gamma-Poisson Distribution Research Articles

A Bayesian adaptive feasibility design for rare diseases

It is important for researchers to carefully assess the feasibility of a clinical trial prior to the launch of the study. One feasibility aspect that needs to be considered includes whether investigators can expect to successfully achieve the sample size needed for their trial. In this manuscript, we present a Bayesian design in which data collected during a pilot study is used to predict the feasibility of a planned phase III trial. Specifically, we outline a model that predicts a target sample size obtained from the Gamma-Poisson distribution. In a simulation study, we showcase the utility of the proposed design by applying it to a phase III trial designed to assess the efficacy of mycophenolate mofetil in individuals with mild systemic sclerosis. We demonstrate that the predictive nature of the proposed design is particularly useful for rare disease clinical trials and has the potential to greatly increase their efficiency.

Exploring the Relationship Between Atorvastatin and Memory Loss: A Comprehensive Analysis Integrating Real-World Pharmacovigilance and Mendelian Randomization.

Atorvastatin is a drug widely used to prevent cardiovascular and cerebrovascular diseases. Current observational studies suggest that atorvastatin may be associated with cognitive dysfunction (especially memory loss). However, some studies have suggested that dyslipidemia may be an important factor in cognitive dysfunction. The purpose of this study was to perform a pharmacovigilance analysis using real-world data from the US Food and Drug Administration's Adverse Event Reporting System (FAERS) to assess whether memory loss is an adverse effect of atorvastatin and to further clarify its causality through Mendelian randomization (MR). We extracted real-world data from the FAERS database (Quarter 1 2004 to Quarter 1 2023). Disproportionality analysis methods and measures of association such as the reporting odds ratio (OR), proportional reporting ratio, Bayesian confidence interval progressive neural network, and polynomial Gamma Poisson distribution reduction were used to assess whether memory loss was an adverse effect of atorvastatin. In addition, we used MR to evaluate causality in depth. In the pharmacovigilance analysis of atorvastatin, we extracted four datasets of clinical symptoms associated with memory loss from the FAERS database [Amnesia (n = 1196), Memory impairment (n = 840), Transient global amnesia (n = 38), and Retrograde amnesia (n = 9)]. The reporting OR, proportional reporting ratio, Bayesian confidence interval progressive neural network, and Gamma Poisson distribution reduction all showed positive results for amnesia, transient global amnesia, and retrograde amnesia, while the reporting OR and Bayesian confidence interval progressive neural network also showed positive results for memory disorders. Thus, memory loss was a frequent side effect of atorvastatin. The MR analyses were used to further evaluate the association between statins and memory loss. The results of the MR analysis (statins and memory loss) are as follows: Ivw (mre) (β = 0.11 [OR = 1.11], P = 0.01 < 0.05) and the OR and β directions of MR-Egger and weighted mode were the same. The results of the MR analysis (statins and mitochondrial DNA copy number) are as follows: Ivw(mre) (β = -0.03 [OR = 0.96], P < 0.01) and the OR and β direction of MR-Egger and weighted mode are the same. The results of the MR analysis (DNA copy number and memory loss) are as follows: Ivw(β = - 0.06 [OR = 0.94], P = 0.04 < 0.05) and the OR and β direction of MR-Egger and weighted mode were the same. The pleiotropy test did not find horizontal diversity in our results. This study suggests that memory loss is a notable adverse event associated with atorvastatin and provides evidence indicating a potential causal relationship between atorvastatin and memory loss. We also found that statins may further affect memory by affecting mitochondrial function. Therefore, in the clinical use of atorvastatin, it is important to carefully monitor the changes in cognitive function of patients. Second, a pharmacovigilance analysis combined with MR was used in this study to provide a new approach for the study of adverse drug reactions. This comprehensive analysis method helps to evaluate the safety of drugs and the risk of adverse reactions more comprehensively and provides doctors with a more accurate clinical decision-making basis.

