Incremental Effect Modeling of Binary Count Data Using Logistic Regression with Categorical Predictors

Conventional approaches for handling missingness in substance use disorder trials commonly rely upon a single deterministic "worst value" imputation that posits a perfect relationship between missingness and drug use ("missing value = presumed drug use"); this yields biased estimates of treatment effects and their standard errors. Instead, deterministic imputations should be replaced by probabilistic versions that encode researchers prior beliefs that those with missing data are more likely to be using drugs at those occasions. Motivated by this problem, we present a method for handling non-monotone missing binary data in longitudinal studies. Specifically, we consider a joint model that combines a not missing at random (NMAR) selection model with a generalized linear mixed model for longitudinal binary data. The selection model links the distribution of a missing outcome to the corresponding distribution of the outcome for those observed at that occasion via a fixed and known sensitivity parameter. The mixed model for longitudinal binary data assumes the random effects have bridge distributions; the latter yields regression parameters that have both subject-specific and marginal interpretations. This approach is completely transparent about what is being assumed about missing data and can be used as the basis for sensitivity analysis.

In this chapter we consider dependent data but move from the linear models of Chap.8 to general regression models. As in Chap.6, we consider generalized linear models (GLMs) and, more briefly, nonlinear models. We first give an outline of this chapter. In Sect.9.2 we describe three motivating datasets to which we return throughout the chapter. The GLMs discussed in Sect.6.3 can be extended to incorporate dependences in observations on the same unit; as with the linear model, an obvious way to carry out modeling in this case is to introduce unit-specific random effects. Within a GLM a natural approach is for these random effects to be included on the linear predictor scale. The resultant conditional models are known as generalized linear mixed models (GLMMs), and these are introduced in Sect.9.3. In Sects.9.4 and9.5 we describe likelihood and conditional likelihood methods of estimation, with Sect.9.6 devoted to a Bayesian treatment. Section9.7 illustrates some of the flexibility of GLMMs by describing and applying a particular model for spatial dependence. An alternative random effects specification, based on conjugacy, is described in Sect.9.8. An important approach to the modeling and analysis of dependent data that is philosophically different from the random effects formulation is via marginal models and generalized estimating equations (GEE), and these are the subject of Sect.9.9. In Sect.9.10, a second GEE approach is described in which the estimating equations for the mean are supplemented with a second set for the variances/covariances. For GLMMs, extra care must be taken with parameter interpretation, and Sect.9.11 discusses this issue, emphasizing how interpretation differs between conditional and marginal models. In PartII of the book, which focused on independent data, Chap.7 was devoted to models for binary data. For dependent data, models binary data are less well developed, and so we do not devote a complete chapter to their description. However, Sect.9.12 introduces the modeling of dependent binary data, and, subsequently, Sects.9.13 and 9.14 describe conditional (mixed) and marginal models for binary data. Section 9.15 considers how nonlinear models, as defined in Sect.6.10, can be extended to the dependent data case. For such models, many applications concentrate on inference for units, and so the introduction of random effects is again suggested. We refer to the resultant class of models as nonlinear mixed models (NLMMs). Section9.16 considers issues related to the parameterization of the nonlinear model. Inference for nonlinear mixed models via likelihood and Bayes approaches is covered in Sects.9.17 and9.18, while GEE is briefly considered in Sect.9.19. The assessment of assumptions for general regression models is described in Sect.9.20, with concluding comments contained in Sect.9.21. Additional references appear in Sect.9.22.

This book on multivariate models, statistical inference, and data analysis contains deep coverage of multivariate non-normal distributions for modeling of binary, count, ordinal, and extreme value response data. It is virtually self-contained, and includes many exercises and unsolved problems.

BackgroundGraphical models were identified as a promising new approach to modeling high-dimensional clinical data. They provided a probabilistic tool to display, analyze and visualize the net-like dependence structures by drawing a graph describing the conditional dependencies between the variables. Until now, the main focus of research was on building Gaussian graphical models for continuous multivariate data following a multivariate normal distribution. Satisfactory solutions for binary data were missing. We adapted the method of Meinshausen and Bühlmann to binary data and used the LASSO for logistic regression. Objective of this paper was to examine the performance of the Bolasso to the development of graphical models for high dimensional binary data. We hypothesized that the performance of Bolasso is superior to competing LASSO methods to identify graphical models.MethodsWe analyzed the Bolasso to derive graphical models in comparison with other LASSO based method. Model performance was assessed in a simulation study with random data generated via symmetric local logistic regression models and Gibbs sampling. Main outcome variables were the Structural Hamming Distance and the Youden Index.We applied the results of the simulation study to a real-life data with functioning data of patients having head and neck cancer.ResultsBootstrap aggregating as incorporated in the Bolasso algorithm greatly improved the performance in higher sample sizes. The number of bootstraps did have minimal impact on performance. Bolasso performed reasonable well with a cutpoint of 0.90 and a small penalty term. Optimal prediction for Bolasso leads to very conservative models in comparison with AIC, BIC or cross-validated optimal penalty terms.ConclusionsBootstrap aggregating may improve variable selection if the underlying selection process is not too unstable due to small sample size and if one is mainly interested in reducing the false discovery rate. We propose using the Bolasso for graphical modeling in large sample sizes.

