Zero-inflated regression models for radiation-induced chromosome aberration data: A comparative study

Establishment of ex vivo calibration curve for X-ray induced "dicentric + ring" and micronuclei in human peripheral lymphocytes for biodosimetry during radiological emergencies, and validation with dose blinded samples

In the modern developing society, application of radiation has increased extensively. With significant improvement in the radiation protection practices, exposure to human could be minimized substantially, but cannot be avoided completely. Assessment of exposure is essential for regulatory decision and medical management as applicable. Until now, cytogenetic changes have served as surrogate marker of radiation exposure and have been extensively employed for biological dose estimation of various planned and unplanned exposures. Dicentric Chromosomal Aberration (DCA) is radiation specific and is considered as gold standard, micronucleus is not very specific to radiation and is considered as an alternative method for biodosimetry. In this study dose response curves were generated for X-ray induced "dicentric + ring" and micronuclei, in lymphocytes of three healthy volunteers [2 females (age 22, 23 years) and 1 male (24 year)]. The blood samples were irradiated with X-ray using LINAC (energy 6 MV, dose rate 6 Gy/min), in the dose range of 0-5Gy. Irradiated blood samples were cultured and processed to harvest metaphases, as per standard procedures recommended by International Atomic Energy Agency. Pooled data obtained from all the three volunteers, were in agreement with Poisson distribution for "dicentric + ring", however over dispersion was observed for micronuclei. Data ("dicentric + ring" and micronuclei) were fitted by linear quadratic model of the expression Y[bond, double bond]C + αD + βD² using Dose Estimate software, version 5.2. The data fit has resulted in linear coefficient α = 0.0006 (±0.0068) "dicentric + ring" cell^-1 Gy^-1 and quadratic coefficient β = 0.0619 (±0.0043) "dicentric + ring" cell^-1 Gy^-2 for "dicentric + ring" and linear coefficient α = 0.0459 ± (0.0038) micronuclei cell^-1 Gy^-1 and quadratic coefficient β = 0.0185 ± (0.0010) micronuclei cell^-1 Gy^-2 for micronuclei, respectively. Background frequencies for "dicentric + ring" and micronuclei were 0.0006 ± 0.0004 and 0.0077 ± 0.0012 cell^-1, respectively. Established curves were validated, by reconstructing the doses of 8 dose blinded samples (4 by DCA and 4 by CBMN) using coefficients generated here. Estimated doses were within the variation of 0.9-16% for "dicentric + ring" and 21.7-31.2% for micronuclei respectively. These established curves have potential to be employed for biodosimetry of occupational, clinical and accidental exposures, for initial triage and medical management.

Dose-Dependent Transmissibility of Chromosome Aberrations in Human Lymphocytes at First Mitosis. II. Biological Effectiveness of Heavy Charged Particles Versus Gamma Rays

Chromosome aberrations (CAs) are large scale structural rearrangements to the genome that have been used as a proxy endpoint of mutagenic and carcinogenic potential. And yet, many types of CAs are incapable of causing either of these effects simply because they are lethal. Using 24-color multi-fluor combinatorial painting (mFISH), we examined CAs in normal human lymphocytes exposed to graded doses of 1 GeV/nucleon accelerated 56Fe ions and 662 keV 137Cs gamma rays. As expected, the high-linear energy transfer (LET) heavy ions were considerably more potent per unit dose at producing total yields of CAs compared to low-LET gamma rays. As also anticipated, the frequency distribution of aberrations per cell exposed to 56Fe ions was significantly overdispersed compared to the Poisson distribution, containing excess numbers of cells devoid of aberrations. We used the zero-inflated negative binomial (ZINB) distribution to model these data. Based on objective cytogenetic criteria that are subject to caveats we discuss, each cell was individually evaluated in terms of likely survival (i.e., its ability to transmit to daughter cell progeny). For 56Fe ion irradiations, the frequency of surviving cells harboring complex aberrations represented a significant portion of aberration-bearing cells, while for gamma irradiation no survivable cells containing complex aberrations were observed. When the dose responses for the two radiation types were compared, and the analysis was limited to surviving cells that contained aberrations, we were surprised to find the high-LET 56Fe ions only marginally more potent than the low-LET gamma rays for doses less than 1 Gy. In fact, based on dose-response modeling, they were predicted to be less effective than gamma rays at somewhat higher doses. The major implication of these findings is that measures of relative biological effectiveness that fail to account for coincident lethality will tend to overstate the impact of transmissible chromosomal damage from high-LET particle exposure.

