Consistency and asymptotic normality of the estimated effective doses in bioassay |
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Authors: | Rabi Bhattacharya Maiying Kong |
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Institution: | 1. Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA;2. Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, Louisville, KY 40292, USA |
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Abstract: | In order to estimate the effective dose such as the 0.5 quantile ED50 in a bioassay problem various parametric and semiparametric models have been used in the literature. If the true dose–response curve deviates significantly from the model, the estimates will generally be inconsistent. One strategy is to analyze the data making only a minimal assumption on the model, namely, that the dose–response curve is non-decreasing. In the present paper we first define an empirical dose–response curve based on the estimated response probabilities by using the “pool-adjacent-violators” (PAV) algorithm, then estimate effective doses ED100p for a large range of p by taking inverse of this empirical dose–response curve. The consistency and asymptotic distribution of these estimated effective doses are obtained. The asymptotic results can be extended to the estimated effective doses proposed by Glasbey 1987. Tolerance-distribution-free analyses of quantal dose–response data. Appl. Statist. 36 (3), 251–259] and Schmoyer 1984. Sigmoidally constrained maximum likelihood estimation in quantal bioassay. J. Amer. Statist. Assoc. 79, 448–453] under the additional assumption that the dose–response curve is symmetric or sigmoidal. We give some simulations on constructing confidence intervals using different methods. |
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Keywords: | Dose-response curve Monotonic regression Pool-adjacent-violators (PAV) algorithm Logistic regression Confidence intervals |
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