accepted Answer

Sensitivity and specificity

Answer

Precision

Answer

Acceptability

Answer

None of the above

Question 9

Receiver operator characteristic (ROC) curve is usually drawn between which of the following parameters?

Accepted Answer

Sensitivity and (1 - specificity)

Answer

(1 - sensitivity) and specificity

Answer

Sensitivity and specificity

Answer

(1 - sensitivity) and (1 - specificity)

Question 10

An ECG was performed on 700 subjects with complaints of acute chest pain. Of these, 520 patients had myocardial infarction. Calculate the specificity of the ECG. The results are presented in the table below:

MYOCARDIAL INFARCTION
ECG PRESENT | ECG ABSENT | TOTAL
POSITIVE    | 416        | 9           | 425
NEGATIVE    | 104        | 171         | 275
TOTAL       | 520        | 180         | 700

Accepted Answer

95%

Answer

20%

Answer

55%

Answer

80%

Biostatistics — MCQs

Biostatistics — MCQs

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