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Infant mortality is an important population health statistic that is often used to make health policy decisions. Unfortunately, these data are not available for all populations. A newly developed method is presented for accounting for the stochastic uncertainty found in infant mortality rates (IMRs) estimated from sample surveys and for the first time applied to a country in the Southeast Asian/Pacific Basin area, the Philippines. The method is founded on the fact that there are two sources of variation in sample-based estimates of IMRs: (1) sample size; and (2) variation of infant deaths. The approach is aimed at taking into account stochastic uncertainty while preserving information concerning the uncertainty due to sampling. In applying the method to the Philippines, the sample-based IMR estimates appear to perform well in terms of accounting for stochastic uncertainty. This finding is consistent with previous research assessing this approach in Africa and with variations, in Canada, Europe and the United States, which suggests that in the form presented here or in one of its variants, it could successfully be employed not only elsewhere in the Southeast Asia/Pacific Basin region but also in East Asia, North Asia, South Asia, and West Asia. [ABSTRACT FROM AUTHOR]

Cognitive functioning in older age profoundly impacts quality of life and health. While most research on cognition in older age has focused on mean levels, intraindividual variability (IIV) around this may have risk factors and outcomes independent of the mean value. Investigating risk factors associated with IIV has typically involved deriving a summary statistic for each person from residual error around a fitted mean. However, this ignores uncertainty in the estimates, prohibits exploring associations with time-varying factors, and is biased by floor/ceiling effects. To address this, we propose a mixed-effects location scale beta-binomial model for estimating average probability and IIV in a word recall test in the English Longitudinal Study of Ageing. After adjusting for mean performance, an analysis of 9,873 individuals across 7 (mean = 3.4) waves (2002–2015) found IIV to be greater at older ages, with lower education, in females, with more difficulties in activities of daily living, in later birth cohorts, and when interviewers recorded issues potentially affecting test performance. Our study introduces a novel method for identifying groups with greater IIV in bounded discrete outcomes. Our findings have implications for daily functioning and care, and further work is needed to identify the impact for future health outcomes. [ABSTRACT FROM AUTHOR]

In meta‐analyses of rare events, it can be challenging to obtain a reliable estimate of the pooled effect, in particular when the meta‐analysis is based on a small number of studies. Recent simulation studies have shown that the beta‐binomial model is a promising candidate in this situation, but have thus far only investigated its performance in a frequentist framework. In this study, we aim to make the beta‐binomial model for meta‐analysis of rare events amenable to Bayesian inference by proposing prior distributions for the effect parameter and investigating the models' robustness to different specifications of priors for the scale parameter. To evaluate the performance of Bayesian beta‐binomial models with different priors, we conducted a simulation study with two different data generating models in which we varied the size of the pooled effect, the degree of heterogeneity, the baseline probability, and the sample size. Our results show that while some caution must be exercised when using the Bayesian beta‐binomial in meta‐analyses with extremely sparse data, the use of a weakly informative prior for the effect parameter is beneficial in terms of mean bias, mean squared error, and coverage. For the scale parameter, half‐normal and exponential distributions are identified as candidate priors in meta‐analysis of rare events using the Bayesian beta‐binomial model. [ABSTRACT FROM AUTHOR]

Abstract Background Meta-analyses are used to summarise the results of several studies on a specific research question. Standard methods for meta-analyses, namely inverse variance random effects models, have unfavourable properties if only very few (2 – 4) studies are available. Therefore, alternative meta-analytic methods are needed. In the case of binary data, the “common-rho” beta-binomial model has shown good results in situations with sparse data or few studies. The major concern of this model is that it ignores the fact that each treatment arm is paired with a respective control arm from the same study. Thus, the randomisation to a study arm of a specific study is disrespected, which may lead to compromised estimates of the treatment effect. Therefore, we extended this model to a version that respects randomisation. The aim of this simulation study was to compare the “common-rho” beta-binomial model and several other beta-binomial models with standard meta-analyses models, including generalised linear mixed models and several inverse variance random effects models. Methods We conducted a simulation study comparing beta-binomial models and various standard meta-analysis methods. The design of the simulation aimed to consider meta-analytic situations occurring in practice. Results No method performed well in scenarios with only 2 studies in the random effects scenario. In this situation, a fixed effect model or a qualitative summary of the study results may be preferable. In scenarios with 3 or 4 studies, most methods satisfied the nominal coverage probability. The “common-rho” beta-binomial model showed the highest power under the alternative hypothesis. The beta-binomial model respecting randomisation did not improve performance. Conclusion The “common-rho” beta-binomial appears to be a good option for meta-analyses of very few studies. As residual concerns about the consequences of disrespecting randomisation may still exist, we recommend a sensitivity analysis with a standard meta-analysis method that respects randomisation.

