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Difficulty: MediumHypothesis Testing and Statistical Power

A quality improvement task force at a regional medical center is designing a prospective trial to evaluate the effectiveness of a new automated sepsis alert system. The primary outcome is the time from triage to the administration of broad-spectrum antibiotics, measured as a continuous variable in minutes.

The investigators conduct a preliminary power analysis and find that their proposed study design achieves a statistical power of only 0.550.55 for detecting a 1515-minute difference in administration times between the new and standard alert systems. The principal investigator requests modifications to the study design or analysis plan to achieve a target power of 0.800.80 before initiating the trial.

Which of the following proposals will appropriately increase the statistical power of this trial? (Select all that apply)

  1. Extending the planned data collection period from 66 months to 1212 months to increase the total number of patient encounters analyzedAnswer
  2. Standardizing the electronic time-tracking methodology across all clinical departments to decrease the variance in the reported administration timesAnswer
  3. C
    Converting the continuous primary outcome into a categorical variable (e.g., <60<60 minutes vs ≥60\geq 60 minutes) and analyzing it using a chi-square test
  4. D
    Stratifying the primary analysis into multiple small age-based subgroups to account for potential effect modification
  5. E
    Pausing the study to perform a root cause analysis (RCA) to prospectively identify and eliminate potential protocol failure modes

Answer

Extending the planned data collection period and standardizing the electronic time-tracking methodology will both appropriately increase the statistical power of the trial.
Statistical power (1−β1 - \beta) is primarily driven by four factors: sample size, variance, effect size, and the chosen significance level (α\alpha). Extending the data collection period increases the total sample size (nn). Standardizing the tracking methodology decreases the measurement variance (σ2\sigma^2). Because power increases as sample size grows and as variance shrinks, both of these methodological changes will successfully increase the statistical power of the trial.

Step-by-Step Solution

1
Identify the current methodological problem.
The study is underpowered at 0.550.55, meaning there is a 45%45\% chance of committing a Type II error (failing to detect a true difference).
Recognizing the risk of Type II error establishes the need to optimize the mathematical parameters that govern statistical power.
2
Recall the variables that determine statistical power.
Statistical power (1−β1 - \beta) is increased by: higher sample size (nn), larger effect size, higher significance level (α\alpha), and smaller variance (σ2\sigma^2).
These are the core components of the power equation for continuous outcomes.
3
Evaluate the proposed modifications against the determinants of power.
Extending data collection increases nn. Standardizing tracking decreases σ2\sigma^2. Both mathematically increase power. Categorizing data, stratifying into smaller groups, or performing an RCA do not increase power.
Only modifications that favorably alter the mathematical determinants of power will solve the investigator's problem.

Key Concept

Statistical power is the probability of correctly rejecting the null hypothesis when a true difference exists. Power is directly increased by increasing the sample size (nn), increasing the expected effect size, accepting a higher Type I error rate (α\alpha), or decreasing the variance (σ2\sigma^2) of the outcome measure.
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Topics

Hypothesis Testing and Statistical Power

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