Biodose Tools: an R shiny application for biological dosimetry

INTRODUCTION

In the event of a radiological accident or incident, the aim of biological dosimetry is to convert the yield of a specific biomarker of exposure to ionizing radiation into an absorbed dose. Since the 1980s, various tools have been used to deal with the statistical procedures needed for biological dosimetry, and in general those who made several calculations for different biomarkers were based on closed source software. Here we present a new open source program, Biodose Tools, that has been developed under the umbrella of RENEB (Running the European Network of Biological and retrospective Physical dosimetry).

MATERIALS AND METHODS

The application has been developed using the R programming language and the shiny package as a framework to create a user-friendly online solution. Since no unique method exists for the different mathematical processes, several meetings and periodic correspondence were held in order to reach a consensus on the solutions to be implemented.

RESULTS

The current version 3.6.1 supports dose-effect fitting for dicentric and translocation assay. For dose estimation Biodose Tools implements those methods indicated in international guidelines and a specific method to assess heterogeneous exposures. The app can include information on the irradiation conditions to generate the calibration curve. Also, in the dose estimate, information about the accident can be included as well as the explanation of the results obtained. Because the app allows generating a report in various formats, it allows traceability of each biological dosimetry study carried out. The app has been used globally in different exercises and training, which has made it possible to find errors and improve the app itself. There are some features that still need consensus, such as curve fitting and dose estimation using micronucleus analysis. It is also planned to include a package dedicated to interlaboratory comparisons and the incorporation of Bayesian methods for dose estimation.

CONCLUSION

Biodose Tools provides an open-source solution for biological dosimetry laboratories. The consensus reached helps to harmonize the way in which uncertainties are calculated. In addition, because each laboratory can download and customize the app's source code, it offers a platform to integrate new features.

Machine learning approach for quantitative biodosimetry of partial-body or total-body radiation exposures by combining radiation-responsive biomarkers

During a large-scale radiological event such as an improvised nuclear device detonation, many survivors will be shielded from radiation by environmental objects, and experience only partial-body irradiation (PBI), which has different consequences, compared with total-body irradiation (TBI). In this study, we tested the hypothesis that applying machine learning to a combination of radiation-responsive biomarkers (ACTN1, DDB2, FDXR) and B and T cell counts will quantify and distinguish between PBI and TBI exposures. Adult C57BL/6 mice of both sexes were exposed to 0, 2.0-2.5 or 5.0 Gy of half-body PBI or TBI. The random forest (RF) algorithm trained on ½ of the data reconstructed the radiation dose on the remaining testing portion of the data with mean absolute error of 0.749 Gy and reconstructed the product of dose and exposure status (defined as 1.0 × Dose for TBI and 0.5 × Dose for PBI) with MAE of 0.472 Gy. Among irradiated samples, PBI could be distinguished from TBI: ROC curve AUC = 0.944 (95% CI: 0.844-1.0). Mouse sex did not significantly affect dose reconstruction. These results support the hypothesis that combinations of protein biomarkers and blood cell counts can complement existing methods for biodosimetry of PBI and TBI exposures.

Dicentric chromosome assay using a deep learning-based automated system

The dicentric chromosome assay is the "gold standard" in biodosimetry for estimating radiation exposure. However, its large-scale deployment is limited owing to its time-consuming nature and requirement for expert reviewers. Therefore, a recently developed automated system was evaluated for the dicentric chromosome assay. A previously constructed deep learning-based automatic dose-estimation system (DLADES) was used to construct dose curves and calculate estimated doses. Blood samples from two donors were exposed to cobalt-60 gamma rays (0-4 Gy, 0.8 Gy/min). The DLADES efficiently identified monocentric and dicentric chromosomes but showed impaired recognition of complete cells with 46 chromosomes. We estimated the chromosome number of each "Accepted" sample in the DLADES and sorted similar-quality images by removing outliers using the 1.5IQR method. Eleven of the 12 data points followed Poisson distribution. Blind samples were prepared for each dose to verify the accuracy of the estimated dose generated by the curve. The estimated dose was calculated using Merkle's method. The actual dose for each sample was within the 95% confidence limits of the estimated dose. Sorting similar-quality images using chromosome numbers is crucial for the automated dicentric chromosome assay. We successfully constructed a dose-response curve and determined the estimated dose using the DLADES.

