A quality improvement committee at a large tertiary care center is evaluating the impact o… — USMLE Step 3

A quality improvement committee at a large tertiary care center is evaluating the impact of a novel electronic health record (EHR) sepsis alert on the time to administration of broad-spectrum antibiotics.

Prior to implementing the alert (pre-implementation cohort), the time to antibiotic administration was right-skewed. Descriptive statistics for this cohort were:
- Mean: $150$ minutes
- Median: $120$ minutes
- Standard deviation (SD): $110$ minutes
- Interquartile range (IQR): $80$ minutes

Following the implementation of the alert (post-implementation cohort), a follow-up analysis of $1,000$ patients reveals a drastically altered distribution:
- $80\%$ of patients trigger the automated order set and receive antibiotics rapidly, with all these patients receiving the medication between $40$ and $50$ minutes.
- The remaining $20\%$ of patients have atypical presentations that bypass the alert. Due to over-reliance on the new system, their antibiotic administration is severely delayed, with their times distributed uniformly between $600$ and $800$ minutes.

Compared to the pre-implementation cohort, which of the following combinations correctly describes the expected changes in the descriptive statistics for the post-implementation cohort?

A
Mean increases; Median decreases; SD increases; IQR increases
B
Mean decreases; Median decreases; SD increases; IQR decreases
Mean increases; Median decreases; SD increases; IQR decreasesCevap
D
Mean decreases; Median decreases; SD decreases; IQR decreases
E
Mean increases; Median increases; SD increases; IQR increases

Cevap

Mean increases; Median decreases; SD increases; IQR decreases

The combination stating 'Mean increases; Median decreases; SD increases; IQR decreases' is correct because it accurately reflects the mathematical behavior of robust versus non-robust statistics. The median and IQR measure the center and spread of the majority of the data, both of which became highly concentrated at a lower value (40-50 minutes). The mean and standard deviation incorporate the extreme outliers (600-800 minutes), which mathematically pull the average higher and massively inflate the variance despite applying to only 20% of the cohort.

Adım Adım Çözüm

Determine the new mean by calculating the weighted average of the two post-implementation groups.

Mean = (

0.80 \times 45

) + (

0.20 \times 700

) =

36 + 140 = 176

minutes. The mean increases from

150

The mean is highly sensitive to extreme values. The

20\%

of patients delayed up to

700

minutes mathematically outweigh the

80\%

reduction.

Determine the new median by identifying the 50th percentile of the new distribution.

Since

80\%

of the data is between

40

and

50

minutes, the 50th percentile falls in this range. The median decreases from

120

<50

The median is a robust statistic that is resistant to extreme outliers and only reflects rank order.

Determine the new interquartile range (IQR) by finding the 25th (Q1) and 75th (Q3) percentiles.

Both Q1 and Q3 fall within the

40

50

minute window. The maximum possible IQR is

10

minutes. The IQR decreases from

80

IQR only measures the spread of the middle

50\%

of the data. The extreme

20\%

tail does not affect Q1 or Q3.

Determine the new standard deviation (SD) by evaluating the impact of the extreme right tail.

The squared deviations of the

20\%

of patients at

600

800

minutes from the new mean of

176

will massively inflate the variance. The SD increases.

Unlike the IQR, the SD incorporates every value in the dataset and squares their distances from the mean, making it extremely sensitive to outliers.

Anahtar Kavram

Robustness of descriptive statistics: The median and IQR are highly resistant to extreme outliers, whereas the mean and standard deviation are highly sensitive to them.

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