Biostatistics Practice Questions

Q: Calculate the mean and mode of the following set of values: 2, 2, 3, 4, 4, 4, 4, 5, 5, 7, 8, 8, 9.

Mean: 5, Mode: 4. **Explanation:** In Biostatistics, measures of central tendency are essential for summarizing medical data. This question tests the ability to calculate the **Mean** (arithmetic average) and identify the **Mode** (most frequent value). **1. Calculation of Mean:** The mean is calculated by the formula: $\text{Mean} = \frac{\sum X}{n}$ (Sum of all observations / Total number of observations). * Sum ($\sum X$): $2+2+3+4+4+4+4+5+5+7+8+8+9 = 65$ * Total count ($n$): $13$ * Mean: $65 / 13 = \mathbf{5}$ **2. Identification of Mode:** The mode is the value that appears most frequently in a data set. * Frequency of 2: (2 times) * Frequency of 3: (1 time) * **Frequency of 4: (4 times)** * Frequency of 5: (2 times) * Frequency of 7: (1 time) * Frequency of 8: (2 times) * Frequency of 9: (1 time) * Since 4 appears most often, the **Mode is 4**. **Analysis of Options:** * **Option B (Correct):** Correctly identifies Mean as 5 and Mode as 4. * **Option A:** Incorrect; 5 is the mean, not the mode. * **Option C:** Incorrect; 9 is the maximum value, not the mode. * **Option D:** Incorrect; 9 is the maximum value, not the mean. **High-Yield Clinical Pearls for NEET-PG:** * **Mean:** Most sensitive measure of central tendency but highly influenced by **outliers** (extreme values). * **Median:** The best measure of central tendency for **skewed data**. * **Mode:** The only measure that can be used for **nominal (qualitative) data** (e.g., most common blood group). * **Relationship:** In a perfectly symmetrical (Normal) distribution: **Mean = Median = Mode**.

Q: In a village of 1 lakh population, among 20,000 exposed to smoking, 200 developed cancer, and among 40,000 unexposed individuals, 40 developed cancer. What is the relative risk of smoking in the development of cancer?

10. ### Explanation **1. Understanding the Correct Answer (B: 10)** Relative Risk (RR) is the ratio of the incidence of a disease among the exposed group to the incidence of the disease among the unexposed group. It is the primary measure of association in **Cohort Studies**. * **Incidence among exposed ($I_e$):** $\frac{\text{Number of cases in exposed}}{\text{Total exposed}} = \frac{200}{20,000} = 0.01$ (or 10 per 1000) * **Incidence among unexposed ($I_u$):** $\frac{\text{Number of cases in unexposed}}{\text{Total unexposed}} = \frac{40}{40,000} = 0.001$ (or 1 per 1000) * **Relative Risk (RR):** $\frac{I_e}{I_u} = \frac{0.01}{0.001} = \mathbf{10}$ This means smokers are 10 times more likely to develop cancer compared to non-smokers. **2. Why Other Options are Incorrect** * **Option A (20):** This would occur if the incidence in the exposed group was doubled or the unexposed incidence was halved. It overestimates the association. * **Option C (5):** This would be the result if the number of cases in the exposed group was only 100 instead of 200. * **Option D (15):** This is a mathematical error, likely arising from subtracting incidences rather than dividing them (Attributable Risk calculation error). **3. NEET-PG High-Yield Pearls** * **Relative Risk (RR):** Measures the **strength of association**. RR > 1 indicates a positive association (risk factor); RR = 1 indicates no association. * **Attributable Risk (AR):** $(I_e - I_u) / I_e \times 100$. It indicates the amount of disease that can be prevented if the exposure is eliminated. * **Odds Ratio (OR):** Used in **Case-Control studies** as an estimate of RR. * **Incidence** can only be calculated in Cohort studies, not Case-Control studies.

Q: A city has a population of 10000 with 500 diabetic patients. A new diagnostic test gives true positive results in 350 patients and false positive results in 1900 patients. Which of the following is/are true regarding the test?

