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Difficulty: HardHypothesis Testing and Statistical Power

A biostatistics consulting group at an academic medical center is evaluating the statistical analysis plans of several proposed clinical studies. The consultants must identify the primary statistical consequence of specific trial design choices. Match each methodological decision to its most direct impact on hypothesis testing parameters.

  • Switching from an independent-groups design to a matched-pairs design with the same total number of participantsIncreases statistical power by reducing the unexplained variance (standard error)
  • Conducting multiple sequential interim analyses for efficacy without adjusting the nominal significance levelSubstantially inflates the overall cumulative Type I error rate (α\alpha) of the study
  • Reducing the anticipated effect size (minimally clinically important difference) used in the planning phase while keeping sample size fixedIncreases the probability of a Type II error (β\beta) and reduces statistical power
  • Applying a Bonferroni adjustment for analyzing multiple secondary endpointsMaintains the family-wise α\alpha but increases the risk of false-negative findings for individual tests

Answer

1) Matched-pairs design -> Increases power by reducing variance. 2) Multiple interim analyses -> Inflates overall Type I error rate. 3) Reducing effect size -> Increases Type II error and reduces power. 4) Bonferroni adjustment -> Maintains family-wise alpha but increases false-negatives.
Each methodological decision manipulates the delicate balance between α\alpha (false positives), β\beta (false negatives), and variance. Matched pairs isolate the intervention effect by stripping away between-subject noise (variance), boosting power. Interim analyses act as multiple 'rolls of the dice,' which compounds the risk of a false positive if unadjusted. Shrinking the target effect size without adding more participants means the study lacks the statistical 'resolution' to detect the difference, raising Type II errors. Finally, Bonferroni corrections strictly control false positives but create a highly conservative threshold that drives up false negatives.

Step-by-Step Solution

1
Evaluate the effect of a matched-pairs design.
It controls for confounding inter-subject baseline variables.
By controlling for baseline variability, the standard error decreases, which mathematically increases the test statistic and statistical power.
2
Assess the impact of unadjusted multiple interim analyses.
It leads to repeated significance testing.
Repeatedly testing data without an alpha-spending function geometrically increases the probability of finding a false positive (inflating the Type I error rate).
3
Determine the consequence of reducing the expected effect size without altering sample size.
The trial is attempting to detect a smaller difference with the same mathematical leverage.
Detecting a smaller effect size requires a larger sample. Keeping the sample size fixed drops the study's power, increasing the risk of a Type II error (false negative).
4
Analyze the trade-off of a Bonferroni adjustment.
It sets a much stricter threshold (α/n\alpha/n) for statistical significance.
While it successfully prevents the inflation of family-wise Type I errors, the stricter threshold inherently makes it harder to detect true differences, lowering power and raising Type II error risk.

Key Concept

Hypothesis Testing and Statistical Power
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Topics

Hypothesis Testing and Statistical Power

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