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper’s primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson–Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators’ empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.

The effect of data aggregation on dispersion estimates in count data models

For the modelling of count data, aggregation of the raw data over certain subgroups or predictor configurations is common practice. This is, for instance, the case for count data biomarkers of radiation exposure. Under the Poisson law, count data can be aggregated without loss of information on the Poisson parameter, which remains true if the Poisson assumption is relaxed towards quasi-Poisson. However, in biodosimetry in particular, but also beyond, the question of how the dispersion estimates for quasi-Poisson models behave under data aggregation have received little attention. Indeed, for real data sets featuring unexplained heterogeneities, dispersion estimates can increase strongly after aggregation, an effect which we will demonstrate and quantify explicitly for some scenarios. The increase in dispersion estimates implies an inflation of the parameter standard errors, which, however, by comparison with random effect models, can be shown to serve a corrective purpose. The phenomena are illustrated by γ-H2AX foci data as used for instance in radiation biodosimetry for the calibration of dose-response curves.

countfitteR: efficient selection of count distributions to assess DNA damage

Background

DNA double-strand breaks can be counted as discrete foci by imaging techniques. In personalized medicine and pharmacology, the analysis of counting data is relevant for numerous applications, e.g., for cancer and aging research and the evaluation of drug efficacy. By default, it is assumed to follow the Poisson distribution. This assumption, however, may lead to biased results and faulty conclusions in datasets with excess zero values (zero-inflation), a variance larger than the mean (overdispersion), or both. In such cases, the assumption of a Poisson distribution would skew the estimation of mean and variance, and other models like the negative binomial (NB), zero-inflated Poisson or zero-inflated NB distributions should be employed. The model chosen has an influence on the parameter estimation (mean value and confidence interval). Yet the choice of the suitable distribution model is not trivial.

Methods

To support, simplify and objectify this process, we have developed the countfitteR software as an R package. We used a Bayesian approach for distribution model selection and the shiny web application framework for interactive data analysis.

Results

We show the application of our software based on examples of DNA double-strand break count data from phenotypic imaging by multiplex fluorescence microscopy. In analyzing numerous datasets of molecular pharmacological markers (phosphorylated histone H2AX and p53 binding protein), countfitteR demonstrated an equal or superior statistical performance compared to the usually employed two-step procedure, with an overall power of up to 98%. In addition, it still gave information in cases with no result at all from the two-step procedure. In our data sample we found that the NB distribution was the most frequent, with the Poisson distribution taking second place.

Conclusions

countfitteR can perform an automated distribution model selection and thus support the data analysis and lead to objective statistically verifiable estimated values. Originally designed for the analysis of foci in biomedical image data, countfitteR can be used in a variety of areas where non-Poisson distributed counting data is prevalent.

A new mixed-effects regression model for the analysis of zero-modified hierarchical count data

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero-modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)-(b) and (b)-(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed-effects regression model based on the hurdle version of the Poisson-Lindley distribution. In this framework, the zero-modification is incorporated by assuming that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well-established mixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p -value and the randomized quantile residuals were considered for model diagnostics.

Improving the accuracy of dose estimates from automatically scored dicentric chromosomes by accounting for chromosome number

PURPOSE

The traditional workflow for biological dosimetry based on manual scoring of dicentric chromosomes is very time consuming. Especially for large-scale scenarios or for low-dose exposures, high cell numbers have to be analyzed, requiring alternative scoring strategies. Semi-automatic scoring of dicentric chromosomes provides an opportunity to speed up the standard workflow of biological dosimetry. Due to automatic metaphase and chromosome detection, the number of counted chromosomes per metaphase is variable. This can potentially introduce overdispersion and statistical methods for conventional, manual scoring might not be applicable to data obtained by automatic scoring of dicentric chromosomes, potentially resulting in biased dose estimates and underestimated uncertainties. The identification of sources for overdispersion enables the development of methods appropriately accounting for increased dispersion levels.

