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Related Concept Videos

One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and...
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Related Experiment Video

Updated: Oct 2, 2025

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Bayesian sample size determination in a three-arm non-inferiority trial with binary endpoints.

Niansheng Tang1, Bin Yu1

  • 1Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming, P. R. China.

Journal of Biopharmaceutical Statistics
|February 25, 2022
PubMed
Summary

This study introduces two Bayesian methods for sample size determination in three-arm non-inferiority trials with binary outcomes. These approaches offer alternatives to frequentist methods that rely on large sample sizes.

Keywords:
Bayes factorposterior variance criterionpower priorsample size determinationthree-arm non-inferiority trial

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Bayesian Statistics

Background:

  • Three-arm non-inferiority trials with binary endpoints are crucial for assessing treatment efficacy and safety.
  • Existing frequentist methods for sample size calculation often depend on large sample approximations.
  • There is a need for robust statistical methods that are less reliant on large sample sizes.

Purpose of the Study:

  • To propose and evaluate two fully Bayesian approaches for determining sample size in three-arm non-inferiority trials.
  • To compare the performance of the proposed Bayesian methods against each other and existing approaches.
  • To provide practical guidance for sample size determination in clinical trial design.

Main Methods:

  • Development of two Bayesian sample size determination methods: posterior variance approach and Bayes factor approach.
  • Utilizing simulation studies to assess the performance and accuracy of the proposed Bayesian methods.
  • Application of the methodologies to a real-world clinical trial example.

Main Results:

  • The Bayes factor approach generally requires smaller sample sizes compared to the posterior variance approach.
  • Incorporating historical data can significantly reduce the required sample size.
  • Simultaneous hypothesis testing necessitates a larger sample size than non-inferiority testing.
  • Hyperparameter selection critically influences the calculated sample size.

Conclusions:

  • Bayesian methods provide effective alternatives for sample size determination in three-arm non-inferiority trials, especially when large sample sizes are not feasible.
  • The Bayes factor approach is recommended for practical applications, particularly when prior clinical trial data is available.
  • The posterior variance criterion offers a straightforward method for initial sample size estimations.