The impact of grassland management regime on the community structure of selected bacterial groups in soils

Association of Clonal Hematopoiesis of Indeterminate Potential with Time to First Treatment, Incidence of Richter's Syndrome, and Overall Survival in Patients with Chronic Lymphocytic Leukemia

1. Introduction 2. Binary regression: the logit model 3. Generalized linear models 4. Modeling of binary data 5. Alternative binary regression models 6. Regularization and variable selection for parametric models 7. Regression analysis of count data 8. Multinomial response models 9. Ordinal response models 10. Semi- and nonparametric generalized regression 11. Tree-based methods 12. The analysis of contingency tables: log-linear and graphical models 13. Multivariate response models 14. Random effects models 15. Prediction and classification Appendix A. Distributions Appendix B. Some basic tools Appendix C. Constrained estimation Appendix D. Kullback-Leibler distance and information-based criteria of model fit Appendix E. Numerical integration and tools for random effects modeling.

This paper is dedicated to the data integration problem. In article the task of practical implementation of mappings between description logic and a binary relational data model is discussed. This method was formulated earlier at a theoretical level. A practical technique to test mapping engines using RDF is provided in the current paper. To transform the constructs of the description logic ALC and its main extensions into RDF triplets the OWL 2-to-RDF mappings are used. To convert RDB to RDF graph, the R2R Mapping Language (R2R ML) was chosen. The mappings DL ALC and its main extensions to the RDF triplets are described in the publication. The mapping of the DL axioms into an RDF triplet also is considered in the publication. The main difficulties in describing DL-to-RDF transformations are given in the corresponding section. For each constructor of concepts and roles a corresponding expression in OWL 2 and its mapping into the RDF triplet. A schematic representation of the resulting RDF graph for each mapping is created. The paper also provides an overview of existing methods that relate to the use of RDF when mapping RDB to ontology and vice versa.

We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative “unfolding” models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and that the additional flexibility leads to preferences’ estimates that more closely match the perceived ideological positions of legislators and justices.

Maximum likelihood estimation of an extended latent Markov model for clustered binary panel data

Clustered binary data occur frequently in biostatistical work. One particular application is in binary longitudinal data, where several visits are available for the same individual. Several approaches have been proposed for the analysis of clustered binary data. In Rosner, a polychotomous logistic regression model was proposed which is a generalization of the beta-binomial distribution and allows for person- and visit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of visits within an individual are equally correlated, which may be inappropriate if several visits are available over a long follow-up period. In this paper, this approach is extended to allow for heterogeneous correlation over time. The total time period is divided into subintervals and a beta-binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of person-, subinterval-, and visit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, MA, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.

A pedigree model for binary data, motivated by log-linear modelling, has been developed to examine evidence for familial aggregation in disease status. From an epidemiological point of view a convenient way to express disease concordance between a pair of relatives is in terms of the odds ratio. For a rare disease this is almost equivalent to the relative risk of one family member being affected given that the other is affected, and in extending this to pedigrees it is assumed that these relative risks are multiplicative. In applying the model to the breast cancer data, pedigrees on a rare disease ascertained through an affected proband, it has been shown that estimation of concordance is dependent critically on knowing the probability that a sampled individual is affected. Therefore known population estimates of prevalence or cumulative risk, and an appropriate ascertainment correction, need to be invoked for the model to give proper estimates of disease concordance. The model is flexible in that measured ancillary risk factors, including genetic marker information, can be incorporated into the analysis. Therefore in future studies this information should be collected on all individuals, not just those affected. Suggested statistics for examining a fitted model are presented.

This study proposes a new model in the family zero-inflated (ZI) binary models, it is called as a ZI Probit Bernoulli (ZIPBer) model. This model can be performed to model or simulate binary data that has an excessive amount of zero counts. At the framework of this research, we first introduce the classical formula, estimating equation (EE) and related functions for the ZIPBer model. Next, the results of asymptotic inferences for the ZIPBer model is studied based on the widespread regularity conditions. For the numerical illustrations, many simulation studies and a practical data set are executed in this paper. Specifically, we perform the fishing data set (FDS) to check the working effectiveness and robustness of the maximum likelihood estimation (MLE) approach in estimating parameters for the ZIPBer model. We also illustrate that this actual data set is more suitable for the proposed model: ZIPBer than other binary models such as logit, probit and ZIBer. The achieved results in this study are very unanimous with reality. It also illustrates that this is a dependable verification for us to know the solution as well as how to proceed to how to catch or take the most fish. This is the contribution of this work in terms of application. Finally, some crucial discussions and conclusions are given in this paper.

The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite mixture of multivariate Gaussians. The aim of the proposed model is twofold: it allows to achieve dimension reduction when the data are dichotomous and, simultaneously, it performs model based clustering in the latent space. Model estimation is obtained by means of a maximum likelihood method via a generalized version of the EM algorithm. In order to evaluate the performance of the model a simulation study and two real applications are illustrated.

This article deals with the issue of using a suitable pseudo-likelihood, instead of an integrated likelihood, when performing Bayesian inference about a scalar parameter of interest in the presence of nuisance parameters. The proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals. Moreover, it is particularly useful when it is difficult, or even impractical, to write the full likelihood function. We focus on Bayesian inference about a scalar regression coefficient in various regression models. First, in the context of non-normal regression-scale models, we give a theroetical result showing that there is no loss of information about the parameter of interest when using a posterior distribution derived from a pseudo-likelihood instead of the correct posterior distribution. Second, we present non trivial applications with high-dimensional, or even infinite-dimensional, nuisance parameters in the context of nonlinear normal heteroscedastic regression models, and of models for binary outcomes and count data, accounting also for possibile overdispersion. In all these situtations, we show that non Bayesian methods for eliminating nuisance parameters can be usefully incorporated into a one-parameter Bayesian analysis.