Biostatistics Practice Questions

Q: If the annual growth rate of a population is 1.2%, in how many years is the population likely to get doubled?

47-50 years. ### Explanation **1. Why the Correct Answer is Right** The time required for a population to double in size is calculated using the **Rule of 70**. This is a simplified mathematical formula used in demography and biostatistics to estimate doubling time based on a constant annual growth rate. The formula is: **Doubling Time (T) = 70 / Annual Growth Rate (r)** Applying the values from the question: * Growth Rate (r) = 1.2% * Doubling Time = 70 / 1.2 = **58.33 years** Looking at the options provided, **Option D (47-50 years)** is the closest approximation to the calculated value. In many standard textbooks (like Park’s Preventive and Social Medicine), the "Rule of 70" or "Rule of 69" is used to explain that a 1% growth rate doubles a population in 70 years, while a 2% rate doubles it in 35 years. At 1.2%, the value falls between 50 and 60 years. **2. Why Other Options are Wrong** * **Option A (18-20 years):** This would require a growth rate of approximately 3.5% to 3.8% ($70/18 \approx 3.8$). * **Option B (20-23 years):** This would require a growth rate of approximately 3% ($70/23 \approx 3$). * **Option C (28-35 years):** This corresponds to a growth rate of 2% to 2.5% ($70/2 \approx 35$). **3. Clinical Pearls & High-Yield Facts for NEET-PG** * **Rule of 70 vs. 69:** While 70 is easier for mental calculation, some statisticians use 69.3 (natural log of 2) for higher precision. * **India’s Context:** According to the 2011 Census, India's annual exponential growth rate was approximately 1.64%. * **Demographic Gap:** The difference between the Crude Birth Rate (CBR) and Crude Death Rate (CDR) determines the natural increase in population. * **Vital Index:** (Births / Deaths) × 100. It measures the population's biological success.

Q: Statistical power of a trial is equal to:

1 - beta (Type II error rate). ### Explanation **1. Understanding the Correct Answer (B):** The **Power of a Study** is the probability that a test will correctly reject a null hypothesis when it is false (i.e., the ability of a study to detect a true difference or effect). * **Type II Error ($\beta$):** Occurs when we fail to reject a null hypothesis that is actually false (a "false negative"). * **Power ($1 - \beta$):** Represents the probability of avoiding a Type II error. If $\beta$ is 0.20 (20%), the power is 0.80 (80%), meaning there is an 80% chance of detecting a statistically significant difference if one truly exists. **2. Analysis of Incorrect Options:** * **Option A ($1 + \alpha$):** This is a mathematically invalid expression in biostatistics. * **Option C ($\alpha + \beta$):** This represents the sum of the probabilities of making a Type I and Type II error, which does not define any specific statistical parameter. * **Option D ($\alpha / \beta$):** This ratio is not used to define power. However, the relationship between $\alpha$ and $\beta$ is inverse; decreasing the risk of a Type I error typically increases the risk of a Type II error for a fixed sample size. **3. NEET-PG High-Yield Pearls:** * **Type I Error ($\alpha$):** "False Positive" – Rejecting the null hypothesis when it is true. (Fixed by the p-value, usually 0.05). * **Type II Error ($\beta$):** "False Negative" – Accepting the null hypothesis when it is false. * **Determinants of Power:** Power increases with **increased sample size**, increased effect size, and increased $\alpha$ level. * **Standard Values:** In most clinical trials, the minimum acceptable power is **80%**. * **Confidence Level:** Defined as **$1 - \alpha$** (the probability of correctly accepting the null hypothesis when it is true).

Q: Which of the following is NOT a distinct feature of a case-control study method?

The unit of study is a group rather than an individual.. **Explanation** In epidemiology, a **Case-Control Study** is an observational, analytical study used to determine the association between an exposure and an outcome. **Why Option B is the correct answer:** The unit of study in a case-control study is the **individual**. Researchers identify individuals with the disease (cases) and individuals without the disease (controls) to compare their past exposures. If the unit of study were a **group or population**, it would be classified as an **Ecological Study**. This is a common "trap" question in NEET-PG regarding levels of organization in study designs. **Analysis of other options:** * **Option A:** This is a hallmark of case-control studies. They are **retrospective**; both the exposure and the outcome have already occurred by the time the investigator begins the study. * **Option C:** Case-control studies proceed from **"Effect to Cause."** You start with the effect (the disease) and look backward in time to find the cause (the risk factor/exposure). * **Option D:** The presence of a **comparison group** (controls) is what makes this an "analytical" study rather than a "descriptive" one. Controls provide the baseline frequency of exposure to support or refute the statistical association. **High-Yield Clinical Pearls for NEET-PG:** * **Measure of Association:** Case-control studies use the **Odds Ratio (OR)**. They cannot calculate Incidence or Relative Risk (RR). * **Best for:** Rare diseases or diseases with long latent periods. * **Main Bias:** **Recall Bias** is the most common disadvantage, as cases may remember past exposures more vividly than controls. * **Starting Point:** Always starts with the **Disease**.

