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Empirical Bayes-based Methods (EBM) is an increasingly popular form of Objective Bayesianism (OB). It is identified in particular with the statistician Bradley Efron. The main aims of this paper are, first, to describe and illustrate its main features and, second, to locate its role by comparing it with two other statistical paradigms, Subjective Bayesianism (SB) and Evidentialism. EBM's main formal features are illustrated in some detail by schematic examples. The comparison between what Efron calls their underlying "philosophies" is by way of a distinction made between confirmation and evidence. Although this distinction is sometimes made in the statistical literature, it is relatively rare and never to the same point as here. That is, the distinction is invariably spelled out intra- and not inter-paradigmatically solely in terms of one or the other accounts. The distinction made in this paper between confirmation and evidence is illustrated by two well-known statistical paradoxes: the base-rate fallacy and Popper's paradox of ideal evidence. The general conclusion reached is that each of the paradigms has a basic role to play and all are required by an adequate account of statistical inference from a technically informed and fine-grained philosophical perspective. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternative distribution to model count data exhibiting uni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined by a parametric weight function that admits up to two modes for the resulting probability mass function. Like the baseline beta-binomial distribution, the proposed distribution performs well in modeling overdispersed binomial data. Structural properties of the new distribution are studied. Raw moments are derived, which are used to describe the dispersion behavior relative to the mean and the skewness behavior. Parameter estimation is carried out using the maximum likelihood method. A simulation study is conducted in order to illustrate the behavior of the estimators. Finally, two applications illustrating the usefulness of the proposal are presented. [ABSTRACT FROM AUTHOR]

Group testing is an important element of biosecurity operations, designed to efficiently reduce the risk of introducing exotic pests and pathogens with imported agricultural products. Groups of units, such as seeds, are selected from a consignment and tested for contamination, with a positive or negative test returned for each group. These schemes are usually designed such that the probability of detecting contamination is high assuming random mixing and a somewhat arbitrary design prevalence. We propose supplementing this approach with an assessment of the distribution of the number of contaminated units conditional on testing results. We develop beta-binomial models that allow for between-consignment variability in contamination levels, as well as including beta random effects to allow for possible clustering within the groups for testing. The latent beta distributions can be considered as priors and chosen based on expert judgement, or estimated from historical test results. We show that the parameter representing within-group clustering is, unsurprisingly, effectively non-identifiable. Sensitivity analysis can be conducted by investigating the consequences of assuming different values of this parameter. We also demonstrate theoretically and empirically that the estimated probability of a consignment containing contamination and evading detection is almost perfectly robust to mis-specification of the clustering parameter. We apply the new models to large cucurbit seed lots imported into Australia where they provide important new insights on the level of undetected contamination. Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

The gamma-Poisson and beta-binomial mixture distributions are used for analyzing count-valued data, and the estimation of the hyper-parameters including the shape and/or scale parameters is important in the empirical Bayes inference. The maximum likelihood method requires the nested loops for solving the non-linear equations at each step of iteration in the EM algorithm. To avoid the extra loops, we derive the closed-form updating procedures at each step of iteration by using the score-adjusted method. The performance is compared by simulation with the maximum likelihood estimators. [ABSTRACT FROM AUTHOR]

Empirical Bayes-based Methods (EBM) is an increasingly popular form of Objective Bayesianism (OB). It is identified in particular with the statistician Bradley Efron. The main aims of this paper are, first, to describe and illustrate its main features and, second, to locate its role by comparing it with two other statistical paradigms, Subjective Bayesianism (SB) and Evidentialism. EBM’s main formal features are illustrated in some detail by schematic examples. The comparison between what Efron calls their underlying “philosophies” is by way of a distinction made between confirmation and evidence. Although this distinction is sometimes made in the statistical literature, it is relatively rare and never to the same point as here. That is, the distinction is invariably spelled out intra- and not inter-paradigmatically solely in terms of one or the other accounts. The distinction made in this paper between confirmation and evidence is illustrated by two well-known statistical paradoxes: the base-rate fallacy and Popper’s paradox of ideal evidence. The general conclusion reached is that each of the paradigms has a basic role to play and all are required by an adequate account of statistical inference from a technically informed and fine-grained philosophical perspective.