Abstract Background Patients with esophageal squamous cell carcinoma (ESCC) with lymph node metastasis may be misclassified as pN0 due to an insufficient number of lymph nodes examined (LNE). The purpose of this study was to confirm that patients with ESCC are indeed pN0 and to propose an adequate number for the correct nodal stage using the nodal staging score (NSS) developed by the beta‐binomial model. Methods A total of 1249 patients from the Surveillance, Epidemiology, and End Results (SEER) database between 2000 and 2017, and 1404 patients diagnosed with ESCC in our database between 2005 and 2018 were included. The NSS was developed to assess the probability of pN0 status based on both databases. The effectiveness of NSS was verified using survival analysis, including Kaplan–Meier curves and Cox models. Results Many patients were misclassified as pN0 based on our algorithm due to insufficient LNE. As the number of LNE increased, false‐negative findings dropped; accordingly, the NSS increased. In addition, NSS was an independent prognostic indicator for pN0 in patients with ESCC in the SEER database (hazard ratio [HR] 0.182, 95% confidence interval [CI] 0.046–0.730, p = 0.016) and our database (HR 0.215, 95% CI 0.055–0.842, p = 0.027). A certain number of nodes must be examined to achieve 90% of the NSS. Conclusions NSS could determine the probability of true pN0 status for patients, and it was sufficient in predicting survival and obtaining adequate numbers for lymphadenectomy.

Infant mortality is an important population health statistic that is often used to make health policy decisions. For a small population, an infant mortality rate is subject to high levels of uncertainty and may not indicate the “underlying” mortality regime affecting the population. This situation leads some agencies to either not report infant mortality for these populations or report infant mortality aggregated over space, time or both. A method is presented for estimating “underlying” infant mortality rates that reflect the intrinsic mortality regimes of small populations. The method is described and illustrated in a case study by estimating IMRs for the 15 counties in California where zero infant deaths are reported at the county level for the period 2009-2011. We know that among these 15 counties there are 50 infant deaths reported at the state level but not for the counties in which they occurred. The method’s validity is tested using a synthetic population in the form of a simulated data set generated from a model life table infant mortality rate, representing Level 23 of the West Family Model Life Table for both sexes. The test indicates that the method is capable of producing estimates that represent underlying rates. In this regard, the method described here may assist in the generation of information about the health status of small populations.

Meta‐analysis of binary data is challenging when the event under investigation is rare, and standard models for random‐effects meta‐analysis perform poorly in such settings. In this simulation study, we investigate the performance of different random‐effects meta‐analysis models in terms of point and interval estimation of the pooled log odds ratio in rare events meta‐analysis. First and foremost, we evaluate the performance of a hypergeometric‐normal model from the family of generalized linear mixed models (GLMMs), which has been recommended, but has not yet been thoroughly investigated for rare events meta‐analysis. Performance of this model is compared to performance of the beta‐binomial model, which yielded favorable results in previous simulation studies, and to the performance of models that are frequently used in rare events meta‐analysis, such as the inverse variance model and the Mantel–Haenszel method. In addition to considering a large number of simulation parameters inspired by real‐world data settings, we study the comparative performance of the meta‐analytic models under two different data‐generating models (DGMs) that have been used in past simulation studies. The results of this study show that the hypergeometric‐normal GLMM is useful for meta‐analysis of rare events when moderate to large heterogeneity is present. In addition, our study reveals important insights with regard to the performance of the beta‐binomial model under different DGMs from the binomial‐normal family. In particular, we demonstrate that although misalignment of the beta‐binomial model with the DGM affects its performance, it shows more robustness to the DGM than its competitors. [ABSTRACT FROM AUTHOR]

When making comparisons between groups of students, a common technique is to analyze whether there are statistically significant differences between the means of each group. This convention, however, is problematic when data are negatively skewed and bounded against a performance ceiling, features that are typical of data in education settings. In such a situation, we might be particularly interested to observe group differences in the left tail, specifically among students who have room to improve, and conventional analyses of group means have limitations for detecting such differences. In this article, an alternative to these conventions is presented. Rather than comparing the means of two groups, we can instead compare how closely student data are concentrated toward the modes of each group. Bayesian methods provide an ideal framework for this kind of analysis because they enable us to make flexible comparisons between parameter estimates in custom analytical models. A Bayesian approach for examining concentration toward the mode is outlined and then demonstrated using public data from a previously reported classroom experiment. Using only the outcome data from this prior experiment, the proposed method observes a credible difference in concentration between groups, whereas conventional tests show no significant overall differences between group means. The present article underscores the limitations of conventional statistical assumptions and hypotheses, especially in school psychology and related fields, and offers a method for making more flexible comparisons in the concentration of data between groups. [ABSTRACT FROM AUTHOR]

