## The Annals of Statistics

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

### Bayesian Bioassay Design

#### 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