Improved estimation in negative binomial regression.
Ontology highlight
ABSTRACT:
SUBMITTER: Kenne Pagui EC
PROVIDER: S-EPMC9314673 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a lognormal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples.
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Project description:Extensive clinical trials indicate that patients with negative sentinel lymph node biopsy do not need axillary lymph node dissection (ALND). However, the ACOSOG Z0011 trial indicates that patients with clinically negative axillary lymph nodes (ALNs) and 1-2 positive sentinel lymph nodes having breast conserving surgery with whole breast radiotherapy do not benefit from ALND. The aim of this study is therefore to identify those patients with 0-2 positive nodes who might avoid ALND. A total of 486 patients were eligible for the study with 212 patients in the modeling group and 274 patients in the validation group, respectively. Clinical lymph node status, histologic grade, estrogen receptor status, and human epidermal growth factor receptor 2 status were found to be significantly associated with ALN metastasis. A negative binomial regression (NBR) model was developed to predict the probability of having 0-2 ALN metastases with the area under the curve of 0.881 (95% confidence interval 0.829-0.921, P < 0.001) in the modeling group and 0.758 (95% confidence interval 0.702-0.807, P < 0.001) in the validation group. Decision curve analysis demonstrated that the model was clinically useful. The NBR model demonstrated adequate discriminative ability and clinical utility for predicting 0-2 ALN metastases.
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Project description:BackgroundThe odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR.MethodsWe propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial.ResultsIn simulation studies, confidence intervals for the OR were 56-65% as wide (geometric model), 75-79% as wide (Poisson model), and 61-69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression.ConclusionsMore precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions.
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Project description:Motivated by a study examining spatiotemporal patterns in inpatient hospitalizations, we propose an efficient Bayesian approach for fitting zero-inflated negative binomial models. To facilitate posterior sampling, we introduce a set of latent variables that are represented as scale mixtures of normals, where the precision terms follow independent Pólya-Gamma distributions. Conditional on the latent variables, inference proceeds via straightforward Gibbs sampling. For fixed-effects models, our approach is comparable to existing methods. However, our model can accommodate more complex data structures, including multivariate and spatiotemporal data, settings in which current approaches often fail due to computational challenges. Using simulation studies, we highlight key features of the method and compare its performance to other estimation procedures. We apply the approach to a spatiotemporal analysis examining the number of annual inpatient admissions among United States veterans with type 2 diabetes.
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Project description:RNA sequencing (RNA-Seq) is the current method of choice for characterizing transcriptomes and quantifying gene expression changes. This next generation sequencing-based method provides unprecedented depth and resolution. The negative binomial (NB) probability distribution has been shown to be a useful model for frequencies of mapped RNA-Seq reads and consequently provides a basis for statistical analysis of gene expression. Negative binomial exact tests are available for two-group comparisons but do not extend to negative binomial regression analysis, which is important for examining gene expression as a function of explanatory variables and for adjusted group comparisons accounting for other factors. We address the adequacy of available large-sample tests for the small sample sizes typically available from RNA-Seq studies and consider a higher-order asymptotic (HOA) adjustment to likelihood ratio tests. We demonstrate that 1) the HOA-adjusted likelihood ratio test is practically indistinguishable from the exact test in situations where the exact test is available, 2) the type I error of the HOA test matches the nominal specification in regression settings we examined via simulation, and 3) the power of the likelihood ratio test does not appear to be affected by the HOA adjustment. This work helps clarify the accuracy of the unadjusted likelihood ratio test and the degree of improvement available with the HOA adjustment. Furthermore, the HOA test may be preferable even when the exact test is available because it does not require ad hoc library size adjustments.
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Project description:BackgroundIdentifying frequently mutated regions is a key approach to discover DNA elements influencing cancer progression. However, it is challenging to identify these burdened regions due to mutation rate heterogeneity across the genome and across different individuals. Moreover, it is known that this heterogeneity partially stems from genomic confounding factors, such as replication timing and chromatin organization. The increasing availability of cancer whole genome sequences and functional genomics data from the Encyclopedia of DNA Elements (ENCODE) may help address these issues.ResultsWe developed a negative binomial regression-based Integrative Method for mutation Burden analysiS (NIMBus). Our approach addresses the over-dispersion of mutation count statistics by (1) using a Gamma-Poisson mixture model to capture the mutation-rate heterogeneity across different individuals and (2) estimating regional background mutation rates by regressing the varying local mutation counts against genomic features extracted from ENCODE. We applied NIMBus to whole-genome cancer sequences from the PanCancer Analysis of Whole Genomes project (PCAWG) and other cohorts. It successfully identified well-known coding and noncoding drivers, such as TP53 and the TERT promoter. To further characterize the burdening of non-coding regions, we used NIMBus to screen transcription factor binding sites in promoter regions that intersect DNase I hypersensitive sites (DHSs). This analysis identified mutational hotspots that potentially disrupt gene regulatory networks in cancer. We also compare this method to other mutation burden analysis methods.ConclusionNIMBus is a powerful tool to identify mutational hotspots. The NIMBus software and results are available as an online resource at github.gersteinlab.org/nimbus.
