Empirical Bayes Estimation for Combinations of Multivariate Bioassays

Abstract

This article presents a new empirical Bayes estimator (EBE) and a shrinkage estimator for determining the relative potency from several multivariate bioassays by incorporating prior information on the model parameters based on Jeffreys' rules. The EBE can account for any extra variability among the bioassays, and if this extra variability is 0, then the EBE reduces to the maximum likelihood estimator for combinations of multivariate bioassays. The shrinkage estimator turns out to be a compromise of the prior information and the estimator from each multivariate bioassay, with the weights depending on the prior variance.

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

“…As the degrees of freedom increases, the t-distribution approaches the normal distribution, which is the most commonly situation in the applications of bioassay as illustrated in Finney (1978) and Chen et al (1999). On the other hand, as the degrees of freedom approaches 1, the t-distribution approaches the Cauchy distribution, which is also an important distribution in bioassay since the log relative potency estimator is a ratio of two normal variables, which is distributed as a Cauchy distribution.…”

“…Most of these methods can be formulated in terms of a general linear model for data following a normal distribution, or in a generalized linear model for other types of data. In the situation of multi-response experiments, multivariate statistics can be used as in Laska et al (1985), Srivastava (1986) and Chen et al (1999).…”

“…With the studies of combination of bioassays, most results appear in Bennett (1962), Armitage (1970), Meisner et al (1986), William (1988), Chen et al (1999), Xiong and Chen (2007), and Chen (2007). Chen et al (1999) proposed a novel empirical Bayesian estimator (EBE) and a shrinkage Bayesian estimator (SBE) for the relative potency from the combination of several multivariate bioassays by incorporating prior information on the model parameters based on Jeffreys' rules. The EBE can account for any extra-variability among the bioassays, and if the extra-variability is zero, the EBE reduces to the maximum likelihood estimator for combinations of bioassays.…”

“…For the proposed shrinkage Bayesian estimator, Chen et al(1999) embedded the Bayesian theory into a bioassay framework by using the Jeffreys' theory for the model parameters.…”

“…

AbstractThis paper 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.

…”