MATERIALS AND METHODS

Calibration curves based on in vitro irradiated (137-Cs; 0.44 Gy/min) blood from three healthy donors were analyzed for systematic overdispersion, especially at higher doses (>2 Gy) of low LET radiation. For each donor, 12 doses in the range of 0-6 Gy were scored semi-automatically. The effect of chromosome number as a potential cause for the observed overdispersion was assessed. Statistical methods based on interaction models accounting for the number of detected chromosomes were developed for the estimation of calibration curves, dose and corresponding uncertainties. The dose estimation was performed based on a Bayesian Markov-Chain-Monte-Carlo method, providing high flexibility regarding the implementation of priors, likelihood and the functional form of the association between predictors and dicentric counts. The proposed methods were validated by simulations based on cross-validation.

RESULTS

Increasing dose dependent overdispersion was observed for all three donors as well as considerable differences in dicentric counts between donors. Variations in the number of detected chromosomes between metaphases were identified as a major source for the observed overdispersion and the differences between donors. Persisting overdispersion beyond the contribution of chromosome number was modeled by a Negative Binomial distribution. Results from cross-validation suggested that the proposed statistical methods for dose estimation reduced bias in dose estimates, variability between dose estimates and improved the coverage of the estimated confidence intervals. However, the 95% confidence intervals were still slightly too permissive, suggesting additional unknown sources of apparent overdispersion.

CONCLUSIONS

A major source for the observed overdispersion could be identified, and statistical methods accounting for overdispersion introduced by variations in the number of detected chromosomes were developed, enabling more robust dose estimation and quantification of uncertainties for semi-automatic counting of dicentric chromosomes.

Accounting for overdispersion of lethal lesions in the linear quadratic model improves performance at both high and low radiation doses

PURPOSE

The linear-quadratic (LQ) model represents a simple and robust approximation for many mechanistically-motivated models of radiation effects. We believe its tendency to overestimate cell killing at high doses derives from the usual assumption that radiogenic lesions are distributed according to Poisson statistics.

MATERIALS AND METHODS

In that context, we investigated the effects of overdispersed lesion distributions, such as might occur from considerations of microdosimetric energy deposition patterns, differences in DNA damage complexities and repair pathways, and/or heterogeneity of cell responses to radiation. Such overdispersion has the potential to reduce dose response curvature at high doses, while still retaining LQ dose dependence in terms of the number of mean lethal lesions per cell. Here we analyze several irradiated mammalian cell and yeast survival data sets, using the LQ model with Poisson errors, two LQ model variants with customized negative binomial (NB) error distributions, the Padé-linear-quadratic, and Two-component models. We compared the performances of all models on each data set by information-theoretic analysis, and assessed the ability of each to predict survival at high doses, based on fits to low/intermediate doses.

RESULTS

Changing the error distribution, while keeping the LQ dose dependence for the mean, enables the NB LQ model variants to outperform the standard LQ model, often providing better fits to experimental data than alternative models.

CONCLUSIONS

The NB error distribution approach maintains the core mechanistic assumptions of the LQ formalism, while providing superior estimates of cell survival following high doses used in radiotherapy. Importantly, it could also be useful in improving the predictions of low dose/dose rate effects that are of major concern to the field of radiation protection.

Optimal experimental design for cytogenetic dose-response calibration curves

Purpose: To introduce optimal experimental design techniques in the cytogenetic biological dosimetry practice. This includes the development of a new optimality criterion for the calibration of radiation doses.Materials and methods: The most typical optimal design criterion and the one developed in this research are introduced and applied in an example from the literature. In another example from the literature, a simulation study has been performed to compare the standard error of the dose estimation using different experimental designs. An RStudio project and a GitHub project have been developed to reproduce these results.Results: In the paper, it is observed that the application of optimal experimental design techniques can reduce the standard error of biodosimetric dose estimations.Conclusions: Optimal experimental design techniques jointly with practitioners' requirements may be applied. This practice would not involve an additional laboratory work.

