The Annals of Statistics

Bayesian Bioassay Design

Lynn Kuo

Full-text: Open access

Abstract

A Bayesian treatment of the quantal bioassay design problem is given. It is assumed that the potency curve is a Dirichlet random distribution $F$ with parameter $\alpha(t) = MF_0(t)$, and that $n_1, \cdots, n_L$ animals are treated at drug levels $t_1, \cdots, t_L$ respectively. The optimal design levels $t_1, \cdots, t_L$ that minimize the Bayes risk for weighted integrated quadratic loss functions are found in the following cases: (i) $L = 1$ and the weight function arbitrary; (ii) uniform prior guess, uniform weight and two animals treated; and (iii) uniform weight and $L$ arbitrary, but $M \rightarrow 0$. These results disprove a conjecture of Antoniak.

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 886-895.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346254

Digital Object Identifier
doi:10.1214/aos/1176346254

Mathematical Reviews number (MathSciNet)
MR707938

Zentralblatt MATH identifier
0521.62086

JSTOR
links.jstor.org

Subjects
Primary: 62K05: Optimal designs
Secondary: 62P10: Applications to biology and medical sciences 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Dirichlet process mixtures of Dirichlet processes quantal bioassay potency curve threshold of tolerance Bayes risk optimal design

Citation

Kuo, Lynn. Bayesian Bioassay Design. Ann. Statist. 11 (1983), no. 3, 886--895. doi:10.1214/aos/1176346254. https://projecteuclid.org/euclid.aos/1176346254


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