title: A random set approach to confidence regions with applications to the effective dose with combinations of agents.
abstract: The effective dose (ED) is the pharmaceutical dosage required to produce a therapeutic response in a fixed proportion of the patients. When only one drug is considered, the problem is a univariate one and has been well-studied. However, in the multidimensional setting, that is, in the presence of combinations of agents, estimation of the ED becomes more difficult. This study is focused on the plug-in logistic regression estimator of the multidimensional ED. We discuss consistency of such estimators and focus on the problem of simultaneous confidence regions. We develop a bootstrap algorithm to estimate confidence regions for the multidimensional ED. Through simulation, we show that the proposed method gives 95% confidence regions, which have better empirical coverage than the previous method for moderate to large sample sizes. The novel approach is illustrated on a cytotoxicity study on the effect of two toxins in the leukemia cell line HL-60 and a decompression sickness study of the effects of the duration and depth of the dive.
authors: Department of Mathematics and Statistics, York University, Toronto, ON, Canada.
authors: Hanna
authors: H
authors: Jankowski
authors: Xiang
authors: X
authors: Ji
authors: Larissa
authors: L
authors: Stanberry
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D016001:Confidence Intervals; D003665:Decompression Sickness / Q000503:physiopathology; D018922:HL-60 Cells; D006801:Humans; D007938:Leukemia / Q000188:drug therapy; D016015:Logistic Models; D008741:Methyl Methanesulfonate / Q000008:administration & dosage; D004364:Pharmaceutical Preparations / Q000008:administration & dosage*; D012756:Sheep; D013755:Tetradecanoylphorbol Acetate / Q000008:administration & dosage
chemical_list: D004364:Pharmaceutical Preparations; D008741:Methyl Methanesulfonate; D013755:Tetradecanoylphorbol Acetate
keywords: drug combinations; logistic regression; multidimensional effective dose; plug-in estimation; simultaneous confidence region