All of the above. To solve this problem, we must first organize the given data into a **2x2 contingency table**. * **Total Population (N):** 10,000 * **Disease Present (Diabetics):** 500 * **Disease Absent (Non-diabetics):** 10,000 - 500 = 9,500 * **True Positives (TP):** 350 * **False Positives (FP):** 1,900 ### Step-by-Step Calculation: 1. **Prevalence:** This is the proportion of the population that has the disease at a specific point in time. * Formula: (Total cases / Total population) × 100 * Calculation: (500 / 10,000) × 100 = **5%**. (**Option A is correct**) 2. **Sensitivity:** The ability of a test to correctly identify those with the disease (True Positive Rate). * Formula: [TP / (TP + FN)] × 100. Since (TP + FN) equals the total diseased (500): * Calculation: (350 / 500) × 100 = **70%**. (**Option B is correct**) 3. **Specificity:** The ability of a test to correctly identify those without the disease (True Negative Rate). * First, find True Negatives (TN): Total Non-diabetics - False Positives = 9,500 - 1,900 = 7,600. * Formula: (TN / Total Non-diabetics) × 100 * Calculation: (7,600 / 9,500) × 100 = **80%**. (**Option C is correct**) Since all individual calculations match the options provided, **Option D (All of the above)** is the correct answer. ### NEET-PG High-Yield Pearls: * **Sensitivity** is used for **Screening** (SnNout: Sensitivity rules OUT disease). * **Specificity** is used for **Confirmation** (SpPin: Specificity rules IN disease). * **Prevalence** affects Predictive Values (PPV/NPV) but does **not** change Sensitivity or Specificity, which are inherent properties of the test.

Q: Which of the following is NOT true about the normal response curve?

Standard deviation = 0. ### Explanation The **Normal Distribution Curve** (also known as the Gaussian distribution) is a fundamental concept in biostatistics used to describe how continuous biological variables (like height, blood pressure, or Hb levels) are distributed in a population. **Why Option C is the correct answer:** In a normal distribution, the **Standard Deviation (SD) cannot be zero**. The SD represents the "spread" or dispersion of data around the mean. If the SD were 0, every single observation in the dataset would be identical to the mean, resulting in a single vertical line rather than a curve. In a **Standard Normal Distribution**, the Mean is 0 and the **Standard Deviation is 1**. **Analysis of Incorrect Options:** * **Option A (Bell-shaped):** This is a defining characteristic. The curve is perfectly symmetrical around the center; the left half is a mirror image of the right half. * **Option B (Total area = 1):** In probability theory, the total area under the normal curve represents the total probability of all possible outcomes, which is always equal to 1 (or 100%). * **Option D (Mean, Median, and Mode coincide):** Because the curve is perfectly symmetrical and unimodal, the peak (Mode), the middle value (Median), and the average (Mean) all fall at the exact same central point. **High-Yield Clinical Pearls for NEET-PG:** * **Empirical Rule (68-95-99.7 Rule):** * Mean ± 1 SD covers **68.3%** of values. * Mean ± 2 SD covers **95.4%** of values. * Mean ± 3 SD covers **99.7%** of values. * **Limits of Normality:** In clinical medicine, the "normal range" for a lab test is typically defined as **Mean ± 2 SD** (encompassing 95% of the healthy population). * **Skewness:** If the tail is longer on the right, it is **Positively Skewed** (Mean > Median > Mode). If the tail is longer on the left, it is **Negatively Skewed** (Mode > Median > Mean).

Q: If the probability of full recovery following polio is 0.3 and the probability of partial recovery is 0.4, what is the total probability of full or partial recovery following polio?

0.7. ### Explanation This question tests the application of the **Addition Rule of Probability** in biostatistics. **1. Why Option B is Correct:** In probability theory, when two events are **mutually exclusive** (meaning they cannot occur at the same time), the probability of either event occurring is the sum of their individual probabilities. * **Event A (Full Recovery):** $P(A) = 0.3$ * **Event B (Partial Recovery):** $P(B) = 0.4$ Since a patient cannot simultaneously have a "full recovery" and a "partial recovery" from the same episode of polio, these are mutually exclusive events. To find the probability of "Full **OR** Partial Recovery," we use the formula: $$P(A \cup B) = P(A) + P(B)$$ $$0.3 + 0.4 = \mathbf{0.7}$$ **2. Why Other Options are Incorrect:** * **Option A (0.12):** This is the result of the **Multiplication Rule** ($0.3 \times 0.4$). This rule is used for independent events occurring simultaneously (Event A **AND** Event B), which is not applicable here. * **Option C (1.2):** Probability can never exceed **1.0**. Any value greater than 1 is mathematically impossible in biostatistics. * **Option D (0.1):** This is the result of subtraction ($0.4 - 0.3$), which has no relevance to the "OR" logic required by the question. **3. NEET-PG Clinical Pearls:** * **Mutually Exclusive Events:** Use the **Addition Rule** (Sum). * **Independent Events:** Use the **Multiplication Rule** (Product). * **Complementary Event:** The probability of "No Recovery" in this scenario would be $1 - 0.7 = 0.3$. * **Polio Fact:** In clinical practice, approximately 1% of polio infections lead to irreversible paralysis (usually asymmetric), while the majority are asymptomatic or mild.

Q: As compared to a routine case-control study, a nested case-control study avoids problems related to which of the following in study design?

