Bayesian nonparametric inference for panel count data with an informative observation process

In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is proposed to jointly model the observation process and the recurrent event process. Bayesian nonparametric inference is proposed for simultaneously estimating regression parameters, bivariate frailty effects, and baseline intensity functions. Inference is done through Markov chain Monte Carlo, with fully developed computational techniques. Predictive inference is also discussed under the Bayesian setting. The proposed method is shown to be efficient via simulation studies. A clinical trial dataset on skin cancer patients is analyzed to illustrate the proposed approach.     

A new Gompertz-type diffusion process with application to random growth

Stochastic models describing growth kinetics are very important for predicting many biological phenomena. In this paper, a new Gompertz-type diffusion process is introduced, by means of which bounded sigmoidal growth patterns can be modeled by time-continuous variables. The main innovation of the process is that the bound can depend on the initial value, a situation that is not provided by the models considered to date. After building the model, a comprehensive study is presented, including its main characteristics and a simulation of sample paths. With the aim of applying this model to real-life situations, and given its possibilities in forecasting via the mean function, discrete sampling based inference is developed. The likelihood equations are not directly solvable, and because of difficulties that arise with the usual numerical methods employed to solve them, an iterative procedure is proposed. The possibilities of the new process are illustrated by means of an application to real data, concretely, to growth in rabbits.     

On Bayesian inference for the K function

The K function is a summary of spatial dependence in spatial point processes. In practice one observes a realization of the spatial point process, called a spatial point pattern. Although the K function of a spatial point process is typically unknown, several estimators of the process K function have been put forth. These estimators, however, are based upon empirical averages; the complicated distributional properties of the estimators unfortunately complicates interval estimation. In this paper, we propose a Bayesian inferential framework, allowing inference for the K function of the spatial point process (including interval estimation). Of particular interest is the unique use of the posterior predictive distribution to (efficiently) enable such inferences. To demonstrate our technique, the well known Swedish pine sapling data (Strand, 1972) is analyzed, including a discussion on evaluating model fit.     

Fire regimes of China: inference from statistical comparison with the United States

Aim Substantial overlap in the climate characteristics of the United States and China results in similar land‐cover types and weather conditions, especially in the eastern half of the two countries. These parallels suggest similarities in fire regimes as well, yet relatively little is known about the historical role of fire in Chinese ecosystems. Consequently, we aimed to infer fire regime characteristics for China based on our understanding of climate–fire relationships in the United States. Location The conterminous United States and the People's Republic of China. Methods We used generalized additive models to quantify the relationship between reference fire regime classes adopted by the LANDFIRE initiative in the United States, and a global climate data set. With the models, we determined which climate variables best described the distribution of fire regimes in the United States then used these models to predict the spatial distribution of fire regimes in China. The fitted models were validated quantitatively using receiver operating characteristic area under the curve (AUC). We validated the predicted fire regimes in China by comparison with palaeoecological fire data and satellite‐derived estimates of current fire activity. Results Quantitative validation using the AUC indicated good discrimination of the distribution of fire regimes by models for the United States. Overall, fire regimes with more frequent return intervals were more likely in the east than in the west. The resolution of available historical and prehistorical fire data for China, including sediment cores, allowed only coarse, qualitative validation, but provided supporting evidence that fire has long been a part of ecosystem function in eastern China. MODIS satellite data illustrated that fire frequency within the last decade supported the classification of much of western China as relatively fire‐free; however, much of south‐eastern China experiences more fire activity than predicted with our models, probably as a function of the extensive use of fire by people. Conclusions While acknowledging there are many cultural, environmental and historical differences between the United States and China, our fire regime models based on climate data demonstrate potential historical fire regimes for China, and propose that large areas of China share historical fire–vegetation–climate complexes with the United States.     

On the correlation between composition and site-specific evolutionary rate: implications for phylogenetic inference

Model-based phylogenetic reconstruction methods traditionally assume homogeneity of nucleotide frequencies among sequence sites and lineages. Yet, heterogeneity in base composition is a characteristic shared by most biological sequences. Compositional variation in time, reflected in the compositional biases among contemporary sequences, has already been extensively studied, and its detrimental effects on phylogenetic estimates are known. However, fewer studies have focused on the effects of spatial compositional heterogeneity within genes. We show here that different sites in an alignment do not always share a unique compositional pattern, and we provide examples where nucleotide frequency trends are correlated with the site-specific rate of evolution in RNA genes. Spatial compositional heterogeneity is shown to affect the estimation of evolutionary parameters. With standard phylogenetic methods, estimates of equilibrium frequencies are found to be biased towards the composition observed at fast-evolving sites. Conversely, the ancestral composition estimates of some time-heterogeneous but spatially homogeneous methods are found to be biased towards frequencies observed at invariant and slow-evolving sites. The latter finding challenges the result of a previous study arguing against a hyperthermophilic last universal ancestor from the low apparent G + C content of its rRNA sequences. We propose a new model to account for compositional variation across sites. A Gaussian process prior is used to allow for a smooth change in composition with evolutionary rate. The model has been implemented in the phylogenetic inference software PHASE, and Bayesian methods can be used to obtain the model parameters. The results suggest that this model can accurately capture the observed trends in present-day RNA sequences.     

The bright and the dark side of human antibody responses to flaviviruses: lessons for vaccine design

Zika and dengue viruses belong to the Flavivirus genus, a close group of antigenically related viruses that cause significant arthropod‐transmitted diseases throughout the globe. Although infection by a given flavivirus is thought to confer lifelong protection, some of the patient's antibodies cross‐react with other flaviviruses without cross‐neutralizing. The original antigenic sin phenomenon may amplify such antibodies upon subsequent heterologous flavivirus infection, potentially aggravating disease by antibody‐dependent enhancement (ADE). The most striking example is provided by the four different dengue viruses, where infection by one serotype appears to predispose to more severe disease upon infection by a second one. A similar effect was postulated for sequential infections with Zika and dengue viruses. In this review, we analyze the molecular determinants of the dual antibody response to flavivirus infection or vaccination in humans. We highlight the role of conserved partially cryptic epitopes giving rise to cross‐reacting and poorly neutralizing, ADE‐prone antibodies. We end by proposing a strategy for developing an epitope‐focused vaccine approach to avoid eliciting undesirable antibodies while focusing the immune system on producing protective antibodies only.     

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta‐analysis and group level studies

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group‐level studies or in meta‐analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log‐odds and arcsine transformations of the estimated probability , both for single‐group studies and in combining results from several groups or studies in meta‐analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta‐analysis and result in abysmal coverage of the combined effect for large K. We also propose bias‐correction for the arcsine transformation. Our simulations demonstrate that this bias‐correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta‐analyses of prevalence.