Standard error of inverse prediction for dose-response relationship: approximate and exact statistical inference

In Vivo Verification of Electron Paramagnetic Resonance Biodosimetry Using Patients Undergoing Radiation Therapy Treatment

PURPOSE

Electron paramagnetic resonance (EPR) biodosimetry, used to triage large numbers of individuals incidentally exposed to unknown doses of ionizing radiation, is based on detecting a stable physical response in the body that is subject to quantifiable variation after exposure. In vivo measurement is essential to fully characterize the radiation response relevant to a living tooth measured in situ. The purpose of this study was to verify EPR spectroscopy in vivo by estimating the radiation dose received in participants' teeth.

METHODS AND MATERIALS

A continuous wave L-band spectrometer was used for EPR measurements. Participants included healthy volunteers and patients undergoing head and neck and total body irradiation treatments. Healthy volunteers completed 1 measurement each, and patients underwent measurement before starting treatment and between subsequent fractions. Optically stimulated luminescent dosimeters and diodes were used to determine the dose delivered to the teeth to validate EPR measurements.

RESULTS

Seventy measurements were acquired from 4 total body irradiation and 6 head and neck patients over 15 months. Patient data showed a linear increase of EPR signal with delivered dose across the dose range tested. A linear least-squares weighted fit of the data gave a statistically significant correlation between EPR signal and absorbed dose (P < .0001). The standard error of inverse prediction (SEIP), used to assess the usefulness of fits, was 1.92 Gy for the dose range most relevant for immediate triage (≤7 Gy). Correcting for natural background radiation based on patient age reduced the SEIP to 1.51 Gy.

CONCLUSIONS

This study demonstrated the feasibility of using spectroscopic measurements from radiation therapy patients to validate in vivo EPR biodosimetry. The data illustrated a statistically significant correlation between the magnitude of EPR signals and absorbed dose. The SEIP of 1.51 Gy, obtained under clinical conditions, indicates the potential value of this technique in response to large radiation events.

Enhanced Dosimetric Accuracy Using Quality Factor Compensation Method for In Vivo Electron Paramagnetic Resonance Tooth Dosimetry

ABSTRACT

We aim to develop a dose assessment method compensating for quality factors (Q factor) observed during in vivo EPR tooth dosimetry. A pseudo-in-vivo phantom made of tissue-equivalent material was equipped with one each of four extracted human central incisors. A range of Q factors was measured at tooth-depths of -2, 0, and 2 mm in the pseudo-in-vivo phantom. In addition, in vivo Q factors were measured from nine human volunteers. For the dose-response data, the above four sample teeth were irradiated at 0, 1, 2, 5, and 10 Gy, and the radiation-induced signals were measured at the same tooth-depths using an in vivo EPR tooth dosimetry system. To validate the method, the signals of two post-radiotherapy patients and three unirradiated volunteers were measured using the same system. The interquartile range of the Q factors measured in the pseudo-in-vivo phantom covered that observed from the human volunteers, which implied that the phantom represented the Q factor distribution of in vivo conditions. The dosimetric sensitivities and background signals were decreased as increasing the tooth-depth in the phantom due to the decrease in Q factors. By compensating for Q factors, the diverged dose-response data due to various Q factors were converged to improve the dosimetric accuracy in terms of the standard error of inverse prediction (SEIP). The Q factors of patient 1 and patient 2 were 98 and 64, respectively, while the three volunteers were 100, 92, and 99. The assessed doses of patient 1 and patient 2 were 2.73 and 12.53 Gy, respectively, while expecting 4.43 and 13.29 Gy, respectively. The assessed doses of the unirradiated volunteers were 0.53, 0.50, and - 0.22 Gy. We demonstrated that the suggested Q factor compensation could mitigate the uncertainty induced by the variation of Q factors.