Temporal association. ### Explanation **1. Why Temporal Association is the Correct Answer:** In a **routine case-control study**, data on exposure is collected retrospectively (after the disease has occurred). This often leads to ambiguity regarding whether the exposure preceded the disease, a problem known as lack of **temporal association**. A **nested case-control study** is conducted within a pre-existing prospective cohort study. Because the exposure data and biological samples are collected at the **baseline** (before any subjects develop the disease), we can definitively prove that the exposure occurred before the outcome. This eliminates the "chicken or egg" dilemma inherent in traditional retrospective designs. **2. Analysis of Incorrect Options:** * **B. Confounding bias:** While nested designs can control for some confounders through matching, they do not inherently "avoid" confounding any more than a routine case-control study. Confounding is addressed via randomization or multivariate analysis. * **C. Need for long follow-up:** This is actually a *disadvantage* or a requirement of nested studies. Since they are "nested" within a cohort, they require waiting for the disease to develop over time. * **D. Randomization:** This is a feature of Interventional Studies (RCTs). Neither routine nor nested case-control studies involve randomization. **3. High-Yield Pearls for NEET-PG:** * **Definition:** A nested case-control study is a "case-control study within a cohort study." * **Efficiency:** It is more **cost-effective** and time-efficient than a full cohort study because only the samples from cases and selected controls are analyzed. * **Bias Reduction:** It significantly reduces **Recall Bias** because exposure data was recorded when the subjects were still healthy. * **Key Advantage:** It combines the **temporal sequence** of a cohort study with the **efficiency** of a case-control study.

Q: Which one of the following statements regarding pre-post clinical trials is most appropriate?

They use the patient as his or her own control. ### Explanation **Concept Overview** A **Pre-Post Clinical Trial** (also known as a "Before-and-After" study) is a type of quasi-experimental design where measurements are taken from the same group of participants both before and after an intervention. **Why Option C is Correct** The defining feature of this study design is that **the patient serves as his or her own control**. By comparing the baseline status (pre-intervention) to the outcome (post-intervention) in the same individual, researchers can minimize the impact of "between-subject" variability (confounding factors like genetics, age, or socioeconomic status), as these remain constant within the individual. **Analysis of Incorrect Options** * **Option A:** While many pre-post studies are non-randomized, they **can be randomized** (e.g., a Crossover Trial is a specialized randomized pre-post design where the order of treatments is randomized). * **Option B:** They are **not ideal for mortality studies**. Mortality is a "one-time" terminal event; once a patient dies, you cannot measure a "post-intervention" state or return them to baseline. These studies are better suited for chronic, stable conditions (e.g., hypertension, asthma). * **Option D:** They are actually **harder to interpret** than parallel trials. They are susceptible to "temporal effects" (natural recovery over time), "regression to the mean," and "carry-over effects" where the first phase influences the second. **High-Yield Pearls for NEET-PG** * **Crossover Design:** A specific type of pre-post trial that includes a **Washout Period** to eliminate the carry-over effect of the first drug. * **Advantage:** Requires a **smaller sample size** than parallel trials to achieve the same statistical power because individual variation is reduced. * **Limitation:** Not suitable for diseases that are cured by the intervention or for conditions that fluctuate rapidly.

Q: A survey was conducted on 7,000 drivers using mobile phones and found that 700 met with an accident. In the same period, out of 3,000 drivers not using mobile phones, 30 met with an accident. Calculate the relative risk?

10. ### Explanation **1. Understanding the Correct Answer (B: 10)** Relative Risk (RR), also known as Risk Ratio, is the ratio of the incidence of a disease (or event) among an exposed group to the incidence among a non-exposed group. It is a key measure of association in **Cohort Studies**. * **Incidence in Exposed ($I_e$):** Drivers using mobile phones. $I_e = \frac{\text{Accidents}}{\text{Total Exposed}} = \frac{700}{7,000} = 0.1$ (or 10%) * **Incidence in Non-exposed ($I_ne$):** Drivers not using mobile phones. $I_ne = \frac{\text{Accidents}}{\text{Total Non-exposed}} = \frac{30}{3,000} = 0.01$ (or 1%) * **Relative Risk (RR):** $\frac{I_e}{I_ne} = \frac{0.1}{0.01} = \mathbf{10}$ This means drivers using mobile phones are 10 times more likely to meet with an accident compared to those who do not. **2. Why Other Options are Incorrect** * **Option A (5):** This would result if the incidence in the exposed group was only 0.05 (5%). * **Option C (3.99):** This is a distractor often seen in questions involving complex Odds Ratio calculations, but it is mathematically irrelevant here. * **Option D (8.33):** This might be reached if a student incorrectly uses the "Attributable Risk" formula or makes a calculation error in the denominator. **3. High-Yield Clinical Pearls for NEET-PG** * **RR = 1:** No association between exposure and outcome. * **RR > 1:** Positive association (Risk factor). * **RR < 1:** Negative association (Protective factor, e.g., vaccines). * **Study Design:** RR is calculated from **Cohort Studies** (Prospective), whereas Odds Ratio (OR) is typically calculated from **Case-Control Studies** (Retrospective). * **Attributable Risk (AR):** $I_e - I_ne$. In this case, $0.1 - 0.01 = 0.09$ (90 per 1000), representing the amount of disease prevented if the exposure is removed.

