Sample Size Calculation for Bioequivalence Tests : A powerTOST Tutorial With Downloadable R Code

Introduction (Downloadable Code)

Sample size calculation is a fundamental aspect of research design, influencing the reliability and validity of study outcomes. Researchers often inquire about the methods and factors involved in this process, which include parameters like the expected effect size, significance level, statistical power, and variability, expressed as the coefficient of variation. This paper aims to explore the methodology of sample size calculation using the two one-sided tests (TOST) procedures implemented in the R programming language. Additionally, it compares these calculations with those performed using the PowerTOST package, highlighting their efficacy and distinctions.

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Methods

The TOST procedure, adapted from “Sample Size Estimation for (Bio)equivalence Testing Between Two Treatments,” forms the basis of our study’s methodology. In bioequivalence studies, hypotheses are structured to test whether the ratio (θ) of pharmacokinetic parameters between a test drug (T) and a reference drug (R) falls within predefined bounds.

Results

Bioequivalence studies are pivotal in pharmaceutical research and drug development, aiming to ensure that a test drug exhibits pharmacokinetic parameters within 80% to 125% of those of a reference drug. Initial calculations using our method revealed that sample sizes tend to be higher near the lower limit (0.8) of the T/R ratio, where significant differences are expected between the drugs. As the T/R ratio approaches 1, indicating closer similarity, sample sizes decrease due to reduced variability and narrower confidence intervals required for equivalence.

Conversely, as the T/R ratio extends towards the upper limit (1.25), sample sizes increase again. This adjustment accommodates wider bioequivalence limits, necessitating larger samples to maintain adequate statistical power. Higher power levels require larger sample sizes to enhance the study’s ability to detect differences or equivalence, ensuring robust and reliable study outcomes.

Visualizations of these relationships through adjusted sample size calculations provide researchers with insights into the interplay between T/R ratio, power, and sample size. This approach aids in effective study planning, ensuring adherence to regulatory bioequivalence criteria while achieving statistically sound conclusions.

Comparison with PowerTOST

To validate our approach, we compared the results obtained from our BESS function with those generated by sampleN.tost() from the PowerTOST package. Remarkably, both methods yielded nearly identical sample sizes, affirming the accuracy and reliability of our computational methodology. sampleN.tost(), like our BESS function, employs sophisticated statistical calculations based on assumptions about variability and effect size to determine sample size requirements.

This consistency underscores the suitability of our approach in ensuring adequate statistical power to detect meaningful differences or similarities between test and reference drugs in bioequivalence studies. By demonstrating comparable results, we highlight the robustness and practical utility of our computational method for sample size determination.

Key Findings and Methodological Insights

1. Methodology Overview: We adopted the TOST procedure to evaluate bioequivalence between a test drug (T) and a reference drug (R). This involved setting hypotheses to test whether the ratio (θ) of pharmacokinetic parameters falls within predefined equivalence bounds, leveraging non-central t distributions and critical values derived from quantile functions.
2. Factors Influencing Sample Size: Our calculations highlighted several critical factors influencing sample size determination:
   • T/R Ratio: Variations in the ratio significantly impact sample size, with higher ratios (closer to 1) requiring fewer participants due to expected similarity between drugs.
   • Statistical Power and Significance Level: Desired power levels and significance thresholds (alpha) dictate the sensitivity of studies to detect differences or equivalence, influencing sample size requirements.
   • Coefficient of Variation (CV): Reflecting the variability in measurements, CV plays a crucial role in determining the precision and confidence intervals of study outcomes.
3. Comparison with PowerTOST: To validate our approach, we compared sample sizes computed using our BESS function with those derived from sampleN.tost() in the PowerTOST package. Encouragingly, both methods produced highly consistent results, underscoring the robustness and reliability of our computational methodology. This consistency supports the suitability of manual implementation in R for sample size determination in bioequivalence studies.

Implications for Research and Practice

1. Study Design and Planning: Effective planning of bioequivalence studies hinges on accurate sample size determination. Our findings emphasize the importance of considering T/R ratios, power requirements, and regulatory criteria to optimize study designs and ensure meaningful results.
2. Regulatory Compliance: Adherence to bioequivalence criteria (e.g., 80% to 125% T/R ratio) is critical for regulatory approval of generic drugs. Our methodological approach provides researchers and pharmaceutical developers with a reliable toolset to meet these stringent criteria and facilitate drug approval processes.
3. Future Directions: Future research could explore further refinements in sample size calculations, considering adaptive designs or Bayesian approaches to enhance efficiency and flexibility in bioequivalence studies. Additionally, expanding the application of computational tools like the BESS function to diverse therapeutic areas and study contexts could broaden its utility and impact.

In conclusion, our study contributes valuable insights into sample size calculation methodologies for bioequivalence studies, validating the efficacy of manual implementation in R and comparing it favourably with established packages like PowerTOST. By enhancing methodological transparency and reliability, our approach supports rigorous and scientifically sound decision-making in pharmaceutical research and development.