Predictive Modelling on Competitor Analysis Performance by using Generalised Linear Models and Machine Learning Approach

Competitive analysis in digital and technology is trending in the business field. However, the field of digital and technology in the business world is vast and challenging to analyse. The purpose of this research is first to identify the success factor which represent the company performance. Second, is to identify the significant services provided by the company to their business user. Then, based on the first and second objectives, a predictive modelling is developed to produce the best solution to their business user. The research is implementing a case study from Telecommunication Company and using data science life cycle methodology. The statistical modelling that is used to develop the competitor’s analysis model is generalised linear model (GLM) which integrated with machine learning approach. Furthermore, the synthetic data set is created by using Gamma Distribution, Gaussian Distribution and Poisson Distribution due to some data from the case study is confidential. The synthetic data set is based on existing real data which are from Telecommunication Company sentiment analysis data, were used to investigate the performance of the proposed model. The machine learning technique is used to get the accuracy of the significant GLM which has been developed. The accuracy is tested by using the error rates of the machine learning technique which are Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and R-squared. This research discovered that the business solution to the significant service for the business user and discovered the best statistical model to be used for the business solution. The results show that the Gumbel distribution is the best fit model for the synthetic dataset where the values of RMSE is 1.0574, MAE is 0.9168 and R-squared is 0.3994, and the significant success factor that has been identified by using the GLM is advertising success factor. The model developed can be improved with another type of data set and different sizes of data. Hence, further studies and real-world data are required for better validation.

Signal detection of adverse reactions for bendamustine based on FDA adverse event reporting system

ABSTRACT Background This study aimed to analyze the adverse events to bendamustine using data obtained from the Food and Drug Administration open public data project (openFDA) and to provide a reference for its use in clinical practice. Research design and methods Adverse events (AEs) due to bendamustine usage reported from 1 January 2008 to 31 March 2023 were collected from the FDA Adverse Event Reporting System (FAERS). The reporting odds ratio (ROR), proportional reporting ratio (PRR), Bayesian plausible propagation neural network (BCPNN), and multinomial gamma-Poisson distribution shrinking (MGPS) algorithms were used to identify signs of adverse reactions caused by bendamustine. Results A total of 4214 AE reports where bendamustine was considered as the first suspected drug were obtained from FAERS. The analysis revealed 214 AE risk signals, among which 141 met the criteria but they were not listed as possible side effects on the drug information sheet provided in the package. Conclusion Our findings identified numerous common AEs with previously reported clinical observations. We also identified some signs of potential new AEs, indicating the need of careful clinical monitoring of patients treated with bendamustine and further risk identification research about this drug.

Optimal Bayesian generalized multiple-dependent state sampling plan for attributes

Over the years, acceptance sampling plans have been crucial to quality assurance in manufacturing. Sample plans are designed using operating characteristic curve conditions to safeguard producers and customers. We propose a conditional probability-based Bayesian generalized multiple-dependent state sampling technique in this paper. The technique relies on Gamma-Poisson distribution. Other performance indicators and acceptance probability are calculated. Also, the new plan's operational method is discussed. The proposed technique is also compared to current attribute sampling schemes for efficacy. Optimal plan parameters for the plan's economic structure are also generated, adding managerial insights to the suggested plan. The entire cost study showed that the suggested plan is cheaper than existing sample plans under identical conditions. To account for inspection flaws, the plan is adjusted. We examine how Type I and Type II errors affect sampling plan outcomes. The plan is demonstrated with numerical examples and a data-driven application.

Research of the model for assessing the workload of passenger port infrastructure using decision-making models under uncertainty

The current situation formed by the changeable influence of the external environment on the interaction of “sea passenger port — sea ferry/cruise company” systems has formulated new decision-making tasks under uncertainty to justify infrastructural changes. It is not enough for the managers of sea passenger ports and terminals to make decisions only on the basis of deterministic models. Probabilistic nature of the processes predetermines the need to form new models and methods to substantiate strategies for the sea passenger ports development. The problem field considered in the paper is topical because today due to such trends as increase in dimension of cruise and ferry vessels and changes in route networks it is necessary to solve the problem of development forecasting on the basis of scenario modeling. Modeling should be performed on the basis of new digital transport models, which take into account the peculiarities of marine ports and terminals infrastructure, and priority of berths. The digital model of “Passenger Port of St. Petersburg “Sea Façade”, developed by the author, is used in the paper and the necessity to single out separate states in the development of sea passenger ports is substantiated. The validity of singling out a set of boundary points, turning points of uncertainty of future development of a complex system of a sea passenger port or terminal, connected with the presence of bifurcation zones — “ramification” of possible ways of the port system evolution is proved. The proof of the proposed approach is presented by means of allocation of individual stages in the development of the sea passenger port of St. Petersburg. Based on the presented approach, a new model for the evolution and management of the sea passenger port system development is proposed. This model on a single assembly field reflects temporary changes in the development of the sea passenger port and analytical data on the increase or decrease in the number of berths. The presented set of transition points allows to determine the time model of the sea passenger port development. A new model of working with data for making decisions on modernization of sea passenger port infrastructure is offered. On the basis of modeling, taking into account different distribution laws (gamma distribution, Poisson distribution, normal distribution and others) the conditions for formation of the individual “fields of utility”, cones of preference and target functions are presented. For precise description of decision-making situation under uncertainty faced by the head of the sea passenger port, the choice of Savage criterion (S-criterion) is substantiated and mathematical model and criteria are given. A solution for formation of acceptable interval on the basis of Dataset utility field data on intensities of ferry and cruise lines work is given. On the basis of the experiment, the accuracy of the proposed decision-making model under uncertainty to justify the conditions on the need for modernization of infrastructure (modernization of berths) of the sea passenger port is substantiated. The presented model and results can be applied to other sea passenger ports and terminals, which determines the universality of the presented approach.

