The incidence and prevalence of autoimmune pulmonary alveolar proteinosis in Japan were previously estimated to be 0.49 and 6.2 per million, respectively. Thereafter, an increase in serological diagnosis forced a re-estimation of the incidence based on more contemporaneous data using more robust methods. Sera of 702 patients were positive for granulocyte-macrophage colony-stimulating factor autoantibody during the 2006-2016 period (group A). Of these patients, 43 were actively surveyed in Niigata prefecture (group B) for estimation of the incidence. To estimate the survival period, 103 patients (group C) were investigated retrospectively for the 1999-2017 period using restricted mean survival time. In group A, the number of patients diagnosed in each prefecture was closely correlated with the corresponding population, indicating no regional integration of onset. In group B, a total of 43 patients were diagnosed, the annual number followed a Poisson distribution and the incidence was thus estimated to be 1.65 per million. In group C, the retrospective cohort study revealed the mean survival period to be 16.1 years. Taken together, the prevalence was estimated to be 26.6 per million, indicating that the previous data for incidence and prevalence was an underestimation.

Modeling of single cell RNA-sequencing (scRNA-seq) data remains challenging due to a high percentage of zeros and data heterogeneity, so improved modeling has strong potential to benefit many downstream data analyses. The existing zero-inflated or over-dispersed models are based on aggregations at either the gene or the cell level. However, they typically lose accuracy due to a too crude aggregation at those two levels.

The answer to many fundamental questions in Immunology requires the quantitative characterization of the T-cell repertoire, namely T cell receptor (TCR) diversity and clonal size distribution. An increasing number of repertoire studies are based on sequencing of the TCR variable regions in T-cell samples from which one tries to estimate the diversity of the original T-cell populations. Hitherto, estimation of TCR diversity was tackled either by a "standard" method that assumes a homogeneous clonal size distribution, or by non-parametric methods, such as the abundance-coverage and incidence-coverage estimators. However, both methods show caveats. On the one hand, the samples exhibit clonal size distributions with heavy right tails, a feature that is incompatible with the assumption of an equal frequency of every TCR sequence in the repertoire. Thus, this "standard" method produces inaccurate estimates. On the other hand, non-parametric estimators are robust in a wide range of situations, but per se provide no information about the clonal size distribution. This paper redeploys Poisson abundance models from Ecology to overcome the limitations of the above inferential procedures. These models assume that each TCR variant is sampled according to a Poisson distribution with a specific sampling rate, itself varying according to some Exponential, Gamma, or Lognormal distribution, or still an appropriate mixture of Exponential distributions. With these models, one can estimate the clonal size distribution in addition to TCR diversity of the repertoire. A procedure is suggested to evaluate robustness of diversity estimates with respect to the most abundant sampled TCR sequences. For illustrative purposes, previously published data on mice with limited TCR diversity are analyzed. Two of the presented models are more consistent with the data and give the most robust TCR diversity estimates. They suggest that clonal sizes follow either a Lognormal or an appropriate mixture of Exponential distributions. According to the ecological interpretation of these models, the T-cell repertoire would be divided in several T-cell niches, themselves created in a series of steps. Definitive conclusions, however, would require larger samples. It is shown here that samples 100-fold larger than hitherto available ones would be sufficient to discriminate candidate models. These large sample sizes are currently affordable using massively parallel sequencing technology. Foreseeing this we provide the package PAM for the R software that will facilitate T-cell repertoire data analysis based on Poisson abundance models.

Newly isolated serotypes of AAV readily cross the endothelial barrier to provide efficient transgene delivery throughout the body. However, tissue-specific expression is preferred in most experimental studies and gene therapy protocols. Previous efforts to restrict gene expression to the myocardium often relied on direct injection into heart muscle or intracoronary perfusion. Here, we report an AAV vector system employing the cardiac troponin T (cTnT) promoter. Using luciferase and enhanced green fluorescence protein (eGFP), the efficiency and specificity of cardiac reporter gene expression using AAV serotype capsids: AAV-1, 2, 6, 8 or 9 were tested after systemic administration to 1-week-old mice. Luciferase assays showed that the cTnT promoter worked in combination with each of the AAV serotype capsids to provide cardiomyocyte-specific gene expression, but AAV-9 followed closely by AAV-8 was the most efficient. AAV9-mediated gene expression from the cTnT promoter was 640-fold greater in the heart compared with the next highest tissue (liver). eGFP fluorescence indicated a transduction efficiency of 96% using AAV-9 at a dose of only 3.15 × 10(10) viral particles per mouse. Moreover, the intensity of cardiomyocyte eGFP fluorescence measured on a cell-by-cell basis revealed that AAV-mediated gene expression in the heart can be modeled as a Poisson distribution, requiring an average of nearly two vector genomes per cell to attain an 85% transduction efficiency.

