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Difficulty: MediumHypothesis Testing and Statistical Power

A primary care network is planning a randomized controlled trial to evaluate a novel pharmacist-led telehealth coaching program. The goal is to reduce systolic blood pressure among adult patients with uncontrolled hypertension. The primary outcome is the mean change in systolic blood pressure at 6 months. Preliminary calculations indicate the study will have 70% power to detect a 4 mmHg4\text{ mmHg} difference between the intervention and standard care groups, assuming a standard deviation of 12 mmHg12\text{ mmHg} and a two-sided significance level (α\alpha) of 0.05. The trial steering committee dictates that the statistical power must be at least 80% before recruitment begins. Which of the following modifications to the trial design or statistical plan would individually increase the statistical power of the study? (Select all that apply)

  1. Enrolling a larger total number of participants by extending the recruitment periodAnswer
  2. Modifying the inclusion criteria to select a patient cohort with a lower expected standard deviation in baseline blood pressureAnswer
  3. C
    Converting the continuous blood pressure outcome into categorical data (e.g., controlled vs. uncontrolled) to analyze via a Chi-square test
  4. D
    Stratifying the study sample into multiple demographic subgroups to analyze for effect modification without increasing the total sample size
  5. E
    Using an enrollment screening tool with a higher positive predictive value to increase the baseline prevalence of severe hypertension in the sample

Answer

The trial's statistical power can be increased by enrolling a larger total number of participants and by modifying inclusion criteria to select a cohort with a lower expected standard deviation.
Statistical power is the likelihood that a study will detect an effect when there is an effect there to be detected. It mathematically depends on four primary factors: sample size, effect size, variance (standard deviation), and the significance level (α\alpha). Expanding the recruitment period to enroll more patients directly increases the sample size. Modifying inclusion criteria to select a cohort with a lower baseline standard deviation decreases the variance in the data. Both of these modifications make it statistically easier to detect a true 4 mmHg4\text{ mmHg} difference, thereby increasing the study's power.

Step-by-Step Solution

1
Identify the components that determine statistical power in a continuous outcome trial.
Power (1−β1 - \beta) is influenced by sample size (nn), effect size (Δ\Delta), significance level (α\alpha), and standard deviation (σ\sigma).
Understanding the mathematical relationships between these variables is necessary to determine which modifications will increase power.
2
Evaluate the effect of changing sample size.
Increasing the number of participants (nn) narrows the standard error of the mean, making it easier to detect a true difference.
Larger sample sizes yield a higher probability of rejecting a false null hypothesis.
3
Evaluate the effect of changing the standard deviation.
Decreasing the standard deviation (σ\sigma) by selecting a more homogenous cohort reduces data spread, which increases power.
Less noise in the data makes the true signal (effect size) easier to detect.
4
Analyze the incorrect design modifications.
Converting continuous data to categorical data, stratifying without increasing sample size, and focusing on predictive value all fail to increase or actively decrease statistical power.
These actions either discard information, reduce available sample size per group, or affect parameters unrelated to the calculation of statistical power.

Key Concept

Statistical power (1−β1 - \beta) can be increased by increasing the sample size, increasing the effect size, increasing the alpha level, or decreasing the variance (standard deviation) of the outcome.
Estimated Time:1m 30s
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Topics

Hypothesis Testing and Statistical Power

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