Frequency-fixed motion compensation system for in-vivo electron paramagnetic resonance tooth dosimetry

This article describes the design process for a motion compensation system that can suppress the spectral distortion caused by human motion and breathing during in-vivo electron paramagnetic resonance (EPR) spectroscopy on an intact incisor. The developed system consists of two elements: an electronically controlled tunable resonator and an automatic control circuit (ACC). The resonator can modify the resonant frequency and impedance by tuning and matching the voltage, while the ACC can generate a feedback signal using phase-sensitive detection (PSD). The signal is transferred into the resonator to maintain the critical coupling state. The tunable frequency range of the resonator was measured at over 10 MHz, offering approximately eight times the required range. The bandwidth of the resonator fluctuated in a negligible range (0.14% relative standard error) following the resonant frequency. With the feedback signal on, in-vivo EPR measurements were demonstrated to be a stable baseline with 35% higher signal-to-noise ratio (SNR). When one incisor sample was irradiated by an X-ray instrument, the EPR signal responses to the absorbed doses of 0-10 Gy exhibited high linearity (R2 = 0.994). In addition, the standard error of inverse prediction was estimated to be 0.35 Gy. The developed system achieved a discrimination ability of 2 Gy, which is required for triage in large-scale radiation accidents. Moreover, the compensation is fully automated, meaning that the system can be operated with simple training in an emergency.

Statistical Uncertainty in Paleoclimate Proxy Reconstructions

A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a "data-forward" approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.

Estimation of pO2 distribution in EPR oximetry

Electron paramagnetic resonance (EPR) oximetry, using oxygen-sensing implant such as OxyChip, is capable of measuring oxygen concentration in vivo - a critical tissue information required for successful medical treatment such as cancer, wound healing and diabetes. Typically, EPR oximetry produces one value of the oxygen concentration, expressed as pO2 at the site of implant. However, it is well recognized that in vivo one deals with a distribution of oxygen concentration and therefore reporting just one number is not representative_a long-standing critique of EPR oximetry. Indeed, when it comes to the assessment of radiation efficacy one should be guided not by the mean or median but the proportion of oxygenated cancer cells which can be estimated only when the whole oxygen distribution in the tumor is known. Although there is a handful of papers attempting estimation of the oxygen distribution they suffer from the problem of negative frequencies and no theoretical justification and no biomedical interpretation. The goal of this work is to suggest a novel method using the empirical Bayesian approach realized via nonlinear mixed modeling with a priori distribution of oxygen following a two-parameter lognormal distribution with parameters estimated from the multi-implant single component EPR scan. Unlike previous work, the result of our estimation is the distribution with positive values for the frequency and the associated pO2 value. Our algorithm based on nonlinear regression is illustrated with EPR measurements on OxyChips equilibrated with gas mixtures containing four values of pO2 and computation of the proportion of volume with pO2 greater than any given threshold. This approach may become crucial for application of the EPR oximetry in clinical setting when the sucsess of the treatment depends of the proportion of tissue oxygenated.

Quantitative structure-property relationship of the photoelectrochemical oxidation of phenolic pollutants at modified nanoporous titanium oxide using supervised machine learning

Here we report on an advanced photoelectrochemical (PEC) oxidation of 22 phenolic pollutants based on modified nanoporous TiO2, which was directly grown on a titanium substrate electrochemically. Their degradation rate constants were experimentally determined and their physicochemical properties were computaionally calculated. The quantitative structure-property relationship (QSPR) was elucidated by employing multiple linear regression (MLR) method. A supervised machine learning approach was employed to build QSPR models. The high predictive abilities of the QSPR model were validated via leave-one-out (LOO) method and a strict regimen of statistical validation tests. The significant descriptors identified in the QSPR Model for the phenolic compounds were also assessed using a typical dye pollutant Rhodamine B, further confirming the high effectiveness and predictability of the optimized model. Our study has shown that the integrated effect of the structural, hydrophobic and topological properties along with electronic property should be considered in order to design an efficient PEC catalytic approach for environmental applications.

A Review of Recent Advances in Benchmark Dose Methodology

In this review, recent methodological developments for the benchmark dose (BMD) methodology are summarized. Specifically, we introduce the advances for the main steps in BMD derivation: selecting the procedure for defining a BMD from a predefined benchmark response (BMR), setting a BMR, selecting a dose-response model, and estimating the corresponding BMD lower limit (BMDL). Although the last decade has shown major progress in the development of BMD methodology, there is still room for improvement. Remaining challenges are the implementation of new statistical methods in user-friendly software and the lack of consensus about how to derive the BMDL.