Background: Meta-analyses are used to summarise the results of several studies on a specific research question. Standard methods for meta-analyses, namely inverse variance random effects models, have unfavourable properties if only very few (2 – 4) studies are available. Therefore, alternative meta-analytic methods are needed. In the case of binary data, the "common-rho" beta-binomial model has shown good results in situations with sparse data or few studies. The major concern of this model is that it ignores the fact that each treatment arm is paired with a respective control arm from the same study. Thus, the randomisation to a study arm of a specific study is disrespected, which may lead to compromised estimates of the treatment effect. Therefore, we extended this model to a version that respects randomisation. The aim of this simulation study was to compare the "common-rho" beta-binomial model and several other beta-binomial models with standard meta-analyses models, including generalised linear mixed models and several inverse variance random effects models. Methods: We conducted a simulation study comparing beta-binomial models and various standard meta-analysis methods. The design of the simulation aimed to consider meta-analytic situations occurring in practice. Results: No method performed well in scenarios with only 2 studies in the random effects scenario. In this situation, a fixed effect model or a qualitative summary of the study results may be preferable. In scenarios with 3 or 4 studies, most methods satisfied the nominal coverage probability. The "common-rho" beta-binomial model showed the highest power under the alternative hypothesis. The beta-binomial model respecting randomisation did not improve performance. Conclusion: The "common-rho" beta-binomial appears to be a good option for meta-analyses of very few studies. As residual concerns about the consequences of disrespecting randomisation may still exist, we recommend a sensitivity analysis with a standard meta-analysis method that respects randomisation. [ABSTRACT FROM AUTHOR]

Background: Patients with esophageal squamous cell carcinoma (ESCC) with lymph node metastasis may be misclassified as pN0 due to an insufficient number of lymph nodes examined (LNE). The purpose of this study was to confirm that patients with ESCC are indeed pN0 and to propose an adequate number for the correct nodal stage using the nodal staging score (NSS) developed by the beta‐binomial model. Methods: A total of 1249 patients from the Surveillance, Epidemiology, and End Results (SEER) database between 2000 and 2017, and 1404 patients diagnosed with ESCC in our database between 2005 and 2018 were included. The NSS was developed to assess the probability of pN0 status based on both databases. The effectiveness of NSS was verified using survival analysis, including Kaplan–Meier curves and Cox models. Results: Many patients were misclassified as pN0 based on our algorithm due to insufficient LNE. As the number of LNE increased, false‐negative findings dropped; accordingly, the NSS increased. In addition, NSS was an independent prognostic indicator for pN0 in patients with ESCC in the SEER database (hazard ratio [HR] 0.182, 95% confidence interval [CI] 0.046–0.730, p = 0.016) and our database (HR 0.215, 95% CI 0.055–0.842, p = 0.027). A certain number of nodes must be examined to achieve 90% of the NSS. Conclusions: NSS could determine the probability of true pN0 status for patients, and it was sufficient in predicting survival and obtaining adequate numbers for lymphadenectomy. [ABSTRACT FROM AUTHOR]

Individual‐based abundance data and sample‐based incidence data are the two most widely used survey data formats to assess the species diversity in a target area, where the sample‐based incidence data are more available and efficient for estimating species richness. For species individual with spatial aggregation, individual‐unit‐based random sampling scheme is difficult to implement, and quadrat‐unit‐based sampling scheme is more available to implement and more likely to fit the model assumption of random sampling. In addition, sample‐based incidence data, without recording the number of individuals of a species and only recording the binary presence or absence of a species in the sampled unit, could considerably reduce the survey loading in the field.In this study, according to sample‐based incidence data and based on a beta‐binomial model assumption, instead of using the maximum likelihood method, I used the moment method to derive the richness estimator. The proposed richness estimation method provides a lower bound estimator of species richness for beta‐binomial models, in which the new method only uses the number of singletons, doubletons and tripletons in the sample to estimate undetected richness.I evaluated the proposed estimator using simulated datasets generated from various species abundance models. For highly heterogeneous communities, the simulation results indicate that the proposed estimator could provide a more stable, less biased estimate and a more accurate 95% confidence interval of true richness compared to other traditional parametric‐based estimators.I also applied the proposed approach to real datasets for assessment and comparison with traditional estimators. The newly proposed richness estimator provides different information and conclusions from other estimators. [ABSTRACT FROM AUTHOR]

DNA methylation is an important epigenetic modification involved in gene regulation. Advances in the next generation sequencing technology have enabled the retrieval of DNA methylation information at single-base-resolution. However, due to the sequencing process and the limited amount of isolated DNA, DNA-methylation-data are often noisy and sparse, which complicates the identification of differentially methylated regions (DMRs), especially when few replicates are available. We present a varying-coefficient model for detecting DMRs by using single-base-resolved methylation information. The model simultaneously smooths the methylation profiles and allows detection of DMRs, while accounting for additional covariates. The proposed model takes into account possible overdispersion by using a beta-binomial distribution. The overdispersion itself can be modeled as a function of the genomic region and explanatory variables. We illustrate the properties of the proposed model by applying it to two real-life case studies. [Display omitted] • Flexible modeling of bisulfite sequencing data assuming beta-binomial distribution. • Estimation of smooth effects of explanatory variables. • Detection of differentially methylated regions. • Applicable to targeted and whole-genome-sequencing data. [ABSTRACT FROM AUTHOR]