A High Throughput Approach to Reconstruct Partial-Body and Neutron Radiation Exposures on an Individual Basis

Biodosimetry-based individualized reconstruction of complex irradiation scenarios (partial-body shielding and/or neutron + photon mixtures) can improve treatment decisions after mass-casualty radiation-related incidents. We used a high-throughput micronucleus assay with automated scanning and imaging software on ex-vivo irradiated human lymphocytes to: a) reconstruct partial-body and/or neutron exposure, and b) estimate separately the photon and neutron doses in a mixed exposure. The mechanistic background is that, compared with total-body photon irradiations, neutrons produce more heavily-damaged lymphocytes with multiple micronuclei/binucleated cell, whereas partial-body exposures produce fewer such lymphocytes. To utilize these differences for biodosimetry, we developed metrics that describe micronuclei distributions in binucleated cells and serve as predictors in machine learning or parametric analyses of the following scenarios: (A) Homogeneous gamma-irradiation, mimicking total-body exposures, vs. mixtures of irradiated blood with unirradiated blood, mimicking partial-body exposures. (B) X rays vs. various neutron + photon mixtures. The results showed high accuracies of scenario and dose reconstructions. Specifically, receiver operating characteristic curve areas (AUC) for sample classification by exposure type reached 0.931 and 0.916 in scenarios A and B, respectively. R² for actual vs. reconstructed doses in these scenarios reached 0.87 and 0.77, respectively. These encouraging findings demonstrate a proof-of-principle for the proposed approach of high-throughput reconstruction of clinically-relevant complex radiation exposure scenarios.

A nonparametric method of estimation of the population size in capture-recapture experiments

A recent method for estimating a lower bound of the population size in capture-recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent for count distributions having a log-convex pgf ( L C -class). This is a large family that includes mixed and compound Poisson distributions, and their independent sums and finite mixtures as well. The finite-sample performance of the lower bound estimator is assessed via simulation showing a better behavior than some close competitors. Several examples of application are also analyzed and discussed.

Double Poisson-Tweedie Regression Models

In this paper, we further extend the recently proposed Poisson-Tweedie regression models to include a linear predictor for the dispersion as well as for the expectation of the count response variable. The family of the considered models is specified using only second-moments assumptions, where the variance of the count response has the form μ+ϕμp $\mu + \phi \mu^p$, where µ is the expectation, ϕ and p are the dispersion and power parameters, respectively. Parameter estimations are carried out using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions. The performance of the fitting algorithm is investigated through simulation studies. The results showed that our estimating function approach provides consistent estimators for both mean and dispersion parameters. The class of models is motivated by a data set concerning CD4 counting in HIV-positive pregnant women assisted in a public hospital in Curitiba, Paraná, Brazil. Specifically, we investigate the effects of a set of covariates in both expectation and dispersion structures. Our results showed that women living out of the capital Curitiba, with viral load equal or larger than 1000 copies and with previous diagnostic of HIV infection, present lower levels of CD4 cell count. Furthermore, we detected that the time to initiate the antiretroviral therapy decreases the data dispersion. The data set and R code are available as supplementary materials.

A statistical framework for radiation dose estimation with uncertainty quantification from the γ-H2AX assay

Over the last decade, the γ–H2AX focus assay, which exploits the phosphorylation of the H2AX histone following DNA double–strand–breaks, has made considerable progress towards acceptance as a reliable biomarker for exposure to ionizing radiation. While the existing literature has convincingly demonstrated a dose–response effect, and also presented approaches to dose estimation based on appropriately defined calibration curves, a more widespread practical use is still hampered by a certain lack of discussion and agreement on the specific dose–response modelling and uncertainty quantification strategies, as well as by the unavailability of implementations. This manuscript intends to fill these gaps, by stating explicitly the statistical models and techniques required for calibration curve estimation and subsequent dose estimation. Accompanying this article, a web applet has been produced which implements the discussed methods.

AN EXACT GOODNESS-OF-FIT TEST BASED ON THE OCCUPANCY PROBLEMS TO STUDY ZERO-INFLATION AND ZERO-DEFLATION IN BIOLOGICAL DOSIMETRY DATA