In this paper, we propose an alternative distribution to model count data exhibiting uni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined by a parametric weight function that admits up to two modes for the resulting probability mass function. Like the baseline beta-binomial distribution, the proposed distribution performs well in modeling overdispersed binomial data. Structural properties of the new distribution are studied. Raw moments are derived, which are used to describe the dispersion behavior relative to the mean and the skewness behavior. Parameter estimation is carried out using the maximum likelihood method. A simulation study is conducted in order to illustrate the behavior of the estimators. Finally, two applications illustrating the usefulness of the proposal are presented.

We study a natural Markov chain on { 0 , 1 , ... , n } with eigenvectors the Hahn polynomials. This explicit diagonalization makes it possible to get sharp rates of convergence to stationarity. The process, the Burnside process, is a special case of the celebrated 'Swendsen–Wang' or 'data augmentation' algorithm. The description involves the beta-binomial distribution and Mallows model on permutations. It introduces a useful generalization of the Burnside process. [ABSTRACT FROM AUTHOR]

The human immunodeficiency virus (HIV) is a viral infection that destroys the human immune system resulting in acquired immunodeficiency syndrome (AIDS). The Zambia HIV prevalence rate (11.3%) remains among the highest in the sub-Saharan Africa. In the treatment of HIV-naive patients, a problem that relates to the transmitted drug resistance mutation strains (TDRMs) occurs in the administration of antiretroviral (ARV) drugs. To address this problem, we propose the use of transition probabilities when prescribing a switch from the first-line to the second-line or to the third-line regimen on the ARV drugs combination. We formulate a statistical technique to determine an optimal ARV drugs combination. To compute a transition probability matrix chart on ARV drugs combinations of the first-line and second-line regimens, we apply a beta-binomial hierarchical model on HIV data. The transition probability matrices corresponding to the ARV drugs combinations TDF+ETC+NVP, TDF+FTC+EFV, AZT+3TC+NVP, AZT+3TC+EFV, D4T+3TC+NVP, and D4T+3TC+EFV provide an upper triangular matrix of probabilities. We observe a higher probability of remaining in the same regimen state than moving to another state. A transition probability chart provides information on the most effective combination to prescribe to a patient in the presence of transmitted drug resistance mutation (TDRM) test results. The transmission probabilities play a major role in aiding the physicians make an informed decision to prescribe an optimal ARV drugs combination. We suggest a TDRM test to be carried out to all newly diagnosed HIV individuals before prescribing any of the ARV drugs combination. [ABSTRACT FROM AUTHOR]

Featured Application: The results in this article are applicable to the signal detection in a service process and the monitoring of an intelligent automated process. Automation in the service industry is emerging as a new wave of industrial revolution. Standardization and consistency of service quality is an important part of the automation process. The quality control methods widely used in the manufacturing industry can provide service quality measurement and service process monitoring. In particular, the control chart as an online monitoring technique can be used to quickly detect whether a service process is out of control. However, the control of the service process is more difficult than that of the manufacturing process because the variability of the service process comes from widespread and complex factors. First of all, the distribution of the service process is usually non-normal or unknown. Moreover, the skewness of the process distribution can be time-varying, even if the process is in control. In this study, a Bayesian procedure is applied to construct a Phase II exponential weighted moving average (EWMA) control chart for monitoring the variance of a distribution-free process. We explore the sampling properties of the new monitoring statistic, which is suitable for monitoring the time-varying process distribution. The average run lengths (ARLs) of the proposed Bayesian EWMA variance chart are calculated, and they show that the chart performs well. The simulation studies for a normal process, exponential process, and the mixed process of normal and exponential distribution prove that our chart can quickly detect any shift of a process variance. Finally, a numerical example of bank service time is used to illustrate the application of the proposed Bayesian EWMA variance chart and confirm the performance of the process control. [ABSTRACT FROM AUTHOR]