Advances in in vivo EPR Tooth BIOdosimetry: Meeting the targets for initial triage following a large-scale radiation event

Several important recent advances in the development and evolution of in vivo Tooth Biodosimetry using Electron Paramagnetic Resonance (EPR) allow its performance to meet or exceed the U.S. targeted requirements for accuracy and ease of operation and throughput in a large-scale radiation event. Ergonomically based changes to the magnet, coupled with the development of rotation of the magnet and advanced software to automate collection of data, have made it easier and faster to make a measurement. From start to finish, measurements require a total elapsed time of 5 min, with data acquisition taking place in less than 3 min. At the same time, the accuracy of the data for triage of large populations has improved, as indicated using the metrics of sensitivity, specificity and area under the ROC curve. Applying these standards to the intended population, EPR in vivo Tooth Biodosimetry has approximately the same diagnostic accuracy as the purported 'gold standard' (dicentric chromosome assay). Other improvements include miniaturisation of the spectrometer, leading to the creation of a significantly lighter and more compact prototype that is suitable for transporting for Point of Care (POC) operation and that can be operated off a single standard power outlet. Additional advancements in the resonator, including use of a disposable sensing loop attached to the incisor tooth, have resulted in a biodosimetry method where measurements can be made quickly with a simple 5-step workflow and by people needing only a few minutes of training (which can be built into the instrument as a training video). In sum, recent advancements allow this prototype to meet or exceed the US Federal Government's recommended targets for POC biodosimetry in large-scale events.

A new inverse regression model applied to radiation biodosimetry

Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by means of Hermite and negative binomial (NB) distributions. For compound Poisson responses, complete and simplified models are provided. The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions. Three examples of applications are given that demonstrate the usefulness of these methodologies in cytogenetic radiation biodosimetry and in radiotherapy. We provide R and SAS codes which reproduce these examples.

Point and Interval Estimators of the Target Dose in Clinical Dose-Finding Studies with Active Control

In a clinical dose finding study with active control a new drug with several dose levels is compared with an active comparator drug. The main focus of such studies often lies on the estimation of a target dose that leads to the same efficacy as the control. This article investigates the finite sample properties of the maximum likelihood estimation of the target dose and compares several approaches for constructing corresponding confidence intervals under the assumption of a linear dose-response curve and normal error terms. Furthermore, the impact of deviations from the model assumptions regarding the error distribution is explored.

In vivo EPR tooth dosimetry for triage after a radiation event involving large populations

The management of radiation injuries following a catastrophic event where large numbers of people may have been exposed to life-threatening doses of ionizing radiation will rely critically on the availability and use of suitable biodosimetry methods. In vivo electron paramagnetic resonance (EPR) tooth dosimetry has a number of valuable and unique characteristics and capabilities that may help enable effective triage. We have produced a prototype of a deployable EPR tooth dosimeter and tested it in several in vitro and in vivo studies to characterize the performance and utility at the state of the art. This report focuses on recent advances in the technology, which strengthen the evidence that in vivo EPR tooth dosimetry can provide practical, accurate, and rapid measurements in the context of its intended use to help triage victims in the event of an improvised nuclear device. These advances provide evidence that the signal is stable, accurate to within 0.5 Gy, and can be successfully carried out in vivo. The stability over time of the radiation-induced EPR signal from whole teeth was measured to confirm its long-term stability and better characterize signal behavior in the hours following irradiation. Dosimetry measurements were taken for five pairs of natural human upper central incisors mounted within a simple anatomic mouth model that demonstrates the ability to achieve 0.5 Gy standard error of inverse dose prediction. An assessment of the use of intact upper incisors for dose estimation and screening was performed with volunteer subjects who have not been exposed to significant levels of ionizing radiation and patients who have undergone total body irradiation as part of bone marrow transplant procedures. Based on these and previous evaluations of the performance and use of the in vivo tooth dosimetry system, it is concluded that this system could be a very valuable resource to aid in the management of a massive radiological event.