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Incorporating historical control information into quantal bioassay with Bayesian approach

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  • Chen, D.G.

Abstract

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 ED(100p) for various values of risk rate p and the potency for any dose level.

Suggested Citation

  • Chen, D.G., 2010. "Incorporating historical control information into quantal bioassay with Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1646-1656, June.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1646-1656
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    References listed on IDEAS

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    1. Chen, D.G., 2007. "Bootstrapping estimation for estimating relative potency in combinations of bioassays," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4597-4604, May.
    2. Smythe, Robert T. & Krewski, Daniel & Murdoch, Duncan, 1986. "The use of historical control information in modelling dose response relationships in carcinogenesis," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 87-93, March.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    1. Kitsche, A. & Hothorn, L.A. & Schaarschmidt, F., 2012. "The use of historical controls in estimating simultaneous confidence intervals for comparisons against a concurrent control," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3865-3875.

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