Dirichlet-multinomial Model Research Articles

Population projections from holey matrices: Using prior information to estimate rare transition events

Population projection matrices are a common means for predicting short- and long-term population persistence for rare, threatened and endangered species. Data from such species can suffer from small sample sizes and consequently miss rare demographic events resulting in incomplete or biologically unrealistic life cycle trajectories. Matrices with missing values (zeros; e.g., no observation of seeds transitioning to seedlings) are often patched using prior information from the literature, other populations, time periods, other species, best guess estimates, or are sometimes even ignored. To alleviate this problem, we propose using a multinomial-Dirichlet model for parameterizing transitions and a Gamma for reproduction to patch missing values in these holey matrices. This formally integrates prior information within a Bayesian framework and explicitly includes the weight of the prior information on the posterior distributions. We show using two real data sets that the weight assigned to the prior information mainly influences the dispersion of the posteriors, the inclusion of priors results in irreducible and ergodic matrices, and more biologically realistic inferences can be made on the transition probabilities. Because the priors are explicitly stated, the results are reproducible and can be re-evaluated if alternative priors are available in the future.

Bayesian approach to the meta-analysis of multi-category prevalence

Multiple category prevalence represents the prevalence of the specific disease with different k-category (k > 2) statuses, such as mild, moderate and severe. This study proposed the Bayesian method for the meta-analysis of studies with multiple category prevalence. The Dirichlet-multinomial model was used to obtain the Bayesian approach. In this way, both the opportunity to consider the preinformation regarding the prevalences and to obtain an effective estimation regardless of the value of the prevalences (around 0.5 or close to 0-1) was possible. The proposed method was compared with the frequentist method based on simulation and Barendregt et al. (2013) data. It was demonstrated that without requiring any transformation, the Bayesian method resulted in more consistency; smaller relative errors and mean squared errors, powerful accepted probability estimators, especially for small total sample sizes; and prevalences close to 0-1.

Bayesian and frequentist approaches to multinomial count models in ecology

Multinomial count data are common in trophic ecology, spatial ecology, and community ecology. Compared to generalized linear models (GLMs) for univariate data, fewer statistical programs have been developed for the multivariate counterpart of GLMs. Studies of spatiotemporal community dynamics and spatial ecology on large spatial scales may generate large or big data on compositional counts or proportions. Fast, reliable computational methods can promote applications of multivariate generalized linear models (MGLMs) in predictive ecology and ecological informatics. The main objective of this study was to build Dirichlet-multinomial (D-M) models for compositional counts using frequentist's maximum likelihood estimation (MLE) with template model builder (TMB), full Bayesian estimation with programs JAGS and Stan, and variational Bayes in Stan. Bayesian and frequentist D-M models were applied to the compositional counts of radio telemetry locations of ring-necked pheasants (Phasianus colchicus) and American beaver (Castor canadensis) in different habitat-cover types to estimate habitat selection index. Bayesian D-M models with JAGS and Stan produced similar estimates as TMB programs. However, TMB programs ran a few hundred times faster than the Bayesian models. Template model builder and Stan are flexible in building complex statistical models and can accommodate a large number of parameters and random effects. The joint use of TMB and Stan may help develop MGLMs and multivariate generalized linear mixed models for large ecological data.

Colouring representation: staff racial employment patterns in US congressional offices

ABSTRACT Members of the United States House of Representatives disproportionately hire Black and Hispanic staffers into constituent service focussed roles as compared to policy development positions. Minority staffers are also underrepresented in the highest paid (arguably the most influential) positions in Congressional offices. I demonstrate these racial employment patterns using a Dirichlet-multinomial likelihood model to investigate a novel dataset that includes information on all of the staffers employed in the offices of 211 US House Members in the 108th Congress. This research compares the patterns of both Black and Hispanic staffers and draws from a more comprehensive sample than previous studies on staff race. The racial asymmetries found in staffers’ roles and responsibilities are cause for concern regarding the voice minorities have in Congressional policymaking.

Topographic heterogeneity of lung microbiota in end-stage idiopathic pulmonary fibrosis: the Microbiome in Lung Explants-2 (MiLEs-2) study

BackgroundLung microbiota profiles in patients with early idiopathic pulmonary fibrosis (IPF) have been associated with disease progression; however, the topographic heterogeneity of lung microbiota and their roles in advanced IPF...

Predictive analysis methods for human microbiome data with application to Parkinson's disease.