In evidence synthesis, dealing with zero‐events studies is an important and complicated task that has generated broad discussion. Numerous methods provide valid solutions to synthesizing data from studies with zero‐events, either based on a frequentist or a Bayesian framework. Among frequentist frameworks, the one‐stage methods have their unique advantages to deal with zero‐events studies, especially for double‐arm‐zero‐events. In this article, we give a concise overview of the one‐stage frequentist methods. We conducted simulation studies to compare the statistical properties of these methods to the two‐stage frequentist method (continuity correction) for meta‐analysis with zero‐events studies when double‐zero‐events studies were included. Our simulation studies demonstrated that the generalized estimating equation with unstructured correlation and beta‐binomial method had the best performance among the one‐stage methods. The random intercepts generalized linear mixed model showed good performance in the absence of obvious between‐study variance. Our results also showed that the continuity correction with inverse‐variance heterogeneous (IVhet) analytic model based on the two‐stage framework had good performance when the between‐study variance was obvious and the group size was balanced for included studies. In summary, the one‐stage framework has unique advantages to deal with studies with zero events and is not susceptive to group size ratio. It should be considered in future meta‐analyses whenever possible. [ABSTRACT FROM AUTHOR]

Biological products are known to have some between-batch variation. However, the traditional method to assess biosimilarity does not consider such between-batch variation. Beta-binomial models and linear random effect models are considered in order to incorporate between-batch variation for the binary endpoints and the continuous endpoints, respectively. In this article, emphasis is on the beta-binomial models for the binary endpoint case. For the linear random effect models of the continuous endpoint case, we cite relevant references along with conducting some simulation studies. Overall, we show that the type I error rates are inflated when biosimilarity is evaluated by the traditional method, which ignores between-batch variation. [ABSTRACT FROM AUTHOR]

Weixing Dai,1,2,* Yaqi Li,1,2,* Zhenyu Wu,3,* Yang Feng,1,2 Sanjun Cai,1,2 Ye Xu,1,2 Qingguo Li,1,2 Guoxiang Cai1,2 1Department of Colorectal Surgery, Fudan University Shanghai Cancer Center, Shanghai 200032, China; 2Department of Oncology, Shanghai Medical College, Fudan University, Shanghai 200032, China; 3Department of Biostatistics, School of Public Health Safety, Ministry of Education, Fudan University, Shanghai 200032, China *These authors contributed equally to this work Background: Lymph node status can predict the prognosis of patients with rectal cancer treated with surgery. Thus, we sought to establish a standard for the minimum number of lymph nodes (LNs) examined in patients with rectal cancer by evaluating the probability that pathologically negative LNs prove positive during surgery. Patients and methods: We extracted information of 31,853 patients with stage I–III rectal carcinoma registered between 2004 and 2013 from the Surveillance, Epidemiology, and End Results database and divided them into two groups: the first group was SURG, including patients receiving surgery directly and the other group was NEO, encompassing those underwent neoadjuvant therapy. Using a beta-binomial model, we developed nodal staging score (NSS) based on pT/ypT stage and the number of LNs retrieved. Results: In both cohorts, the false-negative rate was estimated to be 16% when 12 LNs were examined, but it dropped to 10% when 20 LNs were evaluated. In the SURG cohort, to rule out 90% possibility of false staging, 3, 7, 28, and 32 LNs would be necessarily examined in patients with pT1–4 disease, respectively. While in the NEO cohort, 4, 7, 12, and 16 LNs would be included for examination in patients with ypT1–4 disease to guarantee an NSS of 90%. Conclusion: By determining whether a rectal cancer patient with negative LNs was appropriately staged, the NSS model we developed in this study may assist in tailoring postoperative management. Keywords: nodal staging score, rectal cancer, lymph node, neoadjuvant therapy, beta-binomial model

In Bayesian analysis, the well-known beta–binomial model is largely used as a conjugate structure, and the beta prior distribution is a natural choice to model parameters defined in the (0,1) range. The Kumaraswamy distribution has been used as a natural alternative to the beta distribution and has received great attention in statistics in the past few years, mainly due to the simplicity and the great variety of forms it can assume. However, the binomial–Kumaraswamy model is not conjugate, which may limit its use in situations where conjugacy is desired. This work provides the exact posterior distribution for the binomial–Kumaraswamy model using special functions. Besides the exact forms of the posterior moments, the predictive and the cumulative posterior distributions are provided. An example is used to illustrate the theory, in which the exact computation and the MCMC method are compared. [ABSTRACT FROM AUTHOR]

The pathogenicity of fifteen isolates of Beauveria bassiana against German cockroach (Blattella germanica, Linnaeus, 1767) at three instars was tested and analysed in order to find the best fungal isolate available for the mortality of cockroaches. For the bioassay, three groups of instars were inoculated with a spore suspension, and the subsequent mortality recorded, the response variable was the number of dead cockroaches of a total of 10. For analysing proportion data, three models were analysed: binomial, quasi-binomial, and beta-binomial models. Due overdispersion, binomial model was not appropriate, quasi-binomial and beta-binomial statistical models were suitable for the analysed data. The quasi-binomial model provided a numerically greater standard error than the beta-binomial model although the difference was not significant. All tested isolates of B. bassiana were pathogenic to German cockroaches, although the average mortality percentages differed among isolates. The instar of German cockroach was a significant factor in the pathogenicity of fungal isolates, the pathogenicity of B. bassiana was greater in adult cockroaches and first instars compared with second instars. Four groups of isolates were detected, based on p-values of the hypothesis test of the difference between isolates; Each group of isolates showed statistically the same mortality percentage within the group but differences between groups. The group with the highest percentage of pathogenicity effectiveness against German cockroach (above 74%) only contained isolates derived from Metamasius spinolae at the instar of pupa and larvae, these isolates could be considered for biological control of German cockroach. [ABSTRACT FROM AUTHOR]