Multi-layer perceptron classification method of medical data based on biogeography-based optimization algorithm with probability distributions

In the field of medical informatics, the accuracy of medical data classification plays a vital role. Multi-layer Perceptron (MLP), as one of the most widely used neural networks, has been widely used in the medical fields. In recent years, the Biogeography-based Optimization (BBO) algorithm has been proposed to train MLP, but the original algorithm often encounters local minimums, slow convergence, and sensitivity to initialized values during the optimization process. To this end, this paper adopted the different probability distributions to improve the BBO (PD-BBO) algorithm to train MLP so as to improve medical data classification accuracy. These distributions include Gamma distribution, Beta distribution, Gaussian distribution, Exponential distribution, Poisson distribution, Geometric distribution, Rayleigh distribution and Weber distribution Then these different probability distributions were embed into the migration process of the BBO algorithm to replace the random distribution and the migration probability was defined. Finally, simulation experiments were carried out, and the benchmark function was used to prove the effectiveness of the proposed algorithms. And then it was used to train a multi-layer perceptron, and five medical data sets were selected for classification. After that, the performance of the standard BBO algorithm and five typical meta-heuristic algorithms were compared. The results showed that the PD-BBO algorithms to train MLP was better than the BBO algorithm and the selected meta-heuristic algorithms, and the classification accuracy has been improved to a certain extent.

Economic Design of Quick Switching Sampling System for Resubmitted Lots under Gamma-Poisson Distribution

In this paper, a method of designing quick switching sampling system for resubmitted lots for inspection of attribute quality characteristics based on the gamma-Poisson distribution is proposed. We determine the required parameters by using two-points on the operating characteristic curve approach such that both producer’s and the consumer’s risks are satisfied for some specified values of acceptable quality level and limiting quality level. Tables are constructed for optimal sample size and two acceptance numbers of the proposed sampling system. The relative efficiency of the proposed system over conventional plans is also discussed. In addition, an economic design of the above mentioned sampling system to minimize total cost is also investigated. Consequently, it is proved that the proposed system minimizes the total inspection cost and average total inspection.

GlmGamPoi: fitting Gamma-Poisson generalized linear models on single cell count data.

MotivationThe Gamma-Poisson distribution is a theoretically and empirically motivated model for the sampling variability of single cell RNA-sequencing counts and an essential building block for analysis approaches including differential expression analysis, principal component analysis and factor analysis. Existing implementations for inferring its parameters from data often struggle with the size of single cell datasets, which can comprise millions of cells; at the same time, they do not take full advantage of the fact that zero and other small numbers are frequent in the data. These limitations have hampered uptake of the model, leaving room for statistically inferior approaches such as logarithm(-like) transformation.ResultsWe present a new R package for fitting the Gamma-Poisson distribution to data with the characteristics of modern single cell datasets more quickly and more accurately than existing methods. The software can work with data on disk without having to load them into RAM simultaneously.Availabilityand implementationThe package glmGamPoi is available from Bioconductor for Windows, macOS and Linux, and source code is available on github.com/const-ae/glmGamPoi under a GPL-3 license. The scripts to reproduce the results of this paper are available on github.com/const-ae/glmGamPoi-Paper.Supplementary information Supplementary data are available at Bioinformatics online.

Designing of Chain Sampling Plan underGamma-Poisson Distribution

In this manuscript, we discuss the designing procedure of chain sampling plan which is known as one of the conditional sampling plans under gamma-Poisson distribution. We determine the optimal parameters namely, number of items to be chosen for inspection from the lot and number of preceding lots to be considered in order to dispose the current lot by specifying two points on the operating characteristic curve, which is the usual designing approach of sampling plan. The procedure which is used to execute the proposed plan is provided and comparison is made among the proposed plan and existing sampling plans performance.