Microbiome data consists of operational taxonomic unit (OTU) counts characterized by zero-inflation, over-dispersion, and grouping structure among samples. Currently, statistical testing methods are commonly performed to identify OTUs that are associated with a phenotype. The limitations of statistical testing methods include that the validity of p-values/q-values depend sensitively on the correctness of models and that the statistical significance does not necessarily imply predictivity. Predictive analysis using methods such as LASSO is an alternative approach for identifying associated OTUs and for measuring the predictability of the phenotype variable with OTUs and other covariate variables. We investigate three strategies of performing predictive analysis: (1) LASSO: fitting a LASSO multinomial logistic regression model to all OTU counts with specific transformation; (2) screening+GLM: screening OTUs with q-values returned by fitting a GLMM to each OTU, then fitting a GLM model using a subset of selected OTUs; (3) screening+LASSO: fitting a LASSO to a subset of OTUs selected with GLMM. We have conducted empirical studies using three simulation datasets generated using Dirichlet-multinomial models and a real gut microbiome data related to Parkinson’s disease to investigate the performance of the three strategies for predictive analysis. Our simulation studies show that the predictive performance of LASSO with appropriate variable transformation works remarkably well on zero-inflated data. Our results of real data analysis show that Parkinson’s disease can be predicted based on selected OTUs after the binary transformation, age, and sex with high accuracy (Error Rate = 0.199, AUC = 0.872, AUPRC = 0.912). These results provide strong evidences of the relationship between Parkinson’s disease and the gut microbiome.

Respiratory Tract Dysbiosis Is Associated with Worse Outcomes in Mechanically Ventilated Patients.

Rationale: Host inflammatory responses have been strongly associated with adverse outcomes in critically ill patients, but the biologic underpinnings of such heterogeneous responses have not been defined.Objectives: We examined whether respiratory tract microbiome profiles are associated with host inflammation and clinical outcomes of acute respiratory failure.Methods: We collected oral swabs, endotracheal aspirates (ETAs), and plasma samples from mechanically ventilated patients. We performed 16S ribosomal RNA gene sequencing to characterize upper and lower respiratory tract microbiota and classified patients into host-response subphenotypes on the basis of clinical variables and plasma biomarkers of innate immunity and inflammation. We derived diversity metrics and composition clusters with Dirichlet multinomial models and examined our data for associations with subphenotypes and clinical outcomes.Measurements and Main Results: Oral and ETA microbial communities from 301 mechanically ventilated subjects had substantial heterogeneity in α and β diversity. Dirichlet multinomial models revealed a cluster with low α diversity and enrichment for pathogens (e.g., high Staphylococcus or Pseudomonadaceae relative abundance) in 35% of ETA samples, associated with a hyperinflammatory subphenotype, worse 30-day survival, and longer time to liberation from mechanical ventilation (adjusted P < 0.05), compared with patients with higher α diversity and relative abundance of typical oral microbiota. Patients with evidence of dysbiosis (low α diversity and low relative abundance of "protective" oral-origin commensal bacteria) in both oral and ETA samples (17%, combined dysbiosis) had significantly worse 30-day survival and longer time to liberation from mechanical ventilation than patients without dysbiosis (55%; adjusted P < 0.05).Conclusions: Respiratory tract dysbiosis may represent an important, modifiable contributor to patient-level heterogeneity in systemic inflammatory responses and clinical outcomes.

A Gamma-Poisson Mixture Topic Model for Short Text

Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modelling, the Poisson distribution describes the number of occurrences of a word in documents of fixed length. The Poisson distribution has been successfully applied in text classification, but its application to topic modelling is not well documented, specifically in the context of a generative probabilistic model. Furthermore, the few Poisson topic models in the literature are admixture models, making the assumption that a document is generated from a mixture of topics. In this study, we focus on short text. Many studies have shown that the simpler assumption of a mixture model fits short text better. With mixture models, as opposed to admixture models, the generative assumption is that a document is generated from a single topic. One topic model, which makes this one-topic-per-document assumption, is the Dirichlet-multinomial mixture model. The main contributions of this work are a new Gamma-Poisson mixture model, as well as a collapsed Gibbs sampler for the model. The benefit of the collapsed Gibbs sampler derivation is that the model is able to automatically select the number of topics contained in the corpus. The results show that the Gamma-Poisson mixture model performs better than the Dirichlet-multinomial mixture model at selecting the number of topics in labelled corpora. Furthermore, the Gamma-Poisson mixture produces better topic coherence scores than the Dirichlet-multinomial mixture model, thus making it a viable option for the challenging task of topic modelling of short text.