Outbreaks of emerging and zoonotic infections represent a substantial threat to human health and well-being. These outbreaks tend to be characterised by highly stochastic transmission dynamics with intense variation in transmission potential between cases. The negative binomial distribution is commonly used as a model for transmission in the early stages of an epidemic as it has a natural interpretation as the convolution of a Poisson contact process and a gamma-distributed infectivity. In this study we expand upon the negative binomial model by introducing a beta-Poisson mixture model in which infectious individuals make contacts at the points of a Poisson process and then transmit infection along these contacts with a beta-distributed probability. We show that the negative binomial distribution is a limit case of this model, as is the zero-inflated Poisson distribution obtained by combining a Poisson-distributed contact process with an additional failure probability. We assess the beta-Poisson model's applicability by fitting it to secondary case distributions (the distribution of the number of subsequent cases generated by a single case) estimated from outbreaks covering a range of pathogens and geographical settings. We find that while the beta-Poisson mixture can achieve a closer to fit to data than the negative binomial distribution, it is consistently outperformed by the negative binomial in terms of Akaike Information Criterion, making it a suboptimal choice on parsimonious grounds. The beta-Poisson performs similarly to the negative binomial model in its ability to capture features of the secondary case distribution such as overdispersion, prevalence of superspreaders, and the probability of a case generating zero subsequent cases. Despite this possible shortcoming, the beta-Poisson distribution may still be of interest in the context of intervention modelling since its structure allows for the simulation of measures which change contact structures while leaving individual-level infectivity unchanged, and vice-versa.

Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html.

Serial Analysis of Gene Expressions (SAGE) produces gene expression measurements on a discrete scale, due to the finite number of molecules in the sample. This means that part of the variance in SAGE data should be understood as the sampling error in a binomial or Poisson distribution, whereas other variance sources, in particular biological variance, should be modeled using a continuous distribution function, i.e. a prior on the intensity of the Poisson distribution. One challenge is that such a model predicts a large number of genes with zero counts, which cannot be observed.

The paradigm called genomic selection (GS) is a revolutionary way of developing new plants and animals. This is a predictive methodology, since it uses learning methods to perform its task. Unfortunately, there is no universal model that can be used for all types of predictions; for this reason, specific methodologies are required for each type of output (response variables). Since there is a lack of efficient methodologies for multivariate count data outcomes, in this paper, a multivariate Poisson deep neural network (MPDN) model is proposed for the genomic prediction of various count outcomes simultaneously. The MPDN model uses the minus log-likelihood of a Poisson distribution as a loss function, in hidden layers for capturing nonlinear patterns using the rectified linear unit (RELU) activation function and, in the output layer, the exponential activation function was used for producing outputs on the same scale of counts. The proposed MPDN model was compared to conventional generalized Poisson regression models and univariate Poisson deep learning models in two experimental data sets of count data. We found that the proposed MPDL outperformed univariate Poisson deep neural network models, but did not outperform, in terms of prediction, the univariate generalized Poisson regression models. All deep learning models were implemented in Tensorflow as back-end and Keras as front-end, which allows implementing these models on moderate and large data sets, which is a significant advantage over previous GS models for multivariate count data.

Eukaryotic cells activate the S-phase checkpoint signal transduction pathway in response to DNA replication stress. Affected by the noise in biochemical reactions, such activation process demonstrates cell-to-cell variability. Here, through the analysis of microfluidics-integrated time-lapse imaging, we found multiple S-phase checkpoint activations in a certain budding yeast cell cycle. Yeast cells not only varied in their activation moments but also differed in the number of activations within the cell cycle, resulting in a stochastic multiple activation process. By investigating dynamics at the single-cell level, we showed that stochastic waiting times between consecutive activations are exponentially distributed and independent from each other. Finite DNA replication time provides a robust upper time limit to the duration of multiple activations. The mathematical model, together with further experimental evidence from the mutant strain, revealed that the number of activations under different levels of replication stress agreed well with Poisson distribution. Therefore, the activation events of S-phase checkpoint meet the criterion of Poisson process during DNA replication. In sum, the observed Poisson activation process may provide new insights into the complex stochastic dynamics of signal transduction pathways.

Analytic methods commonly used in epidemiology do not account for spatial correlation between observations. In regression analyses, omission of that autocorrelation can bias parameter estimates and yield incorrect standard error estimates.

Controlling harmful microorganisms, such as Listeria monocytogenes, can require reliable inactivation steps, including those providing conditions (e.g., using high salt content) in which the pathogen could be progressively inactivated. Exposure to osmotic stress could result, however, in variation in the number of survivors, which needs to be carefully considered through appropriate dispersion measures for its impact on intervention practices. Variation in the experimental observations is due to uncertainty and biological variability in the microbial response. The Poisson distribution is suitable for modeling the variation of equi-dispersed count data when the naturally occurring randomness in bacterial numbers it is assumed. However, violation of equi-dispersion is quite often evident, leading to over-dispersion, i.e., non-randomness. This article proposes a statistical modeling approach for describing variation in osmotic inactivation of L. monocytogenes Scott A at different initial cell levels. The change of survivors over inactivation time was described as an exponential function in both the Poisson and in the Conway-Maxwell Poisson (COM-Poisson) processes, with the latter dealing with over-dispersion through a dispersion parameter. This parameter was modeled to describe the occurrence of non-randomness in the population distribution, even the one emerging with the osmotic treatment. The results revealed that the contribution of randomness to the total variance was dominant only on the lower-count survivors, while at higher counts the non-randomness contribution to the variance was shown to increase the total variance above the Poisson distribution. When the inactivation model was compared with random numbers generated in computer simulation, a good concordance between the experimental and the modeled data was obtained in the COM-Poisson process.