Splatter: simulation of single-cell RNA sequencing data

As single-cell RNA sequencing (scRNA-seq) technologies have rapidly developed, so have analysis methods. Many methods have been tested, developed, and validated using simulated datasets. Unfortunately, current simulations are often poorly documented, their similarity to real data is not demonstrated, or reproducible code is not available. Here, we present the Splatter Bioconductor package for simple, reproducible, and well-documented simulation of scRNA-seq data. Splatter provides an interface to multiple simulation methods including Splat, our own simulation, based on a gamma-Poisson distribution. Splat can simulate single populations of cells, populations with multiple cell types, or differentiation paths.

Designing of Bayesian Multiple Deferred State Sampling Plan Based on Gamma–Poisson Distribution

SYNOPTIC ABSTRACTConditional sampling plans such as chain sampling plans can be applied for making decisions on lot disposition utilizing not only information from the lot sampled but also information from preceding lots. The intent in the utilization of prior lot information is to reduce sample size and consequent costs of the decision process. A deferred state sampling plan is a conditional sampling plan in which the decision about previous lots is deferred until successive lots are selected and the outcome of successive lots is observed. In this article, we propose the multiple deferred state sampling plan based on the Bayesian methodology under the gamma–Poisson distribution. Tables of optimal parameters such as the sample size, acceptance numbers, and number of successive lots required to make the decision on the current lot are provided. The optimal parameters are determined using the approach of two points on the operating characteristic curve and by minimizing the average sample number. The advantages of the multiple deferred state sampling plan over the existing sampling plans under gamma–Poisson distribution are also discussed.

Design and Evaluation of Bayesian Dependent State Sampling Inspection Plans

Abstract The theory of sampling inspection procedures by attributes is built upon the general assumptions that the manufacturing process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, the lots formed from any production process will have quality variations, which occur due to random fluctuations. When quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. In such cases, Bayesian acceptance sampling plans (BASP), which use prior information on the process variation for taking decisions about the submitted lots, can be employed as an alternative to conventional plans. This paper focuses on the concept of dependent state sampling inspection plans by attributes for continuous production with small acceptance numbers under Bayesian perspective and highlights the properties of its characteristic curves with reference to various parameters. A procedure for determining the parameters of such plans for two specified points on the operating characteristic curves under the conditions of gamma-Poisson distribution is discussed with illustrations. The closed form expressions for the parameters of the plans are also derived.

Bayesian Design of Special Type of Double Sampling Plans for Compliance Testing

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.

Population size estimation based upon ratios of recapture probabilities

Estimating the size of an elusive target population is of prominent interest in many areas in the life and social sciences. Our aim is to provide an efficient and workable method to estimate the unknown population size, given the frequency distribution of counts of repeated identifications of units of the population of interest. This counting variable is necessarily zero-truncated, since units that have never been identified are not in the sample. We consider several applications: clinical medicine, where interest is in estimating patients with adenomatous polyps which have been overlooked by the diagnostic procedure; drug user studies, where interest is in estimating the number of hidden drug users which are not identified; veterinary surveillance of scrapie in the UK, where interest is in estimating the hidden amount of scrapie; and entomology and microbial ecology, where interest is in estimating the number of unobserved species of organisms. In all these examples, simple models such as the homogenous Poisson are not appropriate since they do not account for present and latent heterogeneity. The Poisson–Gamma (negative binomial) model provides a flexible alternative and often leads to well-fitting models. It has a long history and was recently used in the development of the Chao–Bunge estimator. Here we use a different property of the Poisson–Gamma model: if we consider ratios of neighboring Poisson–Gamma probabilities, then these are linearly related to the counts of repeated identifications. Also, ratios have the useful property that they are identical for truncated and untruncated distributions. In this paper we propose a weighted logarithmic regression model to estimate the zero frequency counts, assuming a Gamma–Poisson distribution for the counts. A detailed explanation about the chosen weights and a goodness of fit index are presented, along with extensions to other distributions. To evaluate the proposed estimator, we applied it to the benchmark examples mentioned above, and we compared the results with those obtained through the Chao–Bunge and other estimators. The major benefits of the proposed estimator are that it is defined under mild conditions, whereas the Chao–Bunge estimator fails to be well defined in several of the examples presented; in cases where the Chao–Bunge estimator is defined, its behavior is comparable to the proposed estimator in terms of Bias and MSE as a simulation study shows. Furthermore, the proposed estimator is relatively insensitive to inclusion or exclusion of large outlying frequencies, while sensitivity to outliers is characteristic of most other methods. The implications and limitations of such methods are discussed.

