Bayesian Analysis of Transition Model for Longitudinal Ordinal Response Data: Application to Insomnia Data

In this paper, we present a Bayesian framework for analyzing longitudinal ordinal response data. In analyzing longitudinal data, the possibility of correlations between responses given by the same individual needs to be taken into account. Various models can be used to handle such correlations such as marginal modeling, random effect modeling and transition (Markov) modeling. Here a transition modeling is used and a Bayesian approach is presented for analyzing longitudinal data. A cumulative logistic regression model and the Bayesian method, using MCMC, are implemented for obtaining the parameters estimates. Our approach is applied on a two-period longitudinal Insomnia data where the Bayesian estimate for measure of association, , between the initial and follow-up ordinal responses is obtained in each level of a treatment variable. Then, the sensitivity of posterior summaries to changes of prior hyperparameters is investigated. We also use Bayes factor criterion for testing some important hypotheses

Spatial and spatio-temporal modeling and mapping of self-reported health among individuals between the ages of 15-49 years in South Africa.

Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.Self-reported health has been commonly used as a measure of individuals health in public health studies. Health presents a complete physical, emotional, and social well-being. It also plays an important role in the development of the country, economically and socially. Poor health still remains a serious problem and it is linked to high burden of diseases in the world. As part of the Healthy People 2020 and Sustainable Development Goals (SDGs) in Sub-Saharan African (SSA), the goals of improving health has not been achieved. Hence, further investigation of the influential factors on health is relevant to improving health inequalities in SSA countries. Disease mapping provides a robust tool to assess geographical variation of disease and has been used in epidemiology and public health studies. The aim of this research is to use two distinct response outcome variables to investigate factors and geographical variations that are associated with self-reported health in South Africa. To accomplish the former and the latter, this research uses data from the National Income Dynamics Study (NIDS). The NIDS datasets are longitudinal data collected every two years from 2008. In this research, several structured additive regression (STAR) models were utilized within a Bayesian methodology, particularly the Bayesian hierarchical models. Models reviewed included Bayesian spatial and spatio-temporal cumulative logit models and logistic regression models, the primary interest was on the conditional autoregressive (CAR) models. Furthermore, the nonlinear effects of individuals age and body mass index (BMI) were part of the research interest. Two applications are discussed; one for the cumulative logit models for the ordinal response, the other for the logistic regression models of the binary response. In the case of the ordinal response, inference was based on the empirical Bayes approach, while for the binary case, a fully Bayesian procedure was used. Similar results were obtained between the two approaches. Findings reveal that age, gender, household income, education, exercising level, alcohol consumption level, smoking, employment, nutrition status, TB, and depression were associated with self-reported health. The BMI was found to have a nonlinear relationship with self-reported health. Also, the findings show that age has a positive linear effect on selfreported health. In addition, the findings reveal significant spatial variation, with higher poor health prevalence in the Siyanda, John Taoli Gaetsewe, Ngaka Modiri Molema, Dr Ruth Segomotsi Mompati, Dr Kenneth Kaunda, Frances Baard, Lejweleputswa, Xhariep, Thabo Mofutsanyane, Fezile Dabi, Mangaung, Chris Hani, Umgungundlovu, Sisonke, Zululand, Umkhanyakude and Gert Sibande districts. Nevertheless, low poor health prevalence was recorded in the West Coast, Cape Winelands, Overberg, Eden, Central Karoo, Uthungulu, iLembe, and eThekwini districts. Interventions to improve individuals health should include addressing of gender inequalities, education, and income inequalities but altogether with employment status and healthy living lifestyle, in particular, targeting districts identified to have highest poor health prevalence