A90 A UTILITY-BASED BAYESIAN OPTIMAL INTERVAL (U-BOIN) PHASE I/II DESIGN TO IDENTIFY THE OPTIMAL BIOLOGICAL DOSE FOR TARGETED AND IMMUNE THERAPIES

Abstract Background In the era of targeted therapy and immunotherapy, the objective of dose finding is often to identify the optimal biological dose (OBD), rather than the maximum tolerated dose (MTD). Aims To develop a utility-based Bayesian optimal interval (U-BOIN) phase I/II design to find the OBD. Methods We jointly model toxicity and efficacy using a multinomial-Dirichlet model, and employ a utility function to measure dose risk-benefit trade-off. The U-BOIN design consists of two seamlessly connected stages. In stage I, the Bayesian optimal interval (BOIN) design is used to quickly explore the dose space and collect preliminary toxicity and efficacy data. In stage II, in light of accumulating efficacy and toxicity from both stages I and II, we continuously update the posterior estimate of the utility for each dose after each cohort, and use this information to direct the dose assignment and selection. Compared to existing phase I/II designs, one prominent advantage of the U-BOIN design is its simplicity for implementation. Once the trial is designed, it can be easily applied using predetermined decision tables, without complex model fitting and estimation. Results Our simulation study shows that, despite its simplicity, the U-BOIN design is robust and has high accuracy to identify the OBD. Conclusions The U-BOIN design provide a practical, easy-to-implement method to identify the OBD for phase I-II clinical trials. It has great potential to accelate the drug development for GI diseases. Funding Agencies NIH

Comparison Between Two Multinomial Overdispersion Models Through Simulation

A key assumption when using the multinomial distribution is that the observations are independent. In many practical situations, the observations could be correlated or clustered and the probabilities within each cluster might vary, which may lead to overdispersion. In this paper we discuss two well-known approaches to model overdispersed multinomial data, the Dirichlet-multinomial model and the finite-mixture model. The difference between these two models has been illustrated via simulation study. The forest pollen data is considered as a practical example of overdisperse multinomial data. The overdispersion parameter,φ, has been estimated using two classical estimators.&#x0D; Dhaka Univ. J. Sci. 68(1): 45-48, 2020 (January)

Estimating overdispersion in sparse multinomial data.

Multinomial data arise in many areas of the life sciences, such as mark-recapture studies and phylogenetics, and will often by overdispersed, with the variance being higher than predicted by a multinomial model. The quasi-likelihood approach to modeling this overdispersion involves the assumption that the variance is proportional to that specified by the multinomial model. As this approach does not require specification of the full distribution of the response variable, it can be more robust than fitting a Dirichlet-multinomial model or adding a random effect to the linear predictor. Estimation of the amount of overdispersion is often based on Pearson's statistic X2 or the deviance D. For many types of study, such as mark-recapture, the data will be sparse. The estimator based on X2 can then be highly variable, and that based on D can have a large negative bias. We derive a new estimator, which has a smaller asymptotic variance than that based on X2 , the difference being most marked for sparse data. We illustrate the numerical difference between the three estimators using a mark-recapture study of swifts and compare their performance via a simulation study. The new estimator has the lowest root mean squared error across a range of scenarios, especially when the data are verysparse.

Vaginal microbiome diversity and preterm birth: results of a nested case–control study in Peru

PurposePreterm birth (PTB) is a major cause of neonatal mortality. The vaginal microbiome is associated with PTB, but results vary across racial/ethnic populations. Some evidence suggests gestational age affects this association. We investigated these associations in a novel population, conducting a post hoc analysis assessing if associations differed between women swabbed at different gestational ages. MethodsWe compared vaginal microbiomes from women with PTB (n = 25) to a random sample of women with term births (n = 100) among participants in the Pregnancy Outcomes, Maternal and Infant Study, conducted in Lima, Peru. Using DADA2, we identified taxa from 16S DNA sequencing and used Dirichlet multinomial mixture models to group into community state types (CSTs). ResultsIf gestational age at sampling was not considered, no CST (diverse, Lactobacillus-dominated or Lactobacillus iners–dominated), was associated with PTB. Among women sampled before 12 weeks' gestation, women with Lactobacillus-dominated CSTs were less likely to have a PTB than those with a diverse CST. Among those swabbed between 12 and 16 weeks' gestation, the reverse was true. ConclusionsOur study supports previous literature suggesting that what constitutes a healthy vaginal microbiome varies by race/ethnicity. Longitudinal studies are necessary to disentangle effects of vaginal microbiome differences over gestation.

