Assessment of small health risks based on exact sample sizes

Area of Science:

• Biostatistics
• Clinical Trial Design
• Epidemiology

Background:

• Accurate sample size calculation is essential for the statistical validity of clinical trials.
• Assessing the probability of rare events requires precise methodologies to avoid erroneous conclusions.

Purpose of the Study:

• To present exact sample sizes and critical numbers for rejecting a known low event probability in favor of a higher one.
• To validate these calculations using confidence interval characteristics for unknown true event probabilities.

Main Methods:

• Statistical analysis involving the calculation of exact sample sizes for hypothesis testing.
• Validation through the characteristics of confidence intervals for event probabilities.
• Demonstration of equivalence between relative risk tolerance and confidence interval upper limits.

Main Results:

• Exact sample sizes are provided for event probabilities ranging from 10^-2 to 10^-6, with increases of 1.5- to 50-fold.
• Calculations are validated for Type I (alpha) and Type II (beta) error levels of 0.05/0.10 and 0.10/0.05.
• Equivalence is established between the maximum tolerated relative risk and the upper confidence limit of the true event probability.

Conclusions:

• The presented tables offer a robust tool for determining necessary sample sizes in studies involving rare events.
• The findings facilitate planned risk reduction strategies and the evaluation of existing data sets.
• This work enhances the rigor of statistical inference in epidemiological and clinical research.