Biostatistics Practice Questions

Q: What is the relative risk of developing tuberculosis among tobacco users as per the information given below?

2.67. **2.67** - To calculate the **relative risk**, we first need to determine the incidence Proportion (IP) of TB in tobacco users and non-tobacco users. - **IP for tobacco users** = (Number of tobacco users with TB) / (Total number of tobacco users) = 40/120 = 0.33. - **IP for non-tobacco users** = (Number of non-tobacco users with TB) / (Total number of non-tobacco users) = 10/80 = 0.125. - **Relative Risk** (RR) = IP of exposed / IP of unexposed = 0.33 / 0.125 = 2.67. *3.90* - This value would be obtained if there was an error in calculating the incidence proportions or the division. - For example, if the calculation for the incidence proportion of non-tobacco users was incorrect. *0.48* - A relative risk value less than 1 would indicate that tobacco use is a **protective factor** against tuberculosis, meaning tobacco users are less likely to develop TB than non-users, which is not the case here. - This value might be obtained by inverting the relative risk calculation (**IP unexposed / IP exposed**). *1.33* - This value is significantly lower than the correct relative risk and would likely result from a miscalculation in the number of cases or total populations for either group. - For instance, if the incidence rate for tobacco users was underestimated or for non-tobacco users was overestimated.

Q: Which one of the following experiments/trials is a part of non-randomized trials?

Uncontrolled trial. ***Uncontrolled trial*** - An **uncontrolled trial** is a single-arm study where all participants receive the same intervention without any control group for comparison. - These are classified as **non-randomized trials** because there is no random allocation between groups (as there is only one group). - Common in early phase drug studies or when ethical considerations prevent withholding treatment. *Before and after comparison studies* - While these are **non-randomized designs**, they are typically classified as **quasi-experimental studies** rather than trials in strict epidemiological terminology. - They measure outcomes in the same population before and after an intervention without random allocation. *Natural experiment* - A **natural experiment** is an **observational study design**, not an experimental trial. - Researchers observe the effects of naturally occurring events or policy changes without any deliberate intervention or random assignment by the investigator. - Example: Comparing health outcomes before and after a public health policy change. *Risk factor trial* - This term is **not standard epidemiological terminology** for trial classification. - Trials are typically classified by design (randomized vs non-randomized) and control status (controlled vs uncontrolled), not by whether they study risk factors. - Most risk factor research uses observational cohort or case-control studies, not trials.

Q: A study was conducted to evaluate the effectiveness of a new antidiabetic drug. The fasting blood glucose levels (mg/dL) of 5 diabetic patients after 3 months of treatment were: 110, 94, 102, 98, 96. Consider the following statements about this data: 1. The range of blood glucose levels is 16 mg/dL 2. The median blood glucose level is 98 mg/dL 3. The standard deviation is √10 mg/dL

1 and 2 only. ***1 and 2 only*** - **Statement 1 is correct**: The **range** is calculated as maximum value minus minimum value. Ordering the data: 94, 96, 98, 102, 110 mg/dL. Range = 110 - 94 = **16 mg/dL** ✓ - **Statement 2 is correct**: For the ordered dataset (94, 96, 98, 102, 110), with n=5 observations, the **median** is the middle (3rd) value = **98 mg/dL** ✓ - **Statement 3 is incorrect**: To calculate standard deviation: - Mean (x̄) = (110 + 94 + 102 + 98 + 96) / 5 = **100 mg/dL** - Deviations from mean: 10, -6, 2, -2, -4 - Sum of squared deviations: 100 + 36 + 4 + 4 + 16 = **160** - Sample variance = 160 / (n-1) = 160 / 4 = **40** - Standard deviation = √40 = **2√10 ≈ 6.32 mg/dL** (NOT √10 ≈ 3.16 mg/dL) ✗ *1, 2 and 3* - This would only be correct if all three statements were true. However, **statement 3 is incorrect** as the actual standard deviation is √40 (or 2√10), not √10. *1 and 3 only* - This is incorrect because **statement 3 is false** (SD = √40, not √10), while statement 2 is actually correct. *2 and 3 only* - This is incorrect because **statement 1 is correct** (range is indeed 16 mg/dL) and **statement 3 is incorrect** (SD ≠ √10).