An approach to imputing destination activities for inclusion in measures of bicycle accessibility

This paper proposes a new method to estimate bicycle accessibility for various trip purposes based on a massive dockless bike-sharing dataset in Shanghai, China. Specifically, a Dirichlet multinomial regression topic model (DMR model) is applied to identify bicycle trajectories' trip purposes, simultaneously considering arrival time and drop-off location. Based on obtained trip purposes, we estimate impedance functions using a negative exponential function. Finally, based on estimated impedance functions, two cases of bicycle accessibility for two different purposes - restaurant and hospital - are presented in Shanghais central area. The results show that almost 90% of bicycle trips are less than 30 min or 5 km. Although the difference between the impedance functions between various trip purposes is not significant, we find that trip purposes of “Work and School” have the highest travel impedance for bicyclists. Cyclists in Shanghai accept longer bicycle travel times for leisure (e.g., shopping) than for commuting (e.g., work or school).

A utility-based Bayesian optimal interval (U-BOIN) phase I/II design to identify the optimal biological dose for targeted and immune therapies.

In the era of targeted therapy and immunotherapy, the objective of dose finding is often to identify the optimal biological dose (OBD), rather than the maximum tolerated dose. We develop a utility-based Bayesian optimal interval (U-BOIN) phase I/II design to find the OBD. We jointly model toxicity and efficacy using a multinomial-Dirichlet model, and employ a utility function to measure dose risk-benefit trade-off. The U-BOIN design consists of two seamless stages. In stage I, the Bayesian optimal interval design is used to quickly explore the dose space and collect preliminary toxicity and efficacy data. In stage II, we continuously update the posterior estimate of the utility for each dose after each cohort, using accumulating efficacy and toxicity from both stages I and II, and then use the posterior estimate to direct the dose assignment and selection. Compared to existing phase I/II designs, one prominent advantage of the U-BOIN design is its simplicity for implementation. Once the trial is designed, it can be easily applied using predetermined decision tables, without complex model fitting and estimation. Our simulation study shows that, despite its simplicity, the U-BOIN design is robust and has high accuracy to identify the OBD. We extend the design to accommodate delayed efficacy by leveraging the short-term endpoint (eg, immune activity or other biological activity of targeted agents), and using it to predict the delayed efficacy outcome to facilitate real-time decision making. A user-friendly software to implement the U-BOIN is freely available at www.trialdesign.org.

Overdispersion models for correlated multinomial data: Applications to blinding assessment.

Overdispersion models have been extensively studied for correlated normal and binomial data but much less so for correlated multinomial data. In this work, we describe a multinomial overdispersion model that leads to the specification of the first two moments of the outcome and allows the estimation of the global parameters using generalized estimating equations (GEE). We introduce a Global Blinding Index as a target parameter and illustrate the application of the GEE method to its estimation from (1) a clinical trial with clustering by practitioner and (2) a meta-analysis on psychiatric disorders. We examine the impact of a small number of clusters, high variability in cluster sizes, and the magnitude of the intraclass correlation on the performance of the GEE estimators of the Global Blinding Index using the data simulated from different models. We compare these estimators with the inverse-variance weighted estimators and a maximum-likelihood estimator, derived under the Dirichlet-multinomial model. Our results indicate that the performance of the GEE estimators was satisfactory even in situations with a small number of clusters, whereas the inverse-variance weighted estimators performed poorly, especially for larger values of the intraclass correlation coefficient. Our findings and illustrations may be instrumental for practitioners who analyze clustered multinomial data from clinical trials and/or meta-analysis.

An optimal Bayesian predictive probability design for phase II clinical trials with simple and complicated endpoints.

Most existing phase II clinical trial designs focus on conventional chemotherapy with binary tumor response as the endpoint. The advent of novel therapies, such as molecularly targeted agents and immunotherapy, has made the endpoint of phase II trials more complicated, often involving ordinal, nested, and coprimary endpoints. We propose a simple and flexible Bayesian optimal phase II predictive probability (OPP) design that handles binary and complex endpoints in a unified way. The Dirichlet-multinomial model is employed to accommodate different types of endpoints. At each interim, given the observed interim data, we calculate the Bayesian predictive probability of success, should the trial continue to the maximum planned sample size, and use it to make the go/no-go decision. The OPP design controls the type I error rate, maximizes power or minimizes the expected sample size, and is easy to implement, because the go/no-go decision boundaries can be enumerated and included in the protocol before the onset of the trial. Simulation studies show that the OPP design has satisfactory operatingcharacteristics.

