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A Bayesian approach to study design and analysis with type I error rate control for response variables of mixed types
Ethan M Alt1, Matthew A Psioda1, Joseph G Ibrahim1
1Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
Statistics in Medicine
|March 17, 2023
Summary
This study introduces Bayesian methods for analyzing mixed-type response variables in studies, enhancing hypothesis testing and sample size planning. The approach offers greater statistical power than traditional methods for complex clinical trial data.
Area of Science:
- Statistics
- Biostatistics
- Clinical Trial Design
Background:
- Studies often involve multiple response variables of mixed types (e.g., continuous and categorical).
- Analyzing such complex data requires robust statistical methods for hypothesis testing and study planning.
- Existing methods may lack power or adequate control for Type I error rates in multivariate settings.
Purpose of the Study:
- To develop Bayesian approaches for hypothesis testing and study planning with multiple mixed-type response variables and covariates.
- To provide a unified framework for analyzing correlated outcomes in clinical trials.
- To enhance statistical power and control Type I error rates in complex study designs.
Main Methods:
- Utilizing a Gaussian copula to model correlations between mixed-type response variables.
- Applying generalized linear models (GLMs) marginally for each response type.
- Implementing a fully Bayesian approach for joint posterior distribution inference.
- Developing a method to control Type I error rates under multiple testing.
Main Results:
- The proposed Bayesian method offers increased statistical power compared to marginal regression models with Bonferroni-Holm correction.
- The joint posterior distribution of parameters allows for comprehensive inference.
- Asymptotic convergence of posterior probabilities to a Gaussian copula distribution is demonstrated.
- A Bayesian approach for sample size determination (Probability of Success) is extended to mixed-type responses.
Conclusions:
- The developed Bayesian framework provides a powerful and flexible tool for analyzing studies with multiple mixed-type outcomes.
- This approach improves upon traditional methods for hypothesis testing and study planning in complex clinical trial settings.
- The method effectively controls Type I error rates and enhances statistical power, leading to more reliable study conclusions.
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