Q: A new test was developed for detection of COVID-19. What is the sensitivity of the test as per the information provided above?

37.5%. ***37.5%*** - **Sensitivity** is calculated as the number of **true positives** divided by the sum of true positives and false negatives (i.e., total number of individuals with the disease). - From the table, **True Positives (Test Positive and Disease +)** = 60, and **False Negatives (Test Negative and Disease +)** = 100. So, sensitivity = 60 / (60 + 100) = 60 / 160 = 0.375 or 37.5%. *97%* - This value is incorrect. It might be confused with **Negative Predictive Value (NPV)**, which is the probability that subjects with a negative test truly don't have the disease (1800/1900 ≈ 0.947 or 94.7%), but it's not 97%. - It does not correctly represent the calculation for sensitivity as described above. *20.5%* - This value is incorrect. It does not correspond to any standard epidemiological measure of test performance based on the provided data. - This percentage might arise from an incorrect division or addition of values from the table. *60%* - This value is incorrect. While 60 **true positives** are present, sensitivity requires dividing this by the total number of diseased individuals, not just any other total. - This could be confused with the ratio of true positives to total positive tests (Positive Predictive Value), which would be 60/100, resulting in 60%, but this is not sensitivity.

Q: What is the Standardized Mortality Ratio (SMR) for the hazardous industry workers (as compared to national population)?

120. ***120*** - To calculate the Standardized Mortality Ratio (SMR), we first need to calculate the **expected deaths** for the hazardous industry workers based on the national death rates. - The formula for expected deaths in each age group is: (National death rate / 1000) × Number of hazardous industry workers - For age group 25-34: Expected deaths = (2.0 / 1000) × 3000 = **6** - For age group 35-44: Expected deaths = (3.5 / 1000) × 2000 = **7** - For age group 45-54: Expected deaths = (6.0 / 1000) × 2000 = **12** - **Total expected deaths** = 6 + 7 + 12 = **25** - **Total observed deaths** = 8 + 9 + 13 = **30** - **SMR formula**: (Total Observed Deaths / Total Expected Deaths) × 100 - **SMR = (30 / 25) × 100 = 1.2 × 100 = 120** - This indicates that the hazardous industry workers have a **20% higher mortality rate** compared to the national population after age-standardization. *100* - An SMR of 100 would indicate that the observed mortality equals the expected mortality (no difference from the national average). - However, the observed deaths (30) exceed the expected deaths (25), so the SMR must be greater than 100. - This option represents the null value where there is no excess mortality. *110* - This option underestimates the actual SMR calculated from the data. - An SMR of 110 would suggest only a 10% excess mortality, which does not match the observed-to-expected ratio of 30:25. - The calculation clearly shows a ratio of 1.2, not 1.1. *130* - This option overestimates the SMR. - An SMR of 130 would require observed deaths to be 1.3 times the expected deaths (32.5 deaths expected for 30 observed). - The actual ratio is 30/25 = 1.2, making this value too high.

Q: Consider the following: 1. Standard deviation 2. Range 3. Mode 4. Median Among the above, which is/are the measure/measures of dispersion?

1 and 2 only. ***1 and 2 only*** - The **standard deviation** quantifies the average amount of variability or dispersion around the mean, representing how spread out the data points are. - The **range** is the difference between the maximum and minimum values in a dataset, providing a simple measure of the total spread. *3 and 4 only* - The **mode** represents the most frequently occurring value in a dataset, which is a measure of central tendency, not dispersion. - The **median** is the middle value when data is ordered, also a measure of central tendency. *1 only* - While **standard deviation** is a measure of dispersion, this option incorrectly excludes the **range**, which also quantifies data spread. - Both **standard deviation** and **range** are fundamental measures used to describe the variability within a dataset. *1, 2, 3 and 4* - This option incorrectly includes the **mode** and **median**, which are measures of **central tendency**, not dispersion. - Measures of dispersion specifically describe the **spread or variability** of data, whereas central tendency measures describe the center of the data.

