Small Sample LD50 Confidence Intervals Using Saddlepoint Approximations

• Published in: Journal of the American Statistical Association 2011-03, Vol.106 (493), p.334-344
• Main Authors: Paige, Robert L., Chapman, Phillip L., Butler, Ronald W.
• Format: Article
• Language: English
• Subjects: Applications; Approximation; Bartlett correction; Binary data; Bootstrap; Bootstrap method; Censorship; Competing risks; Confidence interval; Confidence intervals; Data analysis; Dosage; Dose response relationship; Error rates; Exact sciences and technology; Fieller's method; General topics; Lethal dose 50; Likelihood ratio; Logistics; Mathematics; Maximum likelihood estimation; Methodology; Nonparametric inference; Parametric inference; Parametric models; Probability and statistics; Regression analysis; Risk; Sampling; Sciences and techniques of general use; Score statistic; Statistical analysis; Statistics; Theory and Methods
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2011.tm09784

Confidence intervals for the median lethal dose (LD50) and other dose percentiles in logistic regression models are developed using a generalization of the Fieller theorem for exponential families and saddlepoint approximations. Simulation results show that, in terms of one-tailed and two-tailed coverage, the proposed methodology generally outperforms competing confidence intervals obtained from the classical Fieller, likelihood ratio, and score methods. In terms of two-tailed coverage, the proposed method is comparable to the Bartlett-corrected likelihood ratio method, but generally outperforms it in terms of one-tailed coverage. An extension to the competing risk setting is presented that allows binary response adjustments to be made using observed censoring times. Supplementary materials for this article are available online at http://pubs.amstat.org .