For the restricted parameter space (0,1), we propose Zhang's loss function which satisfies all the 7 properties for a good loss function on (0,1). We then calculate the Bayes rule (estimator), the posterior expectation, the integrated risk, and the Bayes risk of the parameter in (0,1) under Zhang's loss function. We also calculate the usual Bayes estimator under the squared error loss function, and the Bayes estimator has been proved to underestimate the Bayes estimator under Zhang's loss function. Finally, the numerical simulations and a real data example of some monthly magazine exposure data exemplify our theoretical studies of two size relationships about the Bayes estimators and the Posterior Expected Zhang's Losses (PEZLs). [ABSTRACT FROM AUTHOR]

For meta‐analysis of studies that report outcomes as binomial proportions, the most popular measure of effect is the odds ratio (OR), usually analyzed as log(OR). Many meta‐analyses use the risk ratio (RR) and its logarithm because of its simpler interpretation. Although log(OR) and log(RR) are both unbounded, use of log(RR) must ensure that estimates are compatible with study‐level event rates in the interval (0, 1). These complications pose a particular challenge for random‐effects models, both in applications and in generating data for simulations. As background, we review the conventional random‐effects model and then binomial generalized linear mixed models (GLMMs) with the logit link function, which do not have these complications. We then focus on log‐binomial models and explore implications of using them; theoretical calculations and simulation show evidence of biases. The main competitors to the binomial GLMMs use the beta‐binomial (BB) distribution, either in BB regression or by maximizing a BB likelihood; a simulation produces mixed results. Two examples and an examination of Cochrane meta‐analyses that used RR suggest bias in the results from the conventional inverse‐variance–weighted approach. Finally, we comment on other measures of effect that have range restrictions, including risk difference, and outline further research. [ABSTRACT FROM AUTHOR]

In cluster randomized trials, it is often of interest to estimate the common intraclass correlation at the design stage for sample size and power calculations, which are greatly affected by the value of a common intraclass correlation. In this article, we construct confidence intervals (CIs) for the common intraclass correlation coefficient of several treatment groups. We consider the profile likelihood (PL)-based approach using the beta-binomial models and the approach based on the concept of generalized pivots using the ANOVA estimator and its asymptotic variance. We compare both approaches with a number of large sample procedures as well as both parametric and nonparametric bootstrap procedures in terms of coverage and expected CI length through a simulation study, and illustrate the methodology with two examples from biomedical fields. The results support the use of the PL-based CI as it holds the preassigned confidence level very well and overall gives a very competitive length. [ABSTRACT FROM AUTHOR]

We discover three interesting strings of inequalities among six Bayes estimators, where for the parameter space (0, 1), (0, ∞), and ( − ∞, ∞), each case has a string of inequalities. The three strings of inequalities only depend on the loss functions, and the inequalities are independent of the chosen models and the used priors provided the Bayes estimators exist. Therefore, they exist in a general setting which makes them quite interesting. Finally, the numerical simulations exemplify the two strings of inequalities defined on (0, 1) and (0, ∞), and that there does not exist a string of inequalities among the six smallest posterior expected losses. [ABSTRACT FROM PUBLISHER]

Empirical differential privacy (EDP) has been proposed as an alternative to differential privacy (DP), with the important advantages that the procedure can be applied to any bayesian model and requires less technical work from the part of the user. While EDP has been shown to be easy to implement, little is known of its theoretical underpinnings. This paper proposes a careful investigation of the meaning and limits of EDP as a measure of privacy. We show that EDP can not simply be considered an empirical version of DP, and that it could instead be thought of as a sensitivity measure on posterior distributions. We also show that EDP is not well-defined, in that its value depends crucially on the choice of discretization used in the procedure, and that it can be very computationnaly intensive to apply in practice. We illustrate these limitations with two simple conjugate bayesian model: the beta-binomial model and the normal-normal model.

We propose the power-log loss function plotted in Figure 1 for the restricted parameter space, which satisfies all the six properties listed in Table 1 for a good loss function on. In particular, the power-log loss function penalizes gross overestimation and gross underestimation equally, is convex in its argument, and attains its global minimum at the true unknown parameter. The power-log loss function onis an analog of the power-log loss function on, which is the popular Stein's loss function. We then calculate the Bayes rule (estimator) of the parameter inunder the power-log loss function, the posterior expected power-log loss (PEPLL) at the Bayes estimator, and the integrated risk under the power-log loss (IRPLL) at the Bayes estimator, which is also the Bayes risk under the power-log loss (BRPLL). We also calculate the usual Bayes estimator under the squared error loss, which has been proved to be larger than that under the power-log loss. Next, we analytically calculate the Bayes estimators and the PEPLL at the Bayes estimators under a beta-binomial model. Finally, the numerical simulations and a real data example of some monthly magazine exposure data exemplify our theoretical studies of two size relationships about the Bayes estimators and the PEPLLs. [ABSTRACT FROM AUTHOR]

