Biomaterial Database

Confidence bands for logistic regression with restricted predictor variables. 1988

W W Piegorsch, and G Casella

Division of Biometry and Risk Assessment, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709.

Confidence bands are constructed for the logistic response function when there is an interval restriction on each of the predictor variables. The construction involves application of a general fitting procedure using Scheffé's S-method, described by Casella and Strawderman (1980, Journal of the American Statistical Association 75, 862-868). Specific details are given for the case of one predictor variable, along with details for a fixed-width alternative to the S-method bands. In the one-predictor case, Monte Carlo results suggest that both bands are conservative for small sample sizes, such as N = 25. By N = 200 the S-method's coverage probabilities are seen to attain their nominal levels while the fixed-width bands remain conservative. The procedures are exemplified with data from a genetic toxicology experiment.

UI	MeSH Term	Description	Entries
D009010	Monte Carlo Method	In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)	Method, Monte Carlo
D009152	Mutagenicity Tests	Tests of chemical substances and physical agents for mutagenic potential. They include microbial, insect, mammalian cell, and whole animal tests.	Genetic Toxicity Tests,Genotoxicity Tests,Mutagen Screening,Tests, Genetic Toxicity,Toxicity Tests, Genetic,Genetic Toxicity Test,Genotoxicity Test,Mutagen Screenings,Mutagenicity Test,Screening, Mutagen,Screenings, Mutagen,Test, Genotoxicity,Tests, Genotoxicity,Toxicity Test, Genetic
D011336	Probability	The study of chance processes or the relative frequency characterizing a chance process.	Probabilities
D012044	Regression Analysis	Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.	Regression Diagnostics,Statistical Regression,Analysis, Regression,Analyses, Regression,Diagnostics, Regression,Regression Analyses,Regression, Statistical,Regressions, Statistical,Statistical Regressions
D004305	Dose-Response Relationship, Drug	The relationship between the dose of an administered drug and the response of the organism to the drug.	Dose Response Relationship, Drug,Dose-Response Relationships, Drug,Drug Dose-Response Relationship,Drug Dose-Response Relationships,Relationship, Drug Dose-Response,Relationships, Drug Dose-Response
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man