Bayesian spatial modeling of malnutrition and mortality among under-five children in sub-Saharan Africa.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The aim of this thesis is to develop and extend Bayesian statistical models in the area of spatial modeling and apply them to child health outcomes, with particular focus on childhood malnutrition and mortality among under-five children. The easy availability of a geo-referenced database has stimulated a paradigm shift in methodological approaches to spatial analysis. This study reviewed the spatial methods and disease mapping models developed for areal (lattice) data analysis. Observational data collected from complex design surveys and geographical locations often violates the independent assumption of classical regression models. By relaxing the restrictive linearity and normality assumptions of classical regression models, this study first developed a flexible semi-parametric spatial model that accommodates the usual fixed effect, nonlinear and geographical component in a unified model. The approach was explored in the analysis of spatial patterns of child birth outcomes in Nigeria. The study also addressed the issue of disease clustering, which is of interest to epidemiologists and public health officials. The study then proposed a Bayesian hierarchical analysis approach for Poisson count data and formulated a Poisson version of generalized linear mixed models (GLMMs) for analyzing childhood mortality. The model simultaneously addressed the problem of overdispersion and spatial dependence by the inclusion of the risk factors and random effects in a single model. The proposed approach identified regions with elevated relative risk or clustering of high mortality and evaluated the small scale geographical disparities in sub-populations across the regions. The study identified another challenge in spatial data analysis, which are spatial autocorrelation and model misspecification. The study then fitted geoadditive mixed (GAM) models to analyze childhood anaemia data belonging to a family of exponential distributions (Gaussian, binary and multinomial). The GAM models are extension of generalized linear mixed models by allowing the inclusion of splines for continuous covariate (or time) trends with the parametric function. Lastly, the shared component model originally developed for multiple disease mapping was reviewed and modified to suit the binary data at hand. A multivariate conditional autoregressive (MCAR) model was developed and applied to jointly analyze three child malnutrition indicators. The approach facilitated the estimation of conditional correlation between the diseases; assess the spatial association with the regions and geographical variation of individual disease prevalence. The spatial analysis presented in this thesis is useful to inform health-care policy and resource allocation. This thesis contributes to methodological applications in life sciences, environmental sciences, public health and agriculture. The present study expands the existing methods and tools for health impact assessment in public health studies. KEYWORDS: Conditional Autoregressive (CAR) model, Disease Mapping Models, Multiple Disease mapping, Health Geography, Ecology Models, Spatial Epidemiology, Childhood Health outcomes

DATA-DRIVEN BAYESIAN METHOD-BASED TRAFFIC CRASH DRIVER INJURY SEVERITY FORMULATION, ANALYSIS, AND INFERENCE

Traffic crashes have resulted in significant cost to society in terms of life and economic losses, and comprehensive examination of crash injury outcome patterns is of practical importance. By inferring the parameters of interest from prior information and studied datasets, Bayesian models are efficient methods in data analysis with more accurate results, but their applications in traffic safety studies are still limited. By examining the driver injury severity patterns, this research is proposed to systematically examine the applicability of Bayesian methods in traffic crash driver injury severity prediction in traffic crashes. In this study, three types of Bayesian models are defined: hierarchical Bayesian regression model, Bayesian non-regression model and knowledge-based Bayesian non-parametric model, and a conceptual framework is developed for selecting the appropriate Bayesian model based on discrete research purposes. Five Bayesian models are applied accordingly to test their effectiveness in traffic crash driver injury severity prediction and variable impact estimation: hierarchical Bayesian binary logit model, hierarchical Bayesian ordered logit model, hierarchical Bayesian random intercept model with cross-level interactions, multinomial logit (MNL)-Bayesian Network (BN) model, and decision table/na\xefve Bayes (DTNB) model. A complete dataset containing all crashes occurring on New Mexico roadways in 2010 and 2011 is used for model analyses. The studied dataset is composed of three major sub-datasets: crash dataset, vehicle dataset and driver dataset, and all included variables are therefore divided into two hierarchical levels accordingly: crash-level variables and vehicle/driver variables. From all these five models, the model performance and analysis results have shown promising performance on injury severity prediction and variable influence analysis, and these results underscore the heterogeneous impacts of these significant variables on driver injury severity outcomes. The performances of these models are also compared among these methods or with traditional traffic safety models. With the analyzed results, tentative suggestions regarding countermeasures and further research efforts to reduce crash injury severity are proposed. The research results enhance the understandings of the applicability of Bayesian methods in traffic safety analysis and the mechanisms of crash injury severity outcomes, and provide beneficial inference to improve safety performance of the transportation system

