An internal medicine physician is critically reviewing a recently published multicenter co… — USMLE Step 3

An internal medicine physician is critically reviewing a recently published multicenter cohort study evaluating a novel serum biomarker, interleukin-6 (IL-6) receptor level, as a predictor of $30$ -day mortality in patients with septic shock. The study enrolled $2,500$ patients across various intensive care units. In the baseline characteristics table, the authors describe the distribution of the initial IL-6 receptor levels (measured in $pg/mL$ ). They note that the data are highly asymmetrical: the vast majority of patients have very low circulating levels of the biomarker, but a small, distinct subset of patients presents with exceedingly high levels. Based on the characteristics of this continuous variable, which of the following statements regarding its distribution and appropriate descriptive statistics is most accurate?

The distribution is positively skewed with the mean greater than the median, and the median and interquartile range are the most appropriate summary measures.Answer
B
The distribution is positively skewed with the mean greater than the median, and the mean and standard deviation are the most appropriate summary measures.
C
The distribution is negatively skewed with the mean less than the median, and the median and interquartile range are the most appropriate summary measures.
D
The distribution is negatively skewed with the mean less than the median, and the mean and standard deviation are the most appropriate summary measures.
E
The serum biomarker represents an ordinal data type, and frequencies and proportions are the most appropriate summary measures.

Answer

The distribution is positively skewed with the mean greater than the median, and the median and interquartile range are the most appropriate summary measures.

The correct answer accurately identifies the distribution as positively (right) skewed. In this scenario, the statement that the 'vast majority of patients have very low... levels' and a 'small, distinct subset... presents with exceedingly high levels' clearly describes a long tail to the right. Because the mean is heavily influenced by extreme values, these exceptionally high biomarker levels pull the mean to the right, making the mean greater than the median. When continuous data are asymmetrical, traditional parametric measures (mean and standard deviation) become distorted and misleading. Therefore, robust non-parametric measures—specifically, the median for central tendency and the interquartile range (IQR) for dispersion—are the most appropriate statistical summaries.

Step-by-Step Solution

Analyze the description of the data distribution provided in the stem.

The vast majority of values are low, with a small number of extremely high values.

This indicates the direction of the tail. A long tail extending toward the higher values means the data is skewed to the right (positively skewed).

Determine the relationship between the measures of central tendency for this distribution.

In a right-skewed distribution, the mean is pulled strongly in the direction of the long tail of extreme values.

Because the extreme high values inflate the arithmetic average, the mean becomes greater than the median (and the mode).

Select the most appropriate descriptive statistics for this type of data.

The median and interquartile range (IQR) should be used.

Parametric measures like the mean and standard deviation are easily distorted by outliers and skewed distributions. Non-parametric measures (median, IQR) are robust and provide a more accurate representation of the central tendency and dispersion.

Key Concept

In positively (right) skewed distributions, extreme high values pull the mean toward the long tail, resulting in the mean being greater than the median. Skewed continuous variables should be summarized using the median and interquartile range (IQR) because these measures are resistant to outliers.

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