Estimating the precision of a single proportion via a 100(1-α)% confidence interval in the presence of clustered data is an important statistical problem. It is necessary to account for possible over-dispersion, for instance, in animal-based teratology studies with within-litter correlation, epidemiological studies that involve clustered sampling, and clinical trial designs with multiple measurements per subject. Several asymptotic confidence interval methods have been developed, which have been found to have inadequate coverage of the true proportion for small-to-moderate sample sizes. In addition, many of the best-performing of these intervals have not been directly compared with regard to the operational characteristics of coverage probability and empirical length. This study uses Monte Carlo simulations to calculate coverage probabilities and empirical lengths of five existing confidence intervals for clustered data across various true correlations, true probabilities of interest, and sample sizes. In addition, we introduce a new score-based confidence interval method, which we find to have better coverage than existing intervals for small sample sizes under a wide range of scenarios. [ABSTRACT FROM AUTHOR]

Overdispersion is a common phenomenon in count datasets, that can greatly affect inferences about the model. In this paper develop three joint mean and dispersion regression models in order to fit overdispersed data. These models are based on reparameterizations of the beta-binomial and negative binomial distributions. Finally, we propose a Bayesian approach to estimate the parameters of the overdispersion regression models and use it to fit a school absenteeism dataset.

Somatic sequence variants are associated with cancer diagnosis, prognostic stratification, and treatment response. Variant allele frequency (VAF), the percentage of sequence reads with a specific DNA variant over the read depth at that locus, has been used as a metric to quantify mutation rates in these applications. VAF has the potential for feature detection by reflecting changes in tumor clonal composition across treatments or time points. Although there are several packages, including Genome Analysis Toolkit and VarScan, designed for variant calling and rare mutation identification, there is no readily available package for comparing VAFs among and between groups to identify loci of interest. To this end, we have developed the R package easyVAF, which includes parametric and nonparametric tests to compare VAFs among multiple groups. It is accompanied by an interactive R Shiny app. With easyVAF, the investigator has the option between three statistical tests to maximize power while maintaining an acceptable type I error rate. This paper presents our proposed pipeline for VAF analysis, from quality checking to group comparison. We evaluate our method in a wide range of simulated scenarios and show that choosing the appropriate test to limit the type I error rate is critical. For situations where data is sparse, we recommend comparing VAFs with the beta-binomial likelihood ratio test over Fisher's exact test and Pearson's χ 2 test., (© 2023 Wiley Periodicals LLC.)

Automation in the service industry is emerging as a new wave of industrial revolution. Standardization and consistency of service quality is an important part of the automation process. The quality control methods widely used in the manufacturing industry can provide service quality measurement and service process monitoring. In particular, the control chart as an online monitoring technique can be used to quickly detect whether a service process is out of control. However, the control of the service process is more difficult than that of the manufacturing process because the variability of the service process comes from widespread and complex factors. First of all, the distribution of the service process is usually non-normal or unknown. Moreover, the skewness of the process distribution can be time-varying, even if the process is in control. In this study, a Bayesian procedure is applied to construct a Phase II exponential weighted moving average (EWMA) control chart for monitoring the variance of a distribution-free process. We explore the sampling properties of the new monitoring statistic, which is suitable for monitoring the time-varying process distribution. The average run lengths (ARLs) of the proposed Bayesian EWMA variance chart are calculated, and they show that the chart performs well. The simulation studies for a normal process, exponential process, and the mixed process of normal and exponential distribution prove that our chart can quickly detect any shift of a process variance. Finally, a numerical example of bank service time is used to illustrate the application of the proposed Bayesian EWMA variance chart and confirm the performance of the process control.

Patient‐reported outcomes (PROs) are currently being increasingly used as primary outcome measures in observational and experimental studies since they inform clinicians and researchers about the health‐status of patients and generate data to facilitate improved care. PROs usually appear as discrete and bounded with U, J, or inverse J shapes, and hence, exponential family members offer inadequate distributional fits. The beta‐binomial distribution has been proposed in the literature to fit PROs. However, the fact that the beta‐binomial distribution does not belong to the exponential family limits its applicability in the regression model context, and classical estimation approaches are not straightforward. Moreover, PROs are usually measured in a longitudinal framework in which individuals are followed up for a certain period. Hence, each individual obtains several scores of the PRO over time, which leads to the repeated measures and defines the correlation structure in the data. In this work, we have developed and proposed an estimation procedure for the analysis of correlated discrete and bounded outcomes, particularly PROs, by a beta‐binomial mixed‐effects model. Additionally, we have implemented the methodology in the PROreg package in R. Because there are similar approaches in the literature to address the same issue, this work also incorporates a comparison study between our proposal and alternative methodologies commonly implemented in R and shows the superior performance of our estimation procedure. This paper was motivated by the analysis of the health‐status of patients with chronic obstructive pulmonary disease, where the main objective is the assessment of risk factors that may affect the evolution of the disease. The application of the proposed approach in the study leads to clinically relevant results. [ABSTRACT FROM AUTHOR]