The goal in biological dosimetry is to estimate the dose of radiation that a suspected irradiated individual has received. For that, the analysis of aberrations (most commonly dicentric chromosome aberrations) in scored cells is performed and dose response calibration curves are built. In whole body irradiation (WBI) with X- and gamma-rays, the number of aberrations in samples is properly described by the Poisson distribution, although in partial body irradiation (PBI) the excess of zeros provided by the non-irradiated cells leads, for instance, to the Zero-Inflated Poisson distribution. Different methods are used to analyse the dosimetry data taking into account the distribution of the sample. In order to test the Poisson distribution against the Zero-Inflated Poisson distribution, several asymptotic and exact methods have been proposed which are focused on the dispersion of the data. In this work, we suggest an exact test for the Poisson distribution focused on the zero-inflation of the data developed by Rao and Chakravarti (Some small sample tests of significance for a Poisson distribution. Biometrics 1956; 12 : 264-82.), derived from the problems of occupancy. An approximation based on the standard Normal distribution is proposed in those cases where the computation of the exact test can be tedious. A Monte Carlo Simulation study was performed in order to estimate empirical confidence levels and powers of the exact test and other tests proposed in the literature. Different examples of applications based on in vitro data and also data recorded in several radiation accidents are presented and discussed. A Shiny application which computes the exact test and other interesting goodness-of-fit tests for the Poisson distribution is presented in order to provide them to all interested researchers.

A new and intuitive test for zero modification

Abstract:

While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.

Extended Poisson–Tweedie: Properties and regression models for count data

We propose a new class of discrete generalized linear models based on the class of Poisson–Tweedie factorial dispersion models with variance of the form [Formula: see text], where [Formula: see text] is the mean and [Formula: see text] and [Formula: see text] are the dispersion and Tweedie power parameters, respectively. The models are fitted by using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions for the estimation of the regression and dispersion parameters, respectively. This provides a flexible and efficient regression methodology for a comprehensive family of count models including Hermite, Neyman Type A, Pólya–Aeppli, negative binomial and Poisson-inverse Gaussian. The estimating function approach allows us to extend the Poisson–Tweedie distributions to deal with underdispersed count data by allowing negative values for the dispersion parameter [Formula: see text]. Furthermore, the Poisson–Tweedie family can automatically adapt to highly skewed count data with excessive zeros, without the need to introduce zero-inflated or hurdle components, by the simple estimation of the power parameter. Thus, the proposed models offer a unified framework to deal with under-, equi-, overdispersed, zero-inflated and heavy-tailed count data. The computational implementation of the proposed models is fast, relying only on a simple Newton scoring algorithm. Simulation studies showed that the estimating function approach provides unbiased and consistent estimators for both regression and dispersion parameters. We highlight the ability of the Poisson–Tweedie distributions to deal with count data through a consideration of dispersion, zero-inflated and heavy tail indices, and illustrate its application with four data analyses. We provide an R implementation and the datasets as supplementary materials.

Population-Based Pharmacokinetic and Exposure-Efficacy Analyses of Peginterferon Beta-1a in Patients With Relapsing Multiple Sclerosis

Peginterferon beta‐1a reduced annualized relapse rate as compared with placebo and was approved to treat multiple sclerosis patients. A population pharmacokinetic and an exposure‐efficacy model were developed to establish the quantitative relationship between pharmacokinetics and annualized relapse rate. The pharmacokinetics was well described by a 1‐compartment model with first‐order absorption and linear elimination kinetics. Body mass index was the most significant covariate that impacted both clearance and volume of distribution, which in turn impacted area under the curve and maximum serum concentration. Cumulative monthly area under the curve and annualized relapse rate were best described by a Poisson‐gamma (negative binomial) model, demonstrating that the improved efficacy of every‐2‐weeks dosing was driven by greater drug exposure. The results supported the superior efficacy of the every‐2‐week dosing regimen compared with the every‐4‐weeks dosing regimen.

Uncertainty of fast biological radiation dose assessment for emergency response scenarios

PURPOSE

Reliable dose estimation is an important factor in appropriate dosimetric triage categorization of exposed individuals to support radiation emergency response.

MATERIALS AND METHODS

Following work done under the EU FP7 MULTIBIODOSE and RENEB projects, formal methods for defining uncertainties on biological dose estimates are compared using simulated and real data from recent exercises.

RESULTS

The results demonstrate that a Bayesian method of uncertainty assessment is the most appropriate, even in the absence of detailed prior information. The relative accuracy and relevance of techniques for calculating uncertainty and combining assay results to produce single dose and uncertainty estimates is further discussed.

CONCLUSIONS

Finally, it is demonstrated that whatever uncertainty estimation method is employed, ignoring the uncertainty on fast dose assessments can have an important impact on rapid biodosimetric categorization.