Q: In a normal curve, the area between one standard deviation on either side of the mean will include:

Approximately 68% of the values. ***Approximately 68% of the values*** - In a **normal distribution** (bell curve), approximately **68% of data points** fall within one standard deviation ($\pm1\sigma$) from the mean. - This is a fundamental property of the **empirical rule** (or 68-95-99.7 rule) in statistics. *70 – 85% of the values* - This range is too broad and does not accurately reflect the specific percentage for **one standard deviation**. - While it overlaps with the correct value, it is not the precise percentage associated with $\pm1\sigma$. *95% of the values* - This percentage refers to the data included within **two standard deviations** ($\pm2\sigma$) from the mean in a normal distribution, not one. - The **empirical rule** states that approximately 95% of data falls within two standard deviations. *Less than 50% of the values* - This is incorrect, as the range of **one standard deviation** on either side of the mean covers more than half of the data. - The mean itself divides the data into two 50% halves, so incorporating any deviation around it will cover more than 50%.

Question 1

What is the relative risk of developing tuberculosis among tobacco users as per the information given below?

Accepted Answer

2.67

Answer

3.90

Answer

0.48

Answer

1.33

Question 2

Which one of the following experiments/trials is a part of non-randomized trials?

Accepted Answer

Uncontrolled trial

Answer

Before and after comparison studies

Answer

Natural experiment

Answer

Risk factor trial

Question 3

Which one of the following statements regarding predictive value of a positive test is true?

Accepted Answer

It tells the probability that a patient with positive test has the disease in question

Answer

It does not tell about diagnostic power of test

Answer

The more prevalent the disease, the less accurate the test is

Answer

It tells the probability that a patient with positive test does not have the disease in question

Question 4

A study was conducted to evaluate the effectiveness of a new antidiabetic drug. The fasting blood glucose levels (mg/dL) of 5 diabetic patients after 3 months of treatment were: 110, 94, 102, 98, 96.

Consider the following statements about this data:

1. The range of blood glucose levels is 16 mg/dL
2. The median blood glucose level is 98 mg/dL  
3. The standard deviation is √10 mg/dL

Accepted Answer

1 and 2 only

Answer

1, 2 and 3

Answer

1 and 3 only

Answer

2 and 3 only

Question 5

A new test was developed for detection of COVID-19. What is the sensitivity of the test as per the information provided above?

Accepted Answer

37.5%

Answer

97%

Answer

20.5%

Answer

60%

Question 6

What is the Standardized Mortality Ratio (SMR) for the hazardous industry workers (as compared to national population)?

Accepted Answer

120

Answer

110

Answer

100

Answer

130

Question 7

Consider the following:

1. Standard deviation
2. Range
3. Mode
4. Median

Among the above, which is/are the measure/measures of dispersion?

Accepted Answer

1 and 2 only

Answer

3 and 4 only

Answer

1 only

Answer

1, 2, 3 and 4

Question 8

With reference to historical cohort study, which of the following statements is not correct?

Accepted Answer

Control subjects are selected from the current population without exposure.

Answer

Duration of study is shorter as compared to current cohort study.

Answer

Experience of cohort is assessed from existing records.

Answer

Outcomes have occurred before the start of the investigation.

Question 9

Specificity of a test is =

Accepted Answer

(True negatives X 100) / (True negatives + False positives) %

Answer

(True positives X 100) / (True negatives + False positives) %

Answer

(True positives X 100) / (True positives + False negatives) %

Answer

(True negatives X 100) / (True positives + True negatives) %

Question 10

In a normal curve, the area between one standard deviation on either side of the mean will include:

Accepted Answer

Approximately 68% of the values

Answer

70 – 85% of the values

Answer

95% of the values

Answer

Less than 50% of the values

Biostatistics — MCQs

Biostatistics — MCQs

On this page

Practice by Chapter

Want unlimited practice?