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Bootstrap Confidence Intervals for Effective Doses in the Probit Model for Dose‐Response Data
Author(s) -
Müller HansGeorg,
Wang JaneLing
Publication year - 1990
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710320504
Subject(s) - statistics , confidence interval , percentile , studentized range , mathematics , nominal level , coverage probability , probit model , standard deviation , restricted maximum likelihood , parametric statistics , robust confidence intervals , econometrics , maximum likelihood
Parametric bootstrap methods for the construction of confidence intervals for the effective dose at level α(EDα) under the probit model for the dose‐response relationship are investigated. The standard maximum likelihood confidence intervals and percentile, centered percentile, studentized, bias corrected and better bias corrected bootstrap methods are compared in a simulation with 1000 Monte Carlo runs and 1000 bootstrap samples. Among the bootstrap methods, studentized and centered percentile methods are found to behave unfavorably with respect to observed coverage probability, whereas the bias corrected and better bias corrected bootstrap sometimes improve on the maximum likelihood method. The maximum likelihood method yielded very mixed results, but in our simulation none of the currently available bootstrap methods improved uniformly on this standard method. The methods are illustrated by an application to a bioassay.