Robustness of the shrinkage estimator for the relative potency in the combination of multivariate bioassays

ABSTRACT

This article investigates the robustness of the shrinkage Bayesian estimator for the relative potency parameter in the combinations of multivariate bioassays proposed in Chen et al. (1999), which incorporated prior information on the model parameters based on Jeffreys’ rules. This investigation is carried out for the families of t-distribution and Cauchy-distribution based on the characteristics of bioassay theory since the t-distribution approaches the normal distribution which is the most commonly used distribution in the applications of bioassay as the degrees of freedom increases and the t-distribution approaches the Cauchy-distribution as the degrees of freedom approaches 1 which is also an important distribution in bioassay. A real data is used to illustrate the application of this investigation. This analysis further supports the application of the shrinkage Bayesian estimator to the theory of bioassay along with the empirical Bayesian estimator.

Keywords:

• Bayesian analysis
• Noninformative prior
• Posterior likelihood function
• Posterior mode
• Relative potency

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62F15
• Secondary: 62H10

Acknowledgments

I am grateful for the useful suggestions and comments from the two reviewers, Professor Balakrishnan and Dr. Nicole Trabold, which greatly improved the draft manuscript.