Q: In a case-control study on smoking and lung cancer, 33 out of 35 lung cancer patients were smokers. Of 82 controls, 27 were non-smokers. Calculate the odds ratio.

8.1. ### **Explanation** The **Odds Ratio (OR)** is the standard measure of association used in **Case-Control studies**. It represents the ratio of the odds of exposure among cases to the odds of exposure among controls. #### **Step 1: Construct the 2x2 Contingency Table** To calculate OR, we must first organize the data into a standard table: | | Lung Cancer (Cases) | No Lung Cancer (Controls) | | :--- | :---: | :---: | | **Smokers (Exposed)** | **a** = 33 | **b** = 55 (82 total - 27 non-smokers) | | **Non-Smokers (Non-exposed)** | **c** = 2 (35 total - 33 smokers) | **d** = 27 | #### **Step 2: Apply the Formula** The formula for Odds Ratio is: **(a × d) / (b × c)** * **OR** = (33 × 27) / (55 × 2) * **OR** = 891 / 110 = **8.1** An OR of 8.1 indicates that the odds of lung cancer are 8.1 times higher among smokers compared to non-smokers. --- #### **Analysis of Incorrect Options** * **Option A (0.21):** This value is less than 1, which would imply smoking is a "protective factor" against lung cancer. * **Option C (4.1) & D (2.1):** These are mathematical errors resulting from misplacing values in the 2x2 table (e.g., using the total number of subjects instead of the non-exposed cells). --- #### **High-Yield Clinical Pearls for NEET-PG** 1. **Study Design:** Odds Ratio is used for Case-Control studies (retrospective), while **Relative Risk (RR)** is used for Cohort studies (prospective). 2. **Interpretation:** * OR > 1: Positive association (Risk factor). * OR = 1: No association. * OR < 1: Negative association (Protective factor). 3. **Rare Disease Assumption:** If the disease is rare, the Odds Ratio provides a good approximation of the Relative Risk. 4. **Cross-Product Ratio:** OR is also known as the "Cross-product ratio" because it is the product of the diagonals (ad/bc).

Q: Based on the provided graph, what is the order of least margin of error?

3>2>1. ***3>2>1*** - **Margin of error** is inversely related to **sample size** - larger samples have smaller margins of error and narrower distributions. - From the graph, curve **3** has the widest distribution (largest margin of error), curve **2** is medium width, and curve **1** is narrowest (smallest margin of error). *3>1>2* - This incorrectly places curve **1** as having a larger margin of error than curve **2**. - The graph clearly shows curve **1** has the **narrowest distribution**, indicating the smallest margin of error, not medium. *1>3>2* - This reverses the correct order by suggesting curve **1** has the largest margin of error. - Curve **1** actually shows the **narrowest distribution** with the smallest margin of error, contradicting this ordering. *1=2=3* - This suggests all three curves have **equal margins of error**, which contradicts the visual evidence. - The graph clearly shows **different distribution widths**, with curve 1 being narrowest, curve 2 medium, and curve 3 widest.

Q: Which of the following is not an accepted method of randomization?

Odd/even day hospital admission. **Explanation:** Randomization is the "heart" of a Randomized Controlled Trial (RCT). Its primary purpose is to eliminate **selection bias** and ensure that both known and unknown confounding factors are distributed equally between the study and control groups. **Why Option B is correct:** Odd/even day hospital admission is a method of **Quasi-randomization** (systematic allocation). It is not considered true randomization because the allocation sequence is **predictable**. If a researcher or clinician knows that a patient arriving on a Monday (odd day) will receive the intervention, they might subconsciously delay or expedite a patient’s admission to influence which group they join. This violates the principle of concealment and introduces selection bias. **Why other options are incorrect:** * **A, C, and D:** Computer-generated sequences, the Lottery method, and Random Number Tables (like Tippett’s table) are all validated methods of **True Randomization**. They ensure that every participant has an equal, non-zero chance of being assigned to any group, and the sequence remains unpredictable. **High-Yield Clinical Pearls for NEET-PG:** * **Gold Standard:** The RCT is the gold standard study design to establish **causality**. * **Allocation Concealment:** This is the procedure used to prevent selection bias by keeping investigators unaware of the upcoming assignment. It is done *before* the intervention starts. * **Blinding:** This is done *after* allocation to reduce observer and participant bias. * **Types of Randomization:** 1. **Simple:** Like a coin toss or random table. 2. **Stratified:** Used when a specific confounding variable (e.g., age, gender) needs to be balanced. 3. **Block:** Ensures equal sample sizes in both groups throughout the study.

