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Background Whole-genome bisulfite sequencing currently provides the highest-precision view of the epigenome, with quantitative information about populations of cells down to single nucleotide resolution. Several studies have demonstrated the value of this precision: meaningful features that correlate strongly with biological functions can be found associated with only a few CpG sites. Understanding the role of DNA methylation, and more broadly the role of DNA accessibility, requires that methylation differences between populations of cells are identified with extreme precision and in complex experimental designs. Results In this work we investigated the use of beta-binomial regression as a general approach for modeling whole-genome bisulfite data to identify differentially methylated sites and genomic intervals. Conclusions The regression-based analysis can handle medium- and large-scale experiments where it becomes critical to accurately model variation in methylation levels between replicates and account for influence of various experimental factors like cell types or batch effects.

Background Ventilator-free days, which combine mortality and duration of mechanical ventilation into a single measure, are often considered as a primary endpoint in clinical trials involving critically ill patients. Despite the composite nature, ventilator-free days are commonly analyzed as continuous or count data with no distinction between a zero score from a patient who dies and a zero score from a patient who is alive but still on ventilator. In this study, we propose a two-part statistical model to compare the effects of two airway management strategies on mortality and duration of mechanical ventilation among patients with out-of-hospital cardiopulmonary arrest in a cluster randomized cross-over clinical trial. Methods In the proposed two-part model, failure to achieve return of spontaneous circulation (ROSC), death after ROSC, and survival are modeled in the first part; the number of ventilator-free days conditional on survival is modeled in the second part. To account for the cluster randomized cross-over design, each part also includes a random cluster effect that is assumed to be either shared or independent across the two parts. We conducted a simulation study to evaluate type I error rates and power of the two-part shared random cluster effect model and the mis-specified two-part model with independent random cluster effects in detecting an overall intervention effect. Results We found that parameter estimates were similar whether the random cluster effects were assumed to be shared or independent across the two parts whereas the shared random cluster effect approach showed higher log-likelihood, but lower Akaike information criterion (AIC) and Bayesian information criterion (BIC). Initial laryngeal tube insertion reduced odds of failing to achieve ROSC and marginally decreased odds of death after ROSC compared with initial endotracheal intubation in Part 1, whereas initial laryngeal tube insertion was not associated with duration of mechanical ventilation among patients alive in Part 2. The shared random cluster effect approach showed higher odds of death associated with lower odds of being ventilator-free. This confirms the expectation that a patient who is less likely to achieve ROSC and survive is more likely to require prolonged mechanical ventilation if the patient indeed survives during hospitalization. Our simulation studies found that the two-part model with a shared random cluster effect yielded type I error rates close to the nominal level. The two-part shared random cluster effect model has better power to detect an overall intervention effect when intervention effects are present in both parts rather than in only one of the two part. Conclusions The proposed two-part model provides a more comprehensive assessment of intervention effects on ventilator-free days in critical care trials. Researchers and clinicians can obtain greater insights with this approach about the direction and magnitude of the intervention effects on mortality, ROSC, and duration of mechanical ventilation.

This paper analyzes public willingness to support farmer adoption of best management practices in Oklahoma’s Fort Cobb Watershed, a multiuse area for agriculture, residential water provision, and recreation. The study uses Oklahoma’s Meso-Scale Integrated Sociogeographic Network survey to conduct a contingent valuation analysis of a hypothetical, one-time tax that would support farmer adoption of pasture and riparian buffer management practices. Respondent heterogeneity is modeled using beta-binomial regression. Public support for the hypothetical program is stronger for the tandem implementation of riparian buffer establishment and pasture expansion (willingness to pay [WTP] = $290) and riparian buffer establishment (WTP = $317).

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.

Background The Mini-Mental State Examination (MMSE) and the Montreal Cognitive Assessment (MoCA) questionnaires are commonly used to measure global cognition in clinical trials. Because these scales are discrete and bounded with ceiling and floor effects and highly skewed, their analysis as continuous outcomes presents challenges. Normality assumptions of linear regression models are usually violated, which may result in failure to detect associations with variables of interest. Methods Alternative approaches to analyzing the results of these cognitive batteries include transformations (standardization, square root, or log transformation) of the scores in the multivariate linear regression (MLR) model, the use of nonlinear beta-binomial regression (which is not dependent on the assumption of normality), or Tobit regression, which adds a latent variable to account for bounded data. We aim to empirically compare the model performance of all proposed approaches using four large randomized controlled trials (ORIGIN, TRANSCEND, COMPASS, and NAVIGATE-ESUS), and using as metrics the Akaike information criterion (AIC). We also compared the treatment effects for the methods that have the same unit of measure (i.e., untransformed MLR, beta-binomial, and Tobit). Results The beta-binomial consistently demonstrated superior model performance, with the lowest AIC values among nearly all the approaches considered, followed by the MLR with square root and log transformations across all four studies. Notably, in ORIGIN, a substantial AIC reduction was observed when comparing the untransformed MLR to the beta-binomial, whereas other studies had relatively small AIC reductions. The beta-binomial model also resulted in a significant treatment effect in ORIGIN, while the untransformed MLR and Tobit regression showed no significance. The other three studies had similar and insignificant treatment effects among the three approaches. Conclusion When analyzing discrete and bounded outcomes, such as cognitive scores, as continuous variables, a beta-binomial regression model improves model performance, avoids spurious significance, and allows for a direct interpretation of the actual cognitive measure. Trials registration ORIGIN (NCT00069784). Registered on October 1, 2003; TRANSCEND (NCT00153101). Registered on September 9, 2005; COMPASS (NCT01776424). Registered on January 24, 2013; NAVIGATE-ESUS (NCT02313909). Registered on December 8, 2014.