Data in the form of proportions with extra-dispersion (over/under) arise in many biomedical, epidemiological, and toxicological applications. In some situations, two samples of data in the form of proportions with extra-dispersion arise in which the problem is to test the equality of the proportions in the two groups with unspecified and possibly unequal extra-dispersion parameters. This problem is analogous to the traditional Behrens-Fisher problem in which two normal population means with possibly unequal variances are compared. To deal with this problemwe develop eight tests and compare them in terms of empirical size and power, using a simulation study. Simulations show that a C(α) test based on extended quasi-likelihood estimates of the nuisance parameters holds nominal level most effectively (close to the nominal level) and it is at least as powerful as any other statistic that is not liberal. It has the simplest formula, is based on estimates of the nuisance parameters only under the null hypothesis, and is easiest to calculate. Also, it is robust in the sense that no distributional assumption is required to develop this statistic. [ABSTRACT FROM AUTHOR]

The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses, and for its assessment, Bayesian methods are widespread in the forensic field. However, the Bayesian 'recipe' for the LR presented in most of the literature consists of plugging-in Bayesian estimates of the involved nuisance parameters into a frequentist-defined LR: frequentist and Bayesian methods are thus mixed, giving rise to solutions obtained by hybrid reasoning. This paper provides the derivation of a proper Bayesian approach to assess LRs for the 'rare type match problem', the situation in which the expert wants to evaluate a match between the DNA profile of a suspect and that of a trace from the crime scene, and this profile has never been observed before in the database of reference. LR assessment using the two most popular Bayesian models (beta-binomial and Dirichlet-multinomial) is discussed and compared with corresponding plug-in versions. [ABSTRACT FROM AUTHOR]

Longitudinal binomial data are frequently generated from multiple questionnaires and assessments in various scientific settings for which the binomial data are often overdispersed. The standard generalized linear mixed effects model may result in severe underestimation of standard errors of estimated regression parameters in such cases and hence potentially bias the statistical inference. In this paper, we propose a longitudinal beta-binomial model for overdispersed binomial data and estimate the regression parameters under a probit model using the generalized estimating equation method. A hybrid algorithm of the Fisher scoring and the method of moments is implemented for computing the method. Extensive simulation studies are conducted to justify the validity of the proposed method. Finally, the proposed method is applied to analyze functional impairment in subjects who are at risk of Huntington disease from a multisite observational study of prodromal Huntington disease. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Overdispersion is a common feature of models of biological data, but researchers often fail to model the excess variation driving the overdispersion, resulting in biased parameter estimates and standard errors. Quantifying and modeling overdispersion when it is present is therefore critical for robust biological inference. One means to account for overdispersion is to add an observation-level random effect (OLRE) to a model, where each data point receives a unique level of a random effect that can absorb the extra-parametric variation in the data. Although some studies have investigated the utility of OLRE to model overdispersion in Poisson count data, studies doing so for Binomial proportion data are scarce. Here I use a simulation approach to investigate the ability of both OLRE models and Beta-Binomial models to recover unbiased parameter estimates in mixed effects models of Binomial data under various degrees of overdispersion. In addition, as ecologists often fit random intercept terms to models when the random effect sample size is low (

While there is consensus that the efficacy of parasiticides is properly assessed using the Abbott formula, there is as yet no general consensus on the use of arithmetic versus geometric mean numbers of surviving parasites in the formula. The purpose of this paper is to investigate the accuracy and precision of various efficacy estimators based on the Abbott formula which alternatively use arithmetic mean, geometric mean and median numbers of surviving parasites; we also consider a maximum likelihood estimator. Our study shows that the best estimators using geometric means are competitive, with respect to root mean squared error, with the conventional Abbott estimator using arithmetic means, as they have lower average and lower median root mean square error over the parameter scenarios which we investigated. However, our study confirms that Abbott estimators using geometric means are potentially biased upwards, and this upward bias is substantial in particular when the test product has substandard efficacy (90% and below). For this reason, we recommend that the Abbott estimator be calculated using arithmetic means. [ABSTRACT FROM AUTHOR]

Standard measures of batting performance such as batting average and on-base percentage can be decomposed into component rates such as strikeout rates and home run rates. The likelihood of hitting data for a group of players can be expressed as a product of likelihoods of the component probabilities and this motivates the use of Bayesian random effects models to estimate the groups of component rates. By combining the separate component rates, the aggregate predictions of batting performance for subsequent seasons improve upon standard shrinkage methods. This 'separate and aggregate' approach is also illustrated for estimating on-base probabilities and fielding independent pitching (FIP) abilities of pitchers. [ABSTRACT FROM AUTHOR]

The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion-goodness-of-fit-which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4-performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available. [ABSTRACT FROM AUTHOR]

Appropriate monitoring of safety data during the conduct of a clinical trial can ensure timely alteration or termination of the trial to protect patients from potentially harmful treatment. Quantitative evaluation in safety monitoring is important for the study team and the data monitoring committee to make timely recommendations. This article provides an overview of statistical methods for monitoring a prespecified adverse event of interest in a single-arm or controlled clinical trial, including those described in the literature and two proposed methods following a general Bayesian framework using conjugate families. The implementation of statistical methods on safety monitoring is illustrated through clinical trial examples. Practical challenges and considerations are also discussed via simulation studies. [ABSTRACT FROM PUBLISHER]