This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Background: Even in normally cycling women, hormone level shapes may widely vary between cycles and between women. Over decades, finding ways to characterize and compare cycle hormone waves was difficult and most solutions, in particular polynomials or splines, do not correspond to physiologically meaningful parameters.Objective: We present an original concept to characterize most hormone waves with only two parameters.Methods: The modelling attempt considered pregnanediol-3-alpha-glucuronide (PDG) and luteinising hormone (LH) levels in 266 cycles (with ultrasound-identified ovulation day) in 99 normally fertile women aged 18 to 45. The study searched for a convenient wave description process and carried out an extended search for the best fitting density distribution.Results: The highly flexible beta-binomial distribution offered the best fit of most hormone waves and required only two readily available and understandable wave parameters: location and scale. In bell-shaped waves (e.g., PDG curves), early peaks may be fitted with a low location parameter and a low scale parameter; plateau shapes are obtained with higher scale parameters. I-shaped, J-shaped, and U-shaped waves (sometimes the shapes of LH curves) may be fitted with high scale parameter and, respectively, low, high, and medium location parameter. These location and scale parameters will be later correlated with feminine physiological events.Conclusion: Our results demonstrate that, with unimodal waves, complex methods (e.g., functional mixed effects models using smoothing splines, second-order growth mixture models, or functional principal-component- based methods) may be avoided. The use, application, and, especially, result interpretation of four-parameter analyses might be advantageous within the context of feminine physiological events. [ABSTRACT FROM AUTHOR]

In meta-analysis of odds ratios (ORs), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative REM for ORs uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intra-class correlation (ICC) parameter. This model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta-distributed, resulting in beta-binomial distributions. We propose two new estimators of the ICC for meta-analysis in this setting. One is based on the inverted Breslow-Day test, and the other on the improved gamma approximation by Kulinskaya and Dollinger (2015, p. 26) to the distribution of Cochran's Q. The performance of these and several other estimators of ICC on bias and coverage is studied by simulation. Additionally, the Mantel-Haenszel approach to estimation of ORs is extended to the beta-binomial model, and we study performance of various ICC estimators when used in the Mantel-Haenszel or the inverse-variance method to combine ORs in meta-analysis. The results of the simulations show that the improved gamma-based estimator of ICC is superior for small sample sizes, and the Breslow-Day-based estimator is the best for n⩾100. The Mantel-Haenszel-based estimator of OR is very biased and is not recommended. The inverse-variance approach is also somewhat biased for ORs≠1, but this bias is not very large in practical settings. Developed methods and R programs, provided in the Web Appendix, make the beta-binomial model a feasible alternative to the standard REM for meta-analysis of ORs. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

The beta-binomial model has been widely used as an analytically tractable alternative that captures the overdispersion of an intra-correlated, binomial random variable,X. However, the model validation forXhas been rarely investigated. As a beta-binomial mass function takes on a few different shapes, the model validation is examined for each of the classified shapes in this article. Further, the mean square error (MSE) is illustrated for each shape by the maximum likelihood estimator (MLE) based on a beta-binomial model approach and the method of moments estimator (MME) in order to gauge when and how much the MLE is biased. [ABSTRACT FROM PUBLISHER]

Overdispersion is a common phenomenon in count datasets, that can greatly affect inferences about the model. In this paper develop three joint mean and dispersion regression models in order to fit overdispersed data. These models are based on reparameterizations of the beta-binomial and negative binomial distributions. Finally, we propose a Bayesian approach to estimate the parameters of the overdispersion regression models and use it to fit a school absenteeism dataset. [ABSTRACT FROM AUTHOR]