Q: Which of the following statements about a cohort study is false?

It is always prospective.. In epidemiology, a **Cohort Study** is an observational analytical study that starts with a group of people (a cohort) free of the disease, classified by their exposure status, and followed over time to observe the development of the outcome. ### Why Option D is the Correct Answer (The False Statement) While most cohort studies are prospective, they are **not always prospective**. There are three types of cohort studies: 1. **Prospective Cohort:** Starts in the present and follows subjects into the future. 2. **Retrospective (Historical) Cohort:** The investigator goes back in time using records (e.g., occupational or medical records) to identify exposure and follows the cohort up to the present or a point in the past to determine the outcome. 3. **Ambispective Cohort:** Combines both retrospective and prospective elements. ### Why the Other Options are Incorrect (True Statements) * **A. Incidence can be measured:** Since cohort studies follow a disease-free population over time to see who develops the condition, they are the "gold standard" for calculating **Incidence** and **Relative Risk (RR)**. * **B. Used to study chronic diseases:** Cohort studies are excellent for studying chronic conditions (e.g., Framingham Heart Study) because they allow for the assessment of multiple outcomes from a single exposure. * **C. It is expensive:** Because they require large sample sizes and long follow-up periods, cohort studies are significantly more expensive and time-consuming than case-control studies. ### NEET-PG High-Yield Pearls * **Directionality:** Cohort studies always move from **Cause to Effect**. * **Key Metric:** **Relative Risk (RR)** and **Attributable Risk (AR)** are derived from cohort studies. * **Best for:** Rare exposures (e.g., a specific chemical leak). * **Main Bias:** **Attrition Bias** (loss to follow-up) is the most common challenge in cohort studies.

Question 1

Select the true statement regarding correlation.

Accepted Answer

In moderately positive correlation, a rise in one variable leads to a rise in the other.

Answer

In perfectly negative correlation, a rise in one variable leads to a proportional rise in the other.

Answer

In moderately negative correlation, a fall in one variable leads to a proportional fall in the other.

Answer

In perfectly positive correlation, a rise in one variable leads to a proportional fall in the other.

Question 2

If the annual growth rate of a population is 1.2%, in how many years is the population likely to get doubled?

Accepted Answer

47-50 years

Answer

18-20 years

Answer

20-23 years

Answer

28-35 years

Question 3

Statistical power of a trial is equal to:

Accepted Answer

1 - beta (Type II error rate)

Answer

1 + alpha (Type I error rate)

Answer

alpha + beta

Answer

alpha / beta

Question 4

Which of the following is NOT a distinct feature of a case-control study method?

Accepted Answer

The unit of study is a group rather than an individual.

Answer

Both exposure and outcome have occurred before the start of the study.

Answer

The study proceeds backward from effect to cause.

Answer

It uses a control or comparison group to support or refute an inference.

Question 5

A population pyramid is an example of which type of graphical representation?

Accepted Answer

Bar chart

Answer

Histogram

Answer

Frequency polygon

Answer

Pie chart

Question 6

In a case-control study on smoking and lung cancer, 33 out of 35 lung cancer patients were smokers. Of 82 controls, 27 were non-smokers. Calculate the odds ratio.

Accepted Answer

8.1

Answer

0.21

Answer

4.1

Answer

2.1

Question 7

Based on the provided graph, what is the order of least margin of error?

Accepted Answer

3>2>1

Answer

3>1>2

Answer

1>3>2

Answer

1=2=3

Question 8

Which of the following is not an accepted method of randomization?

Accepted Answer

Odd/even day hospital admission

Answer

Computer drawn randomization

Answer

Lottery

Answer

Random number table

Question 9

A diagnostic test for a particular disease has a sensitivity of 0.90 and a specificity of 0.90. The prevalence of the disease in the population is 10%. What is the probability that a person who tests positive actually has the disease?

Accepted Answer

81%

Answer

90%

Answer

50%

Answer

91%

Question 10

Which of the following statements about a cohort study is false?

Accepted Answer

It is always prospective.

Answer

Incidence can be measured.

Answer

It is used to study chronic diseases.

Answer

It is expensive.

Biostatistics — MCQs

Biostatistics — MCQs

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