A key objective of the Regional Tuna Tagging Project—Indian Ocean was to estimate tag-shedding rates, Type-I (immediate tag shedding) and Type-II (long-term tag shedding). To assess this, a series of double-tagging experiments (26,899 double tags released with 4555 recoveries) were conducted as part of the broader tagging program. After omitting data from tags placed by less experienced taggers, the results of our analyses did not show any evidence that individual differences between taggers (i.e., a tagger effect) impacted estimates of tag-shedding rates. However, it was shown that the probability of retaining the second tag (inserted in the left side of the fish) was larger than retaining the first tag (inserted in the right side, i.e., the side typically tagged in single-tagging experiments). We used a Bayesian model averaging approach to account for model uncertainty in the estimates of the parameters α and L used to calculate the probability of tag retention Q ( t ) = α e − ( L t ) for the right tag. The parameter estimates were α = 0.993 and L (per year) = 0.030 (skipjack); α = 0.972 and L (per year) = 0.040 (yellowfin); and α = 0.990 and L (per year) = 0.021 (bigeye). These results agree with estimates obtained by other large-scale tropical tuna tagging projects. We showed that tag loss has a moderate impact on the underestimation of the exploitation rate (bias = 2–6% depending on the tuna species). However, non-reporting leads to a bias of around 7% when using the high reporting rate estimate of purse seiners. Finally, tag shedding (specifically Type-II shedding) modified the individual weights of the samples of recaptures. Consequently, the total instantaneous mortality estimates ( Z ; calculated from mean times-at-large) were reduced by a range of 1–3%. [ABSTRACT FROM AUTHOR]

In hierarchical data settings, be it of a longitudinal, spatial, multi-level, clustered, or otherwise repeated nature, often the association between repeated measurements attracts at least part of the scientific interest. Quantifying the association frequently takes the form of a correlation function, including but not limited to intraclass correlation. Vangeneugden et al. (2010) derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models. Here, we consider the extended model family proposed by Molenberghs et al. (2010). This family flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. The family allows for closed-form means, variance functions, and correlation function, for a variety of outcome types and link functions. Unfortunately, for binary data with logit link, closed forms cannot be obtained. This is in contrast with the probit link, for which such closed forms can be derived. It is therefore that we concentrate on the probit case. It is of interest, not only in its own right, but also as an instrument to approximate the logit case, thanks to the well-known probit-logit ‘conversion.’ Next to the general situation, some important special cases such as exchangeable clustered outcomes receive attention because they produce insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. (2010) and with approximations derived for the so-called logistic-beta-normal combined model. A simulation study explores performance of the method proposed. Data from a schizophrenia trial are analyzed and correlation functions derived. [ABSTRACT FROM PUBLISHER]

When fitting dose–response models to entomological data it is often necessary to take account of natural mortality and/or overdispersion. The standard approach to handle natural mortality is to use Abbott’s formula, which allows for a constant underlying mortality rate. Commonly used overdispersion models include the beta-binomial model, logistic-normal, and discrete mixtures. Here we extend the standard natural mortality model by including a random effect to account for overdispersion. Parameter estimation is based on a combined EM Newton–Raphson algorithm, which provides a simple framework for maximum likelihood estimation of the natural mortality model. We consider the application of this model to data from an experiment on the use of a virus ( PhopGV) for the biological control of worm larvae ( Phthorimaea operculella) in potatoes. For this natural mortality model with a random effect we introduce the likelihood ratio test, effective dose, and the use of a simulated residual envelope for model checking. Comparisons are made with an equivalent beta-binomial model. The procedures are implemented in the R system. [ABSTRACT FROM AUTHOR]

This study evaluated the comparability of a paper–pencil (PP) version and two computer-based (CB) versions of the National Board Dental Hygiene Examination. Comparability was evaluated by validity and psychometric criteria. Data were collected from the following resources: (1) 4,560 candidates enrolled in accredited dental hygiene programs who took the PP version in the Spring 2009, (2) 973 and 1,033 candidates enrolled in accredited dental hygiene programs who took two separate CB versions in 2009, and (3) the survey data from 2,486 candidates who took the CB versions in 2009. The results from the PP and CB versions were found to be comparable on several criteria. [ABSTRACT FROM AUTHOR]

For many years actuaries and demographers have been doing curve fitting of age-specific mortality data. We use the eight-parameter Heligman- Pollard (HP) empirical law to fit the mortality curve. It consists of three nonlinear curves, child mortality, mid-life mortality and adult mortality. It is now well-known that the eight unknown parameters in the HP law are dificult to estimate because numerical algorithms generally do not converge when model fitting is done. We consider a novel idea to fit the three curves (nonlinear splines) separately, and then connect them smoothly at the two knots. To connect the curves smoothly, we express uncertainty about the knots because these curves do not have turning points. We have important prior information about the location of the knots, and this helps in the estimation convergence problem. Thus, the Bayesian paradigm is particularly attractive. We show the theory, method and application of our approach. We discuss estimation of the curve for English and Welsh mortality data. We also make comparisons with the recent Bayesian method. [ABSTRACT FROM AUTHOR]