Q: What does the reliability of a screening test NOT mean?

Validity. ### Explanation In biostatistics, **Reliability** and **Validity** are two distinct pillars used to evaluate the quality of a screening or diagnostic test. **Why "Validity" is the correct answer:** Reliability refers to the **consistency** of a test—the ability of a method to yield the same results upon repeated measurements under the same conditions. **Validity**, on the other hand, refers to **accuracy**—the ability of a test to measure what it is actually intended to measure (i.e., how close the result is to the "True" value or Gold Standard). A test can be highly reliable (giving the same wrong result every time) without being valid. **Analysis of Incorrect Options:** * **A. Reproducibility:** This is a synonym for reliability. It refers to the ability of different observers to get the same results using the same test. * **B. Repeatability:** This is another synonym for reliability. It refers to the consistency of results when the same observer performs the test multiple times on the same subject. * **D. Precision:** In medical statistics, precision is the degree to which repeated measurements show the same results. It is the technical term for reliability. **High-Yield Clinical Pearls for NEET-PG:** 1. **Reliability = Precision = Consistency.** It is influenced by **Random Error**. 2. **Validity = Accuracy.** It is influenced by **Systematic Error (Bias)**. 3. **Components of Validity:** Sensitivity and Specificity are the primary measures of a test's validity. 4. **The Bullseye Analogy:** * Hits clustered together but far from the center = Reliable but not Valid. * Hits scattered but averaging at the center = Valid but not Reliable. * Hits clustered tightly in the center = Both Reliable and Valid.

Question 1

Calculate the mean and mode of the following set of values: 2, 2, 3, 4, 4, 4, 4, 5, 5, 7, 8, 8, 9.

Accepted Answer

Mean: 5, Mode: 4

Answer

Mean: 4, Mode: 5

Answer

Mean: 5, Mode: 9

Answer

Mean: 9, Mode: 5

Question 2

In a village of 1 lakh population, among 20,000 exposed to smoking, 200 developed cancer, and among 40,000 unexposed individuals, 40 developed cancer. What is the relative risk of smoking in the development of cancer?

Accepted Answer

10

Answer

20

Answer

5

Answer

15

Question 3

A city has a population of 10000 with 500 diabetic patients. A new diagnostic test gives true positive results in 350 patients and false positive results in 1900 patients. Which of the following is/are true regarding the test?

Accepted Answer

All of the above

Answer

Prevalence is 5%

Answer

Sensitivity is 70%

Answer

Specificity is 80%

Question 4

Which of the following is NOT true about the normal response curve?

Accepted Answer

Standard deviation = 0

Answer

Bell shaped

Answer

Total area of curve = 1

Answer

Mean, mode, and median coincide

Question 5

If the probability of full recovery following polio is 0.3 and the probability of partial recovery is 0.4, what is the total probability of full or partial recovery following polio?

Accepted Answer

0.7

Answer

0.12

Answer

1.2

Answer

0.1

Question 6

As compared to a routine case-control study, a nested case-control study avoids problems related to which of the following in study design?

Accepted Answer

Temporal association

Answer

Confounding bias

Answer

Need for long follow-up

Answer

Randomization

Question 7

Which one of the following statements regarding pre-post clinical trials is most appropriate?

Accepted Answer

They use the patient as his or her own control

Answer

They cannot be randomized

Answer

They are useful in studies involving mortality

Answer

They are usually easier to interpret than the comparable parallel clinical trial

Question 8

A survey was conducted on 7,000 drivers using mobile phones and found that 700 met with an accident. In the same period, out of 3,000 drivers not using mobile phones, 30 met with an accident. Calculate the relative risk?

Accepted Answer

10

Answer

5

Answer

3.99

Answer

8.339

Question 9

To test the association between a risk factor and a disease, which of the following represents the weakest study design?

Accepted Answer

Ecological study

Answer

Case-control study

Answer

Cohort study

Answer

Cross-sectional study

Question 10

What does the reliability of a screening test NOT mean?

Accepted Answer

Validity

Answer

Reproducibility

Answer

Repeatability

Answer

Precision

Biostatistics — MCQs

Biostatistics — MCQs

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