Affiliations: [a] Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand | [b] Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, USA
Corresponding author: Montip Tiensuwan, Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand. E-mail: [email protected].
Abstract: Standard dose response models, namely, the multistage Weibull, logistic and log-logistic models are considered. These models involve two parameters θ0 and θ1, and we assume θ0 to be known. The maximum likelihood and Berkson’s minimum chi-square methods are employed to estimate the parameter θ1 in each model. The mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators θˆ1 are derived asymptotically to the order of approximation n−2. The results show that the mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators behave differently for different dose groups and dose levels.
Keywords: Asymptotic comparison, Berkson's minimum chi-square, logistic model, log-logistic model, maximum likelihood, multistage Weibull model