Book of Abstracts XVIII Congreso de Biometría CEBMADRID

Abstracts of the XVIII Congreso de Biometría CEBMADRID held from 25 to 27 May in MadridInteractive modelling and prediction of patient evolution via multistate models / Leire Garmendia Bergés, Jordi Cortés Martínez and Guadalupe Gómez Melis : This research was funded by the Ministerio de Ciencia e Innovación (Spain) [PID2019104830RBI00]; and the Generalitat de Catalunya (Spain) [2017SGR622 and 2020PANDE00148].Operating characteristics of a model-based approach to incorporate non-concurrent controls in platform trials / Pavla Krotka, Martin Posch, Marta Bofill Roig : EU-PEARL (EU Patient-cEntric clinicAl tRial pLatforms) project has received funding from the Innovative Medicines Initiative (IMI) 2 Joint Undertaking (JU) under grant agreement No 853966. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and EFPIA and Children’s Tumor Foundation, Global Alliance for TB Drug Development non-profit organisation, Spring works Therapeutics Inc.Modeling COPD hospitalizations using variable domain functional regression / Pavel Hernández Amaro, María Durbán Reguera, María del Carmen Aguilera Morillo, Cristobal Esteban Gonzalez, Inma Arostegui : This work is supported by the grant ID2019-104901RB-I00 from the Spanish Ministry of Science, Innovation and Universities MCIN/AEI/10.13039/501100011033.Spatio-temporal quantile autoregression for detecting changes in daily temperature in northeastern Spain / Jorge Castillo-Mateo, Alan E. Gelfand, Jesús Asín, Ana C. Cebrián / Spatio-temporal quantile autoregression for detecting changes in daily temperature in northeastern Spain : This work was partially supported by the Ministerio de Ciencia e Innovación under Grant PID2020-116873GB-I00; Gobierno de Aragón under Research Group E46_20R: Modelos Estocásticos; and JC-M was supported by Gobierno de Aragón under Doctoral Scholarship ORDEN CUS/581/2020.Estimation of the area under the ROC curve with complex survey data / Amaia Iparragirre, Irantzu Barrio, Inmaculada Arostegui : This work was financially supported in part by IT1294-19, PID2020-115882RB-I00, KK-2020/00049. The work of AI was supported by PIF18/213.INLAMSM: Adjusting multivariate lattice models with R and INLA / Francisco Palmí Perales, Virgilio Gómez Rubio and Miguel Ángel Martínez Beneito : This work has been supported by grants PPIC-2014-001-P and SBPLY/17/180501/000491, funded by Consejería de Educación, Cultura y Deportes (Junta de Comunidades de Castilla-La Mancha, Spain) and FEDER, grant MTM2016-77501-P, funded by Ministerio de Economía y Competitividad (Spain), grant PID2019-106341GB-I00 from Ministerio de Ciencia e Innovación (Spain) and a grant to support research groups by the University of Castilla-La Mancha (Spain). F. Palmí-Perales has been supported by a Ph.D. scholarship awarded by the University of Castilla-La Mancha (Spain)

Statistical Modelling

The book collects the proceedings of the 19th International Workshop on Statistical Modelling held in Florence on July 2004. Statistical modelling is an important cornerstone in many scientific disciplines, and the workshop has provided a rich environment for cross-fertilization of ideas from different disciplines. It consists in four invited lectures, 48 contributed papers and 47 posters. The contributions are arranged in sessions: Statistical Modelling; Statistical Modelling in Genomics; Semi-parametric Regression Models; Generalized Linear Mixed Models; Correlated Data Modelling; Missing Data, Measurement of Error and Survival Analysis; Spatial Data Modelling and Time Series and Econometrics

Random Effect Models in the Statistical Analysis of Human Fecundability Data: Application to artificial insemination with sperm from donor.

The main aim of this dissertation is to explore methodological approaches to correlated binary data and to assess their suitability for the analysis of data on human fertility. The dataset concerns a study of Artificial Insemination by Donor (AID). AID represents an unusual research opportunity to study both male and female fecundability simultaneously. In each attempt to conceive, artificial insemination is carried out in consecutive ovulatory cycles until conception or change of treatment. The probability of conception may differ between women, so that the data are discrete time survival data with censoring and between-subject heterogeneity. There is also potential heterogeneity between donors. Non-systematic allocation of the donor to recipient ensures that the same woman receives semen from several donors, This added heterogeneity as well as other cycle dependent covariates have to be taken into account. The analysis must also take account of covariates, most of them time-varying. Our dataset have a crossed hierarchical structure due to the presence of both, female and male factors. The rather complicated "design" calls for unit specific regression models. These models are presented as well as their lack of tractability except in some rather specific cases. The motivation for choosing Gaussian random effects in unit specific regression models is discussed. We demonstrate the use of an approximate inference method (Penalized Quasi Likelihood). This method is shown to be a useful and practical way of carrying out preliminary data analysis. Finally a Bayesian procedure (Gibbs sampling) provides validation and more accurate results despite the intensive computation it needs. The main substantive finding of the analysis is the unexpectedly pronounced heterogeneity of donor fecundability, even after inclusion of conventional measures of sperm quality into the model. These measures were shown to be predictive at the donor level but not at the level of individual donation