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Project description:OBJECTIVES:This study aimed to examine the link between human mobility and the number of coronavirus disease 2019 (COVID-19)-infected people in countries. STUDY DESIGN:Our data set covers 144 countries for which complete data are available. To analyze the link between human mobility and COVID-19-infected people, our study focused on the volume of air travel, the number of airports, and the Schengen system. METHODS:To analyze the variation in COVID-19-infected people in countries, we used negative binomial regression analysis. RESULTS:Our findings suggest a positive relationship between higher volume of airline passenger traffic carried in a country and higher numbers of patients with COVID-19. We further found that countries which have a higher number of airports are associated with higher number of COVID-19 cases. Schengen countries, countries which have higher population density, and higher percentage of elderly population are also found to be more likely to have more COVID-19 cases than other countries. CONCLUSIONS:The article brings a novel insight into the COVID-19 pandemic from a human mobility perspective. Future research should assess the impacts of the scale of sea/bus/car travel on the epidemic. The findings of this article are relevant for public health authorities, community and health service providers, as well as policy-makers.
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Project description:BACKGROUND: The group testing method has been proposed for the detection and estimation of genetically modified plants (adventitious presence of unwanted transgenic plants, AP). For binary response variables (presence or absence), group testing is efficient when the prevalence is low, so that estimation, detection, and sample size methods have been developed under the binomial model. However, when the event is rare (low prevalence <0.1), and testing occurs sequentially, inverse (negative) binomial pooled sampling may be preferred. METHODOLOGY/PRINCIPAL FINDINGS: This research proposes three sample size procedures (two computational and one analytic) for estimating prevalence using group testing under inverse (negative) binomial sampling. These methods provide the required number of positive pools ([Formula: see text]), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model and inverse (negative) binomial sampling. We give real and simulated examples to show how to apply these methods and the proposed sample-size formula. The Monte Carlo method was used to study the coverage and level of assurance achieved by the proposed sample sizes. An R program to create other scenarios is given in Appendix S2. CONCLUSIONS: The three methods ensure precision in the estimated proportion of AP because they guarantee that the width (W) of the confidence interval (CI) will be equal to, or narrower than, the desired width ([Formula: see text]), with a probability of [Formula: see text]. With the Monte Carlo study we found that the computational Wald procedure (method 2) produces the more precise sample size (with coverage and assurance levels very close to nominal values) and that the samples size based on the Clopper-Pearson CI (method 1) is conservative (overestimates the sample size); the analytic Wald sample size method we developed (method 3) sometimes underestimated the optimum number of pools.
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Project description:Use of zero-inflated count data models is common in applications where the number of zero counts exceeds that predicted from a traditional count data model such as Poisson or negative binomial. When count data exhibiting inflated zero counts are correlated among subjects, a natural approach will be to fit a marginal model with the help of generalized estimating equations (GEE) that can incorporate subject-to-subject correlations. A GEE based zero-inflated negative binomial (ZINB) model is proposed to fit clustered counts with excessive zeros. However, the corresponding sandwich variance estimator appears to underestimate the true variance. The theoretical reasons for its failure are explained and a correction under additional modeling assumptions is offered. In addition, a clustered resampling (bootstrap) procedure is proposed to estimate the variance and it is shown that the bootstrap procedure captures the correct variance under no additional model assumptions. Utility of this marginal GEE based ZINB model over two other competing models has been assessed using a thorough simulation study. The resulting inference procedure is applied to study the association between the dental caries and fluoride exposures using a dataset extracted from the Iowa Fluoride Study. A number of risk factors of clinical significance are reliably identified using the proposed model.
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Project description:OBJECTIVE: To illustrate how the analysis of bimodal U-shaped distributed utilization can be modeled with beta-binomial regression, which is rarely used in health services research. DATA SOURCES/STUDY SETTING: Veterans Affairs (VA) administrative data and Medicare claims in 2001-2004 for 11,123 Medicare-eligible VA primary care users in 2000. STUDY DESIGN: We compared means and distributions of VA reliance (the proportion of all VA/Medicare primary care visits occurring in VA) predicted from beta-binomial, binomial, and ordinary least-squares (OLS) models. PRINCIPAL FINDINGS: Beta-binomial model fits the bimodal distribution of VA reliance better than binomial and OLS models due to the nondependence on normality and the greater flexibility in shape parameters. CONCLUSIONS: Increased awareness of beta-binomial regression may help analysts apply appropriate methods to outcomes with bimodal or U-shaped distributions.
| S-EPMC3796113 | biostudies-literature