Genetic variants affecting gene expression levels in humans have been mapped in the Genotype-Tissue Expression (GTEx) project. Trans -acting variants impacting many genes simultaneously through a shared transcription factor (TF) are of particular interest. Here, we developed a generalized linear model (GLM) to estimate protein-level TF activity levels in an individual-specific manner from GTEx RNA sequencing (RNA-seq) profiles. It uses observed differential gene expression after TF perturbation as a predictor and, by analyzing differential expression within pairs of neighboring genes, controls for the confounding effect of variation in chromatin state along the genome. We inferred genotype-specific activities for 55 TFs across 49 tissues. Subsequently performing genome-wide association analysis on this virtual trait revealed TF activity quantitative trait loci (aQTLs) that, as a set, are enriched for functional features. Altogether, the set of tools we introduce here highlights the potential of genetic association studies for cellular endophenotypes based on a network-based multi-omics approach. The transparent peer review record is available., Competing Interests: H.J.B. is a co-founder and shareholder of Metric Biotechnologies, Inc. T.L. is a paid advisor to GSK, Pfizer, Goldfinch Bio, and Variant Bio and has equity in Variant Bio., (© 2023 The Authors.)

En el modelamiento de datos donde se evidencia la presencia de sobredispersión, usualmente se asume que para todos los efectos de tratamiento el parámetro de sobredispersión es común. Esta situación no siempre se satisface antes; por el contrario, puede ser más frecuente que la variabilidad exhibida por los datos sea mayor que la variación teórica del modelo; debiendo incorporarse en el modelamiento esta situación. En este artículo se llevan a cabo desarrollos teóricos con los cuales se evidencia si es aceptable o no la hipótesis de homogeneidad del parámetro de dispersión entre tratamientos, cuando estos se ensayan en condiciones de uniformidad del material experimental y la respuesta de interés sea conteos o de proporciones, las cuales se modelan a través de la distribución Binomial Negativa (BN) y Beta Binomial (BB), respectivamente. Se usó la Prueba de Razón de Verosimilitud como criterio para decidir acerca de la hipótesis nula de homogeneidad en el parámetro de dispersión. Para determinar la eficiencia de la prueba propuesta, mediante simulación, con procedimientos algorítmicos desarrollados en R, se evaluó la potencia de las pruebas frente al supuesto de homogeneidad del parámetro de dispersión. Bajo el supuesto que los modelos BB y BN son correctos, se propone el ajuste de un modelo lineal generalizado ponderado como una alternativa para el análisis de datos de conteo y proporción con sobredispersión.

When analyzing data in the presence of over dispersion, the usual practice is to assume a common dispersion parameter to all observations. However, there are situations where the assumption of homogeneity of the dispersion parameter does not hold. In this paper we present theoretical developments that allow contrasting the assumption of homogeneity of the dispersion parameter between treatments, in a completely randomized design, with the responses of proportions and counts, modeled through the distributions beta-binomial and negative binomial respectively. The hypothesis is contrasted through the proof of the likelihood ratio. Under the assumption that the beta-binomial and the negative binomial models are correct, it is proposed an adjustment of a generalized linear weighted model as an alternative for the data analysis of counts and proportionswhen over dispersion is present. It is also evaluated, through simulation, the performance of the proposed proofs in terms of its power.En el modelamiento de datos donde se evidencia la presencia de sobredispersión, usualmente se asume que para todos los efectos de tratamiento el parámetro de sobredispersión es común. Esta situación no siempre se satisface antes; por el contrario, puede ser más frecuente que la variabilidad exhibida por los datos sea mayor que la variación teórica del modelo; debiendo incorporarse en el modelamiento esta situación. En este artículo se llevan a cabo desarrollos teóricos con los cuales se evidencia si es aceptable o no la hipótesis de homogeneidad del parámetro de dispersión entre tratamientos, cuando estos se ensayan en condiciones de uniformidad del material experimental y la respuesta de interés sea conteos o de proporciones, las cuales se modelan a través de la distribución Binomial Negativa (BN) y Beta Binomial (BB), respectivamente. Se usó la Prueba de Razón de Verosimilitud como criterio para decidir acerca de la hipótesis nula de homogeneidad en el parámetro de dispersión. Para determinar la eficiencia de la prueba propuesta, mediante simulación, con procedimientos algorítmicos desarrollados en R, se evaluó la potencia de las pruebas frente al supuesto de homogeneidad del parámetro de dispersión. Bajo el supuesto que los modelos BB y BN son correctos, se propone el ajuste de un modelo lineal generalizado ponderado como una alternativa para el análisis de datos de conteo y proporción con sobredispersión.

