Bootstrap Confidence Intervals for Proportions of Unequal Sized Groups Adjusted for Overdispersion

Group testing is a method of pooling a number of units together and performing a single test on the resulting group. It is an appealing option when few individual units are thought to be infected leading to reduced costs of testing as compared to individually testing the units. Group testing aims to identify the positive groups in all the groups tested or to estimate the proportion of positives (p) in a population. Interval estimation methods of the proportions in group testing for unequal group sizes adjusted for overdispersion have been examined. Lately improvement in statistical methods allows the construction of highly accurate confidence intervals (CIs). The aim here is to apply group testing for estimation and generate highly accurate Bootstrap confidence intervals (CIs) for the proportion of defective or positive units in particular. This study provided a comparison of several proven methods of constructing CIs for a binomial proportion after adjusting for overdispersion in group testing with groups of unequal sizes. Bootstrap resampling was applied on data simulated from binomial distribution, and confidence intervals with high coverage probabilities were produced. This data was assumed to be overdispersed and independent between groups but correlated within these groups. Interval estimation methods based on the Wald, the Logit and Complementary log-log (CLL) functions were considered. The criterion used in the comparisons is mainly the coverage probabilities attained by nominal 95% CIs, though interval width is also regarded. Bootstrapping produced CIs with high coverage probabilities for each of the three interval methods.

Community phylogenetic structure of grasslands and its relationship with environmental factors on the Mongolian Plateau

The community assembly rules and species coexistence have always been interested by ecologists. The community phylogenetic structure is the consequence of the interaction process between the organisms and the abiotic environment and has been used to explain the relative impact of abiotic and biotic factors on species co-existence. In recent years, grassland degradation and biodiversity loss have become increasingly severe on the Mongolian Plateau, while the drivers for these changes are not clearly explored, especially whether climate change is a main factor is debated in academia. In this study, we examined the phylogenetic structure of grassland communities along five transects of climate aridity on the Mongolian Plateau, and analyzed their relations with environmental factors, with the aims to understand the formation mechanism of the grassland communities and the role of climatic factors. We surveyed grassland communities at 81 sites along the five transects, and calculated their net relatedness index(NRI) at two different quadrat scales(small scale of 1 m2 and large scale of 5 m2) to characterize the community phylogenetic structure and analyze its relationship with the key 11 environmental factors. We also calculated the generalized UniFrac distance(GUniFrac) among the grassland communities to quantify the influence of spatial distance and environmental distance on the phylogenetic β diversity. The results indicated that plant community survey using the large scale quadrat contained sufficient species to represent community compositions. The community phylogenetic structure of grasslands was significantly overdispersed at both the small and large scales, and the degree of overdispersion was greater at the large scale than at the small scale, suggesting that competitive exclusion instead of habitat filtering played a major role in determination of community composition. Altitude was the main factor affecting the community phylogenetic structure, whereas climatic factors, such as precipitation and temperature, had limited influence. The principal component analysis of the 11 environmental factors revealed that 94.04% of their variation was accounted by the first four principal components. Moreover only 14.29% and 23.26% of the variation in community phylogenetic structure were explained by the first four principal components at the small and large scales, respectively. Phylogenetic β diversity was slightly significantly correlated with both spatial distance and environmental distance, however, environmental distance had a less explanatory power than spatial distance, indicating a limited environmental effect on the community phylogenetic structure of grasslands on the Mongolian Plateau. In view of the limited effect of climatic factors on the community phylogenetic structure of grasslands, climate change may have a smaller impact on grassland degradation than previously thought.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.

A First Order Stationary Branching Negative Binomial Autoregressive Model with Application

In the area of time series modelling, several applications are encountered in real-life that involve analysis of count time series data. The distribution characteristics and dependence structure are the major issues that arise while specifying a modelling strategy to handle the analysis of those kinds of data. Owing to the numerous applications there is a need to develop models that can capture these features. However, accounting for both aspects simultaneously presents complexities while specifying a modeling strategy. In this paper, an alternative statistical model able to deal with issues of discreteness, overdispersion, serial correlation over time is proposed. In particular, we adopt a branching mechanism to develop a first-order stationary negative binomial autoregressive model. Inference is based on maximum likelihood estimation and a simulation study is conducted to evaluate the performance of the proposed approach. As an illustration, the model is applied to a real-life dataset in crime analysis.

Estimating effective reproduction number revisited

Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks.In this study,we improve the estimation of the effective reproduction number through two main approaches.First,we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework.We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme.By doing so,we enhance the accuracy of approximating the underlying epidemic process compared to previous methods,even when the counting period is similar to the mean generation time of an infectious disease.Second,we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion.Specifically,given that observed incidence counts follow a negative binomial distribution,the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution.With this formulation,we establish posterior uncertainty bounds for the effective reproduction number.Finally,we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.

Disease momentum: Estimating the reproduction number in the presence of superspreading

A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces.This so-called reproduction number has significant implications for the disease progression.There has been increasing literature suggesting that superspreading,the significant variability in number of new infections caused by individuals,plays an important role in the spread of SARS-CoV-2.In this paper,we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases.Accordingly,we employ a simple extension to models currently used in the literature to estimate the reproduction number and present a case-study of the progression of COVID-19 in Austria.Our models demonstrate that the estimation uncertainty of the reproduction number increases with superspreading and that this improves the performance of prediction intervals.Of independent interest is the derivation of a transparent formula that connects the extent of superspreading to the width of credible intervals for the reproduction number.This serves as a valuable heuristic for understanding the uncertainty surrounding diseases with superspreading.