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Difficulty: MediumHypothesis Testing and Statistical Power

A state health department is planning a pragmatic clinical trial to evaluate a new smartphone-based behavioral intervention for patients with poorly controlled type 2 diabetes. The primary outcome will be the absolute change in hemoglobin A1c (HbA1c) after 6 months. The investigators initially aimed to achieve 80% power to detect a 0.6% difference in HbA1c between the intervention and standard care groups, utilizing a two-sided alpha of 0.05. During the planning phase, budget constraints necessitate a 20% reduction in the maximum allowable sample size.

To compensate for this loss of sample size, which of the following methodological adjustments would increase the statistical power of the study? (Select all that apply)

  1. Implement stricter inclusion criteria to create a more clinically homogenous study cohortAnswer
  2. B
    Broaden the target population to include patients with well-controlled diabetes, lowering the expected effect size
  3. C
    Modify the analysis plan to evaluate statistical significance at an alpha level of 0.01 instead of 0.05
  4. D
    Change the primary outcome from the continuous absolute change in HbA1c to a dichotomous outcome of achieving an HbA1c below 7.0%
  5. Redesign the intervention to target a patient subset in which the expected mean difference in HbA1c between groups is largerAnswer

Answer

Implementing stricter inclusion criteria to create a more clinically homogenous study cohort, and redesigning the intervention to target a patient subset in which the expected mean difference is larger.
Statistical power (the probability of correctly rejecting a false null hypothesis) is determined by four main factors: sample size, effect size, significance level (alpha), and the variance (standard deviation) of the outcome in the population. When budget constraints force a reduction in sample size, power decreases. To compensate, investigators must alter one of the other three parameters. Implementing stricter inclusion criteria makes the cohort more homogenous, which reduces the variance (spread) of the data. Lower variance narrows the standard error and increases power. Redesigning the intervention to target a subset with a larger expected difference increases the expected effect size. A larger effect size means the distribution curve of the alternative hypothesis is shifted further away from the null hypothesis curve, making a true difference easier to detect (increased power).

Step-by-Step Solution

1
Identify the primary relationship between sample size and statistical power.
A reduction in sample size directly decreases the statistical power of the study.
Smaller sample sizes lead to wider standard errors, making it more difficult to detect a true difference between groups.
2
Determine which variables can be manipulated to increase statistical power to offset the smaller sample size.
Statistical power can be increased by increasing the effect size, increasing the alpha level, or decreasing the population variance.
Power is a mathematical function of sample size, effect size, variance, and the predetermined significance level (alpha).
3
Evaluate each option based on its effect on power.
Increasing population homogeneity decreases variance (increases power). Increasing the expected difference increases effect size (increases power).
These adjustments mathematically narrow the distribution curves and shift them further apart, respectively, leading to a higher probability of correctly rejecting the null hypothesis.

Key Concept

Statistical power is directly proportional to sample size, effect size, and alpha level, and inversely proportional to population variance.
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Topics

Hypothesis Testing and Statistical Power

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