ArticleStatistics in medicine2013
Standard error of inverse prediction for dose-response relationship: approximate and exact statistical inference.
Article in Statistics in medicine, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
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- OxyTrack: A Novel Needle Sensor for In Situ Oximetry.Magnetic resonance in medicine · 2026Article
- A Flexible RF Coil Design (OxyTrack) for Oxygen Measurements in Body Cavities.Magnetic resonance in medicine · 2026Article
- In Vivo Verification of Electron Paramagnetic Resonance Biodosimetry Using Patients Undergoing Radiation Therapy Treatment.International journal of radiation oncology, biology, physics · 2024Article
- Abductive statistical methods improve the results of calibration curve bioassays: An example of determining zinc bioavailability in broiler chickens.Animal nutrition (Zhongguo xu mu shou yi xue hui) · 2022Article
- Statistical Uncertainty in Paleoclimate Proxy Reconstructions.Geophysical research letters · 2021Article
- Estimation of pOJournal of magnetic resonance (San Diego, Calif. : 1997) · 2021Article
- Advances in in vivo EPR Tooth BIOdosimetry: Meeting the targets for initial triage following a large-scale radiation event.Radiation protection dosimetry · 2016Review
- A new inverse regression model applied to radiation biodosimetry.Proceedings. Mathematical, physical, and engineering sciences · 2015Article
- Point and Interval Estimators of the Target Dose in Clinical Dose-Finding Studies with Active Control.Journal of biopharmaceutical statistics · 2015Article
- In vivo EPR tooth dosimetry for triage after a radiation event involving large populations.Radiation and environmental biophysics · 2014Article
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Authors and funding
4 authors.
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Abstract
This paper develops a new metric, the standard error of inverse prediction (SEIP), for a dose-response relationship (calibration curve) when dose is estimated from response via inverse regression. SEIP can be viewed as a generalization of the coefficient of variation to regression problem when x is predicted using y-value. We employ nonstandard statistical methods to treat the inverse prediction, which has an infinite mean and variance due to the presence of a normally distributed variable in the denominator. We develop confidence intervals and hypothesis testing for SEIP on the basis of the normal approximation and using the exact statistical inference based on the noncentral t-distribution. We derive the power functions for both approaches and test them via statistical simulations. The theoretical SEIP, as the ratio of the regression standard error to the slope, is viewed as reciprocal of the signal-to-noise ratio, a popular measure of signal processing. The SEIP, as a figure of merit for inverse prediction, can be used for comparison of calibration curves with different dependent variables and slopes. We illustrate our theory with electron paramagnetic resonance tooth dosimetry for a rapid estimation of the radiation dose received in the event of nuclear terrorism.
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