A pharmacovigilance team is evaluating the time to adverse event onset (measured in discre… — USMLE Step 3

A pharmacovigilance team is evaluating the time to adverse event onset (measured in discrete whole days) for a newly approved biologic medication in a post-marketing surveillance registry of $10,000$ patients. The initial dataset has a heavily right-skewed distribution, and the team calculates the following summary statistics:

- Mean: $45.5$ days
- Median: $14$ days
- Mode: $7$ days (accounting for $9\%$ of patients)
- Standard Deviation: $52.3$ days
- 75th percentile: $30$ days

For a standardized regulatory safety report, the team creates a revised dataset by recoding any time to onset exceeding $60$ days as exactly $60$ days. A review of the initial data reveals that $15\%$ of the patients had a time to onset strictly greater than $60$ days.

Which of the following best describes the expected changes to the mode, median, mean, and standard deviation in the revised dataset compared to the initial dataset?

The mode will increase; the mean and standard deviation will decrease; the median will remain unchangedAnswer
B
The mean and standard deviation will decrease; the mode and median will remain unchanged
C
The mean, median, and standard deviation will decrease; the mode will remain unchanged
D
The median and mode will increase; the mean and standard deviation will decrease
E
The mean, median, standard deviation, and mode will all decrease

Answer

The mode will increase; the mean and standard deviation will decrease; the median will remain unchanged

In the revised dataset, all extreme high values (greater than 60 days) are reduced to exactly 60 days. This lowers the total sum of the dataset, causing the mean to decrease. Truncating the long right tail reduces the overall variance and dispersion, causing the standard deviation to decrease. The median remains unchanged because it represents the 50th percentile (14 days); recoding only the top 15% of the dataset does not alter the values or relative ordering of the bottom 85%, leaving the middle value completely unaffected. Finally, the mode increases. Originally, the most frequent value was 7 days (9% of patients). By recoding all patients with onset times > 60 days (15% of the cohort) to exactly 60 days, the new frequency of '60 days' becomes at least 15%, surpassing the old mode. Thus, the mode shifts from 7 to 60, meaning the mode increases.

Step-by-Step Solution

Evaluate the effect of capping on the mean and standard deviation.

Both the mean and standard deviation will decrease.

Converting all values > 60 days to exactly 60 days removes the long right tail. This lowers the sum of all values (decreasing the mean) and reduces the overall dispersion of the data (decreasing the standard deviation).

Determine the effect on the median.

The median remains unchanged.

The median is the 50th percentile (

14

days). Capping only affects the top

15\%

of the data (the 85th to 100th percentiles). The ordering and values of the bottom

85\%

are untouched, so the 50th percentile stays exactly the same.

Calculate the impact on the mode.

The mode will increase from

7

60

The original mode was

7

days, representing

9\%

of patients. After recoding, the

15\%

of patients who originally had times > 60 days now all have a time of exactly

60

days. Since

15\% > 9\%

, the new most frequent value (mode) is

60

Key Concept

Impact of data transformation (capping/truncation) on descriptive statistics in skewed distributions.

Estimated Time:2m 0s

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