Abstract: Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper starts from the broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary and binomial cases are our focus. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical integration. The methodology is applied to two datasets of which the outcomes are binary and binomial, respectively. [Copyright &y& Elsevier]

This article considers the issue of measuring segregation in a population of units that contain few individuals (e.g., establishments, classrooms). When units are small, the usual segregation indices, which are based on sample proportions, are biased. We propose a parametric solution: the probability that an individual within a given unit belongs to the minority is assumed to be distributed as a mixture of Beta distributions. The model can be estimated and indices deduced. Simulations show that this new method performs well compared to existing ones, even in the case of misspecification. An application to residential segregation in France according to parents’ nationalities is then undertaken. This article has online supplementary materials. [ABSTRACT FROM AUTHOR]

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms by using indirect inference. ABC methods are useful for posterior inference in the presence of an intractable likelihood function. In the indirect inference approach to ABC the parameters of an auxiliary model fitted to the data become the summary statistics. Although applicable to any ABC technique, we embed this approach within a sequential Monte Carlo algorithm that is completely adaptive and requires very little tuning. This methodological development was motivated by an application involving data on macroparasite population evolution modelled by a trivariate stochastic process for which there is no tractable likelihood function. The auxiliary model here is based on a beta-binomial distribution. The main objective of the analysis is to determine which parameters of the stochastic model are estimable from the observed data on mature parasite worms. [ABSTRACT FROM AUTHOR]

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper proposes a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary, count and time-to-event cases are given particular emphasis. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical integration. Implications for the derivation of marginal correlations functions are discussed. The methodology is applied to data from a study in epileptic seizures, a clinical trial in toenail infection named onychomycosis and survival data in children with asthma. [ABSTRACT FROM AUTHOR]

In animal studies of ectoparasiticide efficacy the total number of parasites with which experimental animals are infested is not always equal to the intended number of parasites (usually n = 50 per experimental animal in the case of ticks, and n = 50 or n = 100 in the case of fleas). That is, in the practical implementation of a study protocol, the infestation of experimental animals may be subject to variability so that total infestation is not known precisely. The purpose of the present study is to assess the impact of this variability on the accuracy and precision of efficacy estimates. The results of a thorough simulation study show clearly that uncertainty in total parasite infestation – of the magnitude encountered in well-controlled animal studies – has virtually no effect on the accuracy and precision of estimators of ectoparasiticide efficacy. [ABSTRACT FROM AUTHOR]

In toxicity studies, model mis-specification could lead to serious bias or faulty conclusions. As a prelude to subsequent statistical inference, model selection plays a key role in toxicological studies. It is well known that the Bayes factor and the cross-validation method are useful tools for model selection. However, exact computation of the Bayes factor is usually difficult and sometimes impossible and this may hinder its application. In this paper, we recommend to utilize the simple Schwarz criterion to approximate the Bayes factor for the sake of computational simplicity. To illustrate the importance of model selection in toxicity studies, we consider two real data sets. The first data set comes from a study of dietary fortification with carbonyl iron in which the Bayes factor and the cross-validation are used to determine the number of sub-populations in a mixture normal model. The second example involves a developmental toxicity study in which the selection of dose–response functions in a beta-binomial model is explored. [ABSTRACT FROM AUTHOR]

The different genetic variation discovery projects (The SNP Consortium, the International HapMap Project, the 1000 Genomes Project, etc.) aim to identify as much as possible of the underlying genetic variation in various human populations. The question we address in this article is how many new variants are yet to be found. This is an instance of the species problem in ecology, where the goal is to estimate the number of species in a closed population. We use a parametric beta-binomial model that allows us to calculate the expected number of new variants with a desired minimum frequency to be discovered in a new dataset of individuals of a specified size. The method can also be used to predict the number of individuals necessary to sequence in order to capture all (or a fraction of) the variation with a specified minimum frequency. We apply the method to three datasets: the ENCODE dataset, the Seattle SNPs dataset, and the National Institute of Environmental Health Sciences SNPs dataset. Consistent with previous descriptions, our results show that the African population is the most diverse in terms of the number of variants expected to exist, the Asian populations the least diverse, with the European population in-between. In addition, our results show a clear distinction between the Chinese and the Japanese populations, with the Japanese population being the less diverse. To find all common variants (frequency at least 1%) the number of individuals that need to be sequenced is small (∼350) and does not differ much among the different populations; our data show that, subject to sequence accuracy, the 1000 Genomes Project is likely to find most of these common variants and a high proportion of the rarer ones (frequency between 0.1 and 1%). The data reveal a rule of diminishing returns: a small number of individuals (∼150) is sufficient to identify 80% of variants with a frequency of at least 0.1%, while a much larger number (>3,000 individuals) is necessary to find all of those variants. Finally, our results also show a much higher diversity in environmental response genes compared with the average genome, especially in African populations. [ABSTRACT FROM AUTHOR]