The problems of the control charts for attributes are analyzed. In particular, it is seen that the traditional procedure to obtain the control limits has several difficulties: it does not incorporate the uncertainty in the estimate of the parameter of the distribution, it does not include the variation of the process, and the procedure requires a base period to obtain the control limits. Along this period it does not have a control chart to analyze the process. It is seen that these problems are solved applying Bayesian methods. It is described a sequential procedure to obtain the Bayesian control limits for p, np, c and u charts, from the first observation. This eliminates the necessity of the base period. Lastly it is analyzed the problem of the p chart when it is based on a large subgroup size and it is proposed a Bayesian solution for this problem.Se analizan los problemas de las cartas de control para atributos. En particular, se ve que el procedimiento tradicional para obtener los límites de control tiene varias dificultades: no incorpora la incertidumbre sobre la estimación del parámetro del modelo, no contempla las variaciones en el parámetro del proceso y requiere un período base para obtener datos. Durante este período base no se tiene una carta de control para monitorear el proceso. Se ve que estos problemas son resueltos con métodos Bayesianos. Se ve cómo establecer los límites de control Bayesianos para las cartas de control p, np, c y u, en forma secuencial desde la primera observación. Esto elimina la necesidad del período base. Por último se analiza el problema de la carta p cuando esta se basa en un tamaño de subgrupo grande y se propone una solución Bayesiana para este problema.

Se analizan los problemas de las cartas de control para atributos. En particular, se ve que el procedimiento tradicional para obtener los límites de control tiene varias dificultades: no incorpora la incertidumbre sobre la estimación del parámetro del modelo, no contempla las variaciones en el parámetro del proceso y requiere un período base para obtener datos. Durante este período base no se tiene una carta de control para monitorear el proceso. Se ve que estos problemas son resueltos con métodos Bayesianos. Se ve cómo establecer los límites de control Bayesianos para las cartas de control p, np, c y u, en forma secuencial desde la primera observación. Esto elimina la necesidad del período base. Por último se analiza el problema de la carta p cuando esta se basa en un tamaño de subgrupo grande y se propone una solución Bayesiana para este problema.The problems of the control charts for attributes are analyzed. In particular, it is seen that the traditional procedure to obtain the control limits has several difficulties: it does not incorporate the uncertainty in the estimate of the parameter of the distribution, it does not include the variation of the process, and the procedure requires a base period to obtain the control limits. Along this period it does not have a control chart to analyze the process. It is seen that these problems are solved applying Bayesian methods. It is described a sequential procedure to obtain the Bayesian control limits for p, np, c and u charts, from the first observation. This eliminates the necessity of the base period. Lastly it is analyzed the problem of the p chart when it is based on a large subgroup size and it is proposed a Bayesian solution for this problem.

The 2014 West African outbreak of Ebola virus ravaged Liberia, Sierra Leone, and Guinea, causing hemorrhagic fever and death. The need to identify effective therapeutics was acute. The usual drug development paradigm of phase I, followed by phase II, and then phase III trials would take too long. These and other factors led to the design of a clinical trial of Ebola virus disease therapeutics that differs from more conventional clinical trial designs. This article describes the Ebola virus disease medical countermeasures trial design and the thinking behind it. [ABSTRACT FROM AUTHOR]