Chain Sampling Inspection Plans Based on Bayesian Methodology

Acceptance sampling in quality control is a statistical methodology and consists of procedures for sentencing one or more incoming lots of finished products based on the inspection of sampled items drawn randomly from the lots. The theory of such procedures by attributes is often built upon the assumptions that the production process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, any production process exhibits quality variations, which occur due to random fluctuations. When the quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. In such cases, for sentencing the processes generating the lots, Bayesian acceptance sampling plans, which use prior information on the process variation, can be employed as an alternative to conventional plans. This paper presents the concept of chain sampling inspection plans by attributes for continuous production using Bayesian methodology. The operating characteristic (OC) function of Bayesian chain sampling plans as a measure of performance is defined and the properties of OC curves of the plans with reference to their parameters are studied empirically. A procedure for determining the parameters of such plans for two specified points on the operating characteristic curves under the conditions of gamma-Poisson distribution is discussed. The closed form expressions for the parameters of the plans are derived.

Selection of Bayesian Double Sampling Inspection Plans by Attributes with Small Acceptance Numbers

Sampling inspection is a product control technique and consists of rules or procedures for taking decisions on the disposition of lots of finished products based on the inspection of individual units in one or more random samples drawn from the lots. The basic assumption underlying the theory of such procedures by attributes is that the lot or process fraction nonconforming is a constant. Evidently, this assumption is not fulfilled, even if the production process is stable, i.e., if the nonconforming probability is a constant. However, in practice, the lots formed from a process will have different fractions nonconforming, which occur due to random fluctuations. In such cases, Bayesian acceptance sampling plans (BASP), which use prior information on the process variation for taking decisions about the submitted lots, can be employed as alternative to conventional plans. This paper presents a double sampling inspection plan by attributes with small acceptance numbers using the Bayesian methodology. The properties of its characteristic curves with reference to various parameters are highlighted. The design problem of selecting such sampling plans with reference to two prescribed points on the operating characteristic curve under the condition of gamma-Poisson distribution is addressed.

A Gamma-Poisson Distribution of Point to k Nearest Event Distance

Abstract Distance sampling of events in natural or seminatural populations often indicates a larger variance in the distance to the kth nearest event than expected for events distributed completely at random. Overdispersion contributes to the well-known bias problem of distance sampling density estimators. Distance distribution models that accommodate overdispersion in the data should lead to more robust estimators of density. To this end we propose a gamma-Poisson distribution model for distances from a point to k nearest events. The model assumes a gamma distribution of local densities of randomly distributed events. Properties of the distribution and estimation of the parameters and event density are detailed for both constrained and unconstrained sampling. Four examples, one with simulated data from a known negative binomial distribution and three with simulated distance sampling in natural and seminatural stem-mapped tree stands, illustrate the promising performance of this new distribution, both as a model for distances and for density estimation. The modeling approach extends to other mixing distributions.

ゼロトランケーションのあるカウントデータの解析

An analysis method is considered that concerns count data with zero truncation, i.e. frequencies of occurrence of an event greater than or equal to 1 are only reported and the frequency of zero occurrence is not available. Relationship between the counts of occurrences of two related events is particularly interested. Such relationship is modeled by a bivariate gamma-Poisson distribution in this paper. To estimate the unknown parameters involved in the model, a simple method based on sample means is proposed. The estimation procedure is applied to some real datasets and interpretations of the results obtained are given. An additional point emphasized in this paper is that the frequency of zero count is not always trusted even the number is reported.

Exact Credibility and Tweedie Models

Kaas, Dannenburg &amp; Goovaerts (1997) generalized Jewell’s theorem on exact credibility, from the classical Bühlmann model to the (weighted) Bühlmann-Straub model. We extend this result further to the “Bühlmann-Straub model with a priori differences” (Bühlmann &amp; Gisler, 2005). It turns out that exact credibility holds for a class of Tweedie models, including the Poisson, gamma and compound Poisson distribution – the most important distributions for insurance applications of generalized linear models (GLMs). Our results can also be viewed as an alternative to the HGLM approach for combining credibility and GLMs, see Nelder and Verrall (1997).