Generalized Confidence Intervals for Ratios of Regression Coefficients with Applications to Bioassays |
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Authors: | Ionut Bebu Françoise Seillier‐Moiseiwitsch Thomas Mathew |
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Institution: | 1. Department of Biostatistics, Bioinformatics, and Biomathematics, Georgetown University Medical Center, 4000 Reservoir Road NW, Washington, DC 20057, USA;2. Department of Mathematics and Statistics, University of Maryland Baltimore Country, 1000 Hilltop Circle, Baltimore, MD 21250, USA |
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Abstract: | The problem of constructing a confidence interval for the ratio of two regression coefficients is addressed in the context of multiple regression. The concept of a Generalized Confidence Interval is used, and the resulting confidence interval is shown to perform well in terms of coverage probability. The proposed methodology always results in an interval, unlike the confidence region generated from Fieller's theorem. The procedure can easily be implemented for parallel‐line assays, slope‐ratio assays, and quantal assays under a probit model. Furthermore, this approach can also be extended to compute confidence intervals based on data from multiple bioassays. The results are illustrated using several examples. |
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Keywords: | Bioassay LD50 Log potency Ratio of two regression coefficients |
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