Incorporating historical control information into quantal bioassay with Bayesian approach

• Published in: Computational statistics & data analysis Vol. 54; no. 6; pp. 1646 - 1656
• Main Author: Chen, D.G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-06-2010; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Applications; Bayesian analysis; Beta-binomial; Bioassay; Confidence intervals; Dose-response model Logit-normal Beta-binomial Potency ED100p Empirical and full Bayes; Dose–response model; Empirical and full Bayes; Estimates; Estimators; Exact sciences and technology; formula omitted; General topics; Inclusions; Logit-normal; Mathematics; Medical sciences; Multivariate analysis; Normal distribution; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Potency; Probability and statistics; Sciences and techniques of general use; Statistics; Logit-normal; E D 100 p; Potency; Empirical and full Bayes; Dose–response model; Beta-binomial; Biometrics; Gaussian distribution; Iterative method; Dose activity relation; Medical science; Beta binomial distribution; Estimator efficiency; Least squares method; Confidence band; Dose-response model; Bayes decision; Likelihood function; ED; Bayes estimation; Data analysis; Bioassay; Statistical decision; Marginal likelihood; Statistical method; Laplace method; Risk rate; Statistical computation; Decision theory
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.01.023

A Bayesian approach with an iterative reweighted least squares is used to incorporate historical control information into quantal bioassays to estimate the dose–response relationship, where the logit of the historical control responses are assumed to have a normal distribution. The parameters from this normal distribution are estimated from both empirical and full Bayesian approaches with a marginal likelihood function being approximated by Laplace’s Method. A comparison is made using real data between estimates that include the historical control information and those that do not. It was found that the inclusion of the historical control information improves the efficiency of the estimators. In addition, this logit-normal formulation is compared with the traditional beta-binomial for its improvement in parameter estimates. Consequently the estimated dose–response relationship is used to formulate the point estimator and confidence bands for
E
D
(
100
p
)
for various values of risk rate
p
and the potency for any dose level.