For decades, conventional wisdom maintained that binary 0–1 Bernoulli random variables cannot contain extra-binomial variation. Taking an unorthodox stance, Hilbe actively disagreed, especially for correlated observation instances, arguing that the universally adopted diagnostic Pearson or deviance dispersion statistics are insensitive to a variance anomaly in a binary context, and hence simply fail to detect it. However, having the intuition and insight to sense the existence of this departure from standard mathematical statistical theory, but being unable to effectively isolate it, he classified this particular over-/under-dispersion phenomenon as implicit. This paper explicitly exposes his hidden quantity by demonstrating that the variance in/deflation it represents occurs in an underlying predicted beta random variable whose real number values are rounded to their nearest integers to convert to a Bernoulli random variable, with this discretization masking any materialized extra-Bernoulli variation. In doing so, asymptotics linking the beta-binomial and Bernoulli distributions show another conventional wisdom misconception, namely a mislabeling substitution involving the quasi-Bernoulli random variable; this undeniably is not a quasi-likelihood situation. A public bell pepper disease dataset exhibiting conspicuous spatial autocorrelation furnishes empirical examples illustrating various features of this advocated proposition.

The aim of the study was to identify the validity of effect estimates for serious rare adverse events in clinical study reports of antidepressants trials, across different meta-analysis methods. Four serious rare adverse events (all-cause mortality, suicidality, aggressive behavior, and akathisia) were meta-analyzed using different methods. The Yusuf-Peto odds ratio ignores studies with no events and was compared with the alternative approaches of generalized linear mixed models (GLMMs), conditional logistic regression, a Bayesian approach using Markov Chain Monte Carlo (MCMC), and a beta-binomial regression model. The estimates for the four outcomes did not change substantially across the different methods; the Yusuf-Peto method underestimated the treatment harm and overestimated its precision, especially when the estimated odds ratio deviated greatly from 1. For example, the odds ratio for suicidality for children and adolescents was 2.39 (95% confidence interval = 1.32–4.33), using the Yusuf-Peto method but increased to 2.64 (1.33–5.26) using conditional logistic regression, to 2.69 (1.19–6.09) using beta-binomial, to 2.73 (1.37–5.42) using the GLMM, and finally to 2.87 (1.42–5.98) using the MCMC approach. The method used for meta-analysis of rare events data influences the estimates obtained, and the exclusion of double-zero event studies can give misleading results. To ensure reduction of bias and erroneous inferences, sensitivity analyses should be performed using different methods instead of the Yusuf-Peto approach, in particular the beta-binomial method, which was shown to be superior through a simulation study.

Consider a class of discrete probability distributions with a limited support. A typical example of such support is some variant of a Likert scale, with a response mapped to either the {1,2,…,5} or {-3,-2,…,2,3} set. Such type of data is common for Multimedia Quality Assessment but can also be found in many other research fields. For modelling such data a latent variable approach is usually used (e.g., Ordered Probit). In many cases it is convenient or even necessary to avoid latent variable approach (e.g., when dealing with too small sample size). To avoid it the proper class of discrete distributions is needed. The main idea of this paper is to propose a family of discrete probability distributions with only two parameters that play the same role as the parameters of the normal distribution. We call the new class the Generalised Score Distribution (GSD). The proposed GSD class covers the entire set of possible means and variances, for any fixed and finite support. Furthermore, the GSD class can be treated as an underdispersed continuation of a reparametrized beta-binomial distribution. The GSD class parameters are intuitive and can be easily estimated by the method of moments. We also offer a Maximum Likelihood Estimation (MLE) algorithm for the GSD class and evidence that the class properly describes response distributions coming from 24 Multimedia Quality Assessment experiments. At last, we show that the GSD class can be represented as a sum of dichotomous zero–one random variables, which points to an interesting interpretation of the class.

In the branch of forensic science known as firearm evidence identification, estimating error rates is a fundamental challenge. Recently, a new quantitative approach known as the congruent matching cells (CMC) method was developed to improve the accuracy of ballistic identifications and provide a basis for estimating error rates. To estimate error rates, the key is to find an appropriate probability distribution for the relative frequency distribution of observed CMCs overlaid on a relevant measured firearm surface such as the breech face of a cartridge case. Several probability models based on the assumption of independence between cell pair comparisons have been proposed, but the assumption of independence among the cell pair comparisons from the CMC method may not be valid. This article proposes statistical models based on dependent Bernoulli trials, along with corresponding methodology for parameter estimation. To demonstrate the potential improvement from the use of the dependent Bernoulli trial model, the methodology is applied to an actual data set of fired cartridge cases.

In retrospective studies, odds ratio is often used as the measure of association. Under independent beta prior assumption, the exact posterior distribution of odds ratio given a single 2 × 2 table has been derived in the literature. However, independence between risks within the same study may be an oversimplified assumption because cases and controls in the same study are likely to share some common factors and thus to be correlated. Furthermore, in a meta-analysis of case–control studies, investigators usually have multiple 2 × 2 tables. In this article, we first extend the published results on a single 2 × 2 table to allow within study prior correlation while retaining the advantage of closed-form posterior formula, and then extend the results to multiple 2 × 2 tables and regression setting. The hyperparameters, including within study correlation, are estimated via an empirical Bayes approach. The overall odds ratio and the exact posterior distribution of the study-specific odds ratio are inferred based on the estimated hyperparameters. We conduct simulation studies to verify our exact posterior distribution formulas and investigate the finite sample properties of the inference for the overall odds ratio. The results are illustrated through a twin study for genetic heritability and a meta-analysis for the association between the N-acetyltransferase 2 (NAT2) acetylation status and colorectal cancer.