Bayesian Analysis of Skills Importance in World Champions Men’s Volleyball across Ages

Abstract In volleyball, due to the sequential structure of the game, each outcome results from events that follow consistent consecutive patterns: pass–set–attack–outcome, serve–outcome and block–dig–set–counter attack–outcome. There are three possible outcomes: point won, point lost, and rally continuation. With the aim of quantifying the importance of volleyball skills, data of world champions of the male International Volleyball Federation tournaments for three age categories (Youth, Juniors and Men) were used to construct a transition matrix between subsequent moves and skills within the game. A Dirichlet-Multinomial Bayesian model was used to estimate the transition probabilities between the subsequent moves along with the marginal probability of success of each skill in the complex. The prior distribution of each transition probabilities between moves/skills was elicited to incorporate experts' opinion. For the final evaluation of the skills a simple Monte Carlo scheme was applied to obtain a random sample from the posterior distribution. The findings of the study indicate that the relative importance of volleyball skills is robust across world champions of different age categories. Slight variations are observed on specific skills. A new index (Quantile Mid-range Ratio) is proposed for highlighting skills that are valuable for team’s gameplay.

KOALA: a new paradigm for election coverage

Common election poll reporting is often misleading as sample uncertainty is addressed insufficiently or not covered at all. Furthermore, main interest usually lies beyond the simple party shares. For a more comprehensive opinion poll and election coverage, we propose shifting the focus toward the reporting of survey-based probabilities for specific events of interest. We present such an approach for multi-party electoral systems, focusing on probabilities of coalition majorities. A Monte Carlo approach based on a Bayesian Multinomial-Dirichlet model is used for estimation. Probabilities are estimated, assuming the election was held today (“now-cast”), not accounting for potential shifts in the electorate until election day (“fore-cast”). Since our method is based on the posterior distribution of party shares, the approach can be used to answer a variety of questions related to the outcome of an election. We also introduce visualization techniques that facilitate a more adequate depiction of relevant quantities as well as respective uncertainties. The benefits of our approach are discussed by application to the German federal elections in 2013 and 2017. An open-source implementation of our methods is freely available in the R package coalitions.

Habitat selection by American beaver at multiple spatial scales

BackgroundSemiaquatic mammals require both aquatic and terrestrial habitats, particularly interfaces between the two habitats. As ecosystem engineers, American beaver (Castor canadensis) consume and fell a great amount of deciduous trees. We tested the prediction that open water and amounts of food resources, including hardwood forests (i.e., deciduous trees as the dominant form of vegetation), herbaceous and woody wetlands, and shrubs, would influence the second-order habitat selection (i.e., placing home ranges on the landscape) by American beaver, whereas the third-order habitat selection of American beaver would be associated with woody wetland and shrub edges. We investigated hierarchical habitat selection by American beaver using location data from very high frequency telemetry. Dirichlet-multinomial models were used to determine the second-order habitat selection at landscape scales. Bayesian spatial resource selection function was used to assess the third-order habitat selection within home ranges.ResultsSecond-order habitat selection by American beaver was associated with herbaceous wetland, shrubs, hardwood forest, grassland, and woody wetland more than open water bodies at landscape scales. At the third-order scale, American beaver selected herbaceous wetlands as well as the edges of shrubs and woody wetland within established home ranges.ConclusionsSpatial distributions of food resources affected both the second- and third-order habitat selection by American beaver. Herbaceous wetlands were more important habitat components than water bodies in the second- and third-order habitat selection by American beaver. Dirichlet-multinomial distribution models for the second-order habitat selection and Bayesian spatial resource selection functions for the third-order habitat selection do not need pseudo-absence locations, providing alternative approaches to the presence–absence methods for habitat selection by animals.

A stage-structured hierarchical Bayes model for the babassu palm tree population dynamics – Estimated from anthropogenic open area data sets

The babassu palm tree (Attalea speciosa Mart. ex Spreng.) is an endemic species of Amazon forests, and has social and economical impact/utility. Deforestation highlights this palm tree in anthropogenic open areas (pastures and cultivated fields). Simultaneously, knowledge concerning the sustainable functioning of the species within these manmade environments is sorely lacking: its life cycle is not well known, and its population dynamics remains unstudied. In this study, our objective was to generate a model of the population dynamics of the babassu palm tree, validated by in situ analysis, to understand how babassu, a forest species, adapts to pastureland and, under certain conditions, becomes invasive. We propose a random matrix model with aggregated variables based on the biological stages of the species as the input. The probabilities of the between-stage transition matrix were modelled using a Dirichlet-multinomial model with a hierarchy taking geographical organization, i.e. transect level, into account. The integration of prior information was formulated through a Bayesian approach. This Bayesian hierarchical matrix model enabled us to demonstrate a bottleneck in the population dynamics and a high year-dependent mortality rate at an early stage.