Given the aging population in the UK, statistical modelling of cognitive function in the older population is of interest. Joint models are formulated for survival and cognitive function in the older population. Because tests of cognitive function often result in discrete outcomes, binomial and beta--binomial mixed effects regression models are applied to analyse longitudinal measurements. Dropout due to death is accounted for by parametric survival models, where the choice of a Gompertz baseline hazard and the specification of the random-effects structure are of specific interest. The measurement model and the survival model are combined in a shared parameter joint model. Estimation is by marginal likelihood. The methods are used to analyse data from the Cambridge City over-75s cohort study and the English Longitudinal Study of Ageing. [ABSTRACT FROM AUTHOR]

We introducecube models with covariates, a class of discrete mixture distributions able to take uncertainty and overdispersion of ordinal data into account. The main result of the paper concerns the analytical derivation of the observed variance–covariance matrix of this model, a necessary step for the asymptotic inference about estimated parameters and model validation. We emphasize some computational aspects of the procedure and discuss the usefulness of the approach on a real case study. [ABSTRACT FROM AUTHOR]

In this paper we describe the parameter estimation of the beta-binomial distribution using the procedure NLMIXED of the SAS software. The beta-binomial distribution is a discrete mixture distribution which can capture overdispersion in the data. The estimation of parameters of the beta-binomial distribution can lead to computational problems, since it does not belong to the exponential family and there are not explicit solutions for the maximum likelihood estimation. Using a real dataset, we show that the SAS software can be satisfactorily used for the estimation of the parameters. We also consider the possibility of including a covariate in the model. The SAS codes used in this paper are given in an Appendix. [ABSTRACT FROM AUTHOR]

In real life and somewhat contrary to biostatistical textbook knowledge, sensitivity and specificity (and not only predictive values) of diagnostic tests can vary with the underlying prevalence of disease. In meta-analysis of diagnostic studies, accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects. In this paper, a new model is proposed using trivariate copulas and beta-binomial marginal distributions for sensitivity, specificity, and prevalence as an expansion of the bivariate model. Two different copulas are used, the trivariate Gaussian copula and a trivariate vine copula based on the bivariate Plackett copula. This model has a closed-form likelihood, so standard software (e.g., sas proc nlmixed) can be used. The results of a simulation study have shown that the copulamodels perform at least as good but frequently better than the standard model. The methods are illustrated by two examples. [ABSTRACT FROM AUTHOR]

This study presents a framework to assess the fair economic value of ambiguous loan portfolios, i.e. when the credit qualities of the loans within are deeply masked or simply undetermined through traditional techniques. In this case, the second best choice for approximating the portfolio’s economic value would be to lean on the past performance of the designated credit officer who either approved or rejected the loan applications. The article presents a Beta-Binomial distribution model that captures the entire spectrum of possible economic valuations and their respective likelihoods and shows that this dissemination can be summarized to a single fair economic value for any ambiguous loan portfolios. This methodology exhibits high importance to regulators, policy makers, and internal auditors. [ABSTRACT FROM AUTHOR]

Studying the incidence of inbreeding avoidance is important for understanding the evolution of mating systems, especially in the context of mate choice for genetic compatibility. We investigated whether inbreeding avoidance mechanisms have evolved in the malt fly, Drosophila montana, by measuring mating latency (a measure of male attractiveness), copulation duration, days to remating, offspring production, and the proportion of offspring sired by the first (P) and second (P) male to mate in full-sibling and unrelated pairs. SNP markers were used for paternity analysis and for calculating pairwise relatedness values (genotype sharing) between mating pairs. We found 18 % inbreeding depression in egg-to-adult viability, suggesting that mating with close relatives is costly. Copulation duration was shorter between previously mated females and their brothers than with unrelated males. Based on an earlier study, shorter copulation is likely to decrease the number of inbred progeny by decreasing female remating time. However, shorter copulations did not lead to lower paternity (P) of full-sibling males. Progeny production of double-mated females was lower when the second male was a full-sibling as compared to an unrelated male, but we could not distinguish between inbreeding depression and lower female reproductive effort after mating with a relative. Relatedness estimates based on 34 SNPs did not detect any quantitative effect of relatedness variation on copulation duration and progeny production. We suggest that inbreeding depression has been strong enough to select for inbreeding avoidance mechanisms in our Finnish D. montana population. [ABSTRACT FROM AUTHOR]