Injury-related mortality rate estimates are often analyzed under the assumption that case counts follow a Poisson distribution. Certain types of injury incidents occasionally involve multiple fatalities, however, resulting in dependencies between cases that are not reflected in the simple Poisson model and which can affect even basic statistical analyses. This paper explores the compound Poisson process model as an alternative, emphasizing adjustments to some commonly used interval estimators for population-based rates and rate ratios. The adjusted estimators involve relatively simple closed-form computations, which in the absence of multiple-case incidents reduce to familiar estimators based on the simpler Poisson model. Summary data from the National Violent Death Reporting System are referenced in several examples demonstrating application of the proposed methodology.

Deep sequencing of RNAs (RNA-seq) has been a useful tool to characterize and quantify transcriptomes. However, there are significant challenges in the analysis of RNA-seq data, such as how to separate signals from sequencing bias and how to perform reasonable normalization. Here, we focus on a fundamental question in RNA-seq analysis: the distribution of the position-level read counts. Specifically, we propose a two-parameter generalized Poisson (GP) model to the position-level read counts. We show that the GP model fits the data much better than the traditional Poisson model. Based on the GP model, we can better estimate gene or exon expression, perform a more reasonable normalization across different samples, and improve the identification of differentially expressed genes and the identification of differentially spliced exons. The usefulness of the GP model is demonstrated by applications to multiple RNA-seq data sets.

The protocol provides an extensive guide to apply the generalized linear model framework to neurophysiological recordings. This flexible technique can be adapted to test and quantify the contributions of many different parameters (e.g., kinematics, target position, choice, reward) on neural activity. To weight the influence of each parameter, we developed an intuitive metric ("w-value") that can be used to build a "functional fingerprint" characteristic for each neuron. We also provide suggestions to extract complementary useful information from the method. For complete details on the use and execution of this protocol, please refer to Diomedi et al. (2020).

DelPhi is a popular scientific program which numerically solves the Poisson-Boltzmann equation (PBE) for electrostatic potentials and energies of biomolecules immersed in water via finite difference method. It is well known for its accuracy, reliability, flexibility, and efficiency. In this work, a new edition of DelPhi that uses a novel Newton-like method to solve the nonlinear PBE, in addition to the already implemented Successive Over Relaxation (SOR) algorithm, is introduced. Our tests on various examples have shown that this new method is superior to the SOR method in terms of stability when solving the nonlinear PBE, being able to converge even for problems involving very strong nonlinearity.

Many epidemiological methods for analysing follow-up studies require the calculation of rates based on accumulating person-time and events, stratified by various factors. Managing this stratification and accumulation is often the most difficult aspect of this type of analysis.

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach.

Serial analysis of gene expression (SAGE) is used to obtain quantitative snapshots of the transcriptome. These profiles are count-based and are assumed to follow a Binomial or Poisson distribution. However, tag counts observed across multiple libraries (for example, one or more groups of biological replicates) have additional variance that cannot be accommodated by this assumption alone. Several models have been proposed to account for this effect, all of which utilize a continuous prior distribution to explain the excess variance. Here, a Poisson mixture model, which assumes excess variability arises from sampling a mixture of distinct components, is proposed and the merits of this model are discussed and evaluated.

When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments.

We present a mixture model-based analysis for identifying differences in the distribution of RNA polymerase II (Pol II) in transcribed regions, measured using ChIP-seq (chromatin immunoprecipitation following massively parallel sequencing technology). The statistical model assumes that the number of Pol II-targeted sequences contained within each genomic region follows a Poisson distribution. A Poisson mixture model was then developed to distinguish Pol II binding changes in transcribed region using an empirical approach and an expectation-maximization (EM) algorithm developed for estimation and inference. In order to achieve a global maximum in the M-step, a particle swarm optimization (PSO) was implemented. We applied this model to Pol II binding data generated from hormone-dependent MCF7 breast cancer cells and antiestrogen-resistant MCF7 breast cancer cells before and after treatment with 17beta-estradiol (E2). We determined that in the hormone-dependent cells, approximately 9.9% (2527) genes showed significant changes in Pol II binding after E2 treatment. However, only approximately 0.7% (172) genes displayed significant Pol II binding changes in E2-treated antiestrogen-resistant cells. These results show that a Poisson mixture model can be used to analyze ChIP-seq data.