Statistical model for overdispersed count outcome with many zeros: an approach for direct marginal inference

Marginalized models are in great demand by most researchers in the life sciences particularly in clinical trials, epidemiology, health-economics, surveys and many others since they allow generalization of inference to the entire population under study. For count data, standard procedures such as the Poisson regression and negative binomial model provide population average inference for model parameters. However, occurrence of excess zero counts and lack of independence in empirical data have necessitated their extension to accommodate these phenomena. These extensions, though useful, complicates interpretations of effects. For example, the zero-inflated Poisson model accounts for the presence of excess zeros but the parameter estimates do not have a direct marginal inferential ability as its base model, the Poisson model. Marginalizations due to the presence of excess zeros are underdeveloped though demand for such is interestingly high. The aim of this paper is to develop a marginalized model for zero-inflated univariate count outcome in the presence of overdispersion. Emphasis is placed on methodological development, efficient estimation of model parameters, implementation and application to two empirical studies. A simulation study is performed to assess the performance of the model. Results from the analysis of two case studies indicated that the refined procedure performs significantly better than models which do not simultaneously correct for overdispersion and presence of excess zero counts in terms of likelihood comparisons and AIC values. The simulation studies also supported these findings. In addition, the proposed technique yielded small biases and mean square errors for model parameters. To ensure that the proposed method enjoys widespread use, it is implemented using the SAS NLMIXED procedure with minimal coding efforts.Comment: 28 page

Bayesian latent time joint mixed-effects model of progression in the Alzheimer's Disease Neuroimaging Initiative.

IntroductionWe characterize long-term disease dynamics from cognitively healthy to dementia using data from the Alzheimer's Disease Neuroimaging Initiative.MethodsWe apply a latent time joint mixed-effects model to 16 cognitive, functional, biomarker, and imaging outcomes in Alzheimer's Disease Neuroimaging Initiative. Markov chain Monte Carlo methods are used for estimation and inference.ResultsWe find good concordance between latent time and diagnosis. Change in amyloid positron emission tomography shows a moderate correlation with change in cerebrospinal fluid tau (ρ = 0.310) and phosphorylated tau (ρ = 0.294) and weaker correlation with amyloid-β 42 (ρ = 0.176). In comparison to amyloid positron emission tomography, change in volumetric magnetic resonance imaging summaries is more strongly correlated with cognitive measures (e.g., ρ = 0.731 for ventricles and Alzheimer's Disease Assessment Scale). The average disease trends are consistent with the amyloid cascade hypothesis.DiscussionThe latent time joint mixed-effects model can (1) uncover long-term disease trends; (2) estimate the sequence of pathological abnormalities; and (3) provide subject-specific prognostic estimates of the time until onset of symptoms

A Marginalized Model for Zero-Inflated, Overdispersed, and Correlated Count Data

Iddi and Molenberghs (2012) merged the attractive features of the so-called combined model of Molenberghs {\em et al\/} (2010) and the marginalized model of Heagerty (1999) for hierarchical non-Gaussian data with overdispersion. In this model, the fixed-effect parameters retain their marginal interpretation. Lee et al (2011) also developed an extension of Heagerty (1999) to handle zero-inflation from count data, using the hurdle model. To bring together all of these features, a marginalized, zero-inflated, overdispersed model for correlated count data is proposed. Using two empirical sets of data, it is shown that the proposed model leads to important improvements in model fit

A combined beta and normal random-effects model for repeated, overdispersed binary and binomial data

AbstractNon-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper starts from the broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary and binomial cases are our focus. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical integration. The methodology is applied to two datasets of which the outcomes are binary and binomial, respectively

Predicting the course of Alzheimer's progression.

Alzheimer's disease is the most common neurodegenerative disease and is characterized by the accumulation of amyloid-beta peptides leading to the formation of plaques and tau protein tangles in brain. These neuropathological features precede cognitive impairment and Alzheimer's dementia by many years. To better understand and predict the course of disease from early-stage asymptomatic to late-stage dementia, it is critical to study the patterns of progression of multiple markers. In particular, we aim to predict the likely future course of progression for individuals given only a single observation of their markers. Improved individual-level prediction may lead to improved clinical care and clinical trials. We propose a two-stage approach to modeling and predicting measures of cognition, function, brain imaging, fluid biomarkers, and diagnosis of individuals using multiple domains simultaneously. In the first stage, joint (or multivariate) mixed-effects models are used to simultaneously model multiple markers over time. In the second stage, random forests are used to predict categorical diagnoses (cognitively normal, mild cognitive impairment, or dementia) from predictions of continuous markers based on the first-stage model. The combination of the two models allows one to leverage their key strengths in order to obtain improved accuracy. We characterize the predictive accuracy of this two-stage approach using data from the Alzheimer's Disease Neuroimaging Initiative. The two-stage approach using a single joint mixed-effects model for all continuous outcomes yields better diagnostic classification accuracy compared to using separate univariate mixed-effects models for each of the continuous outcomes. Overall prediction accuracy above 80% was achieved over a period of 2.5 years. The results further indicate that overall accuracy is improved when markers from multiple assessment domains, such as cognition, function, and brain imaging, are used in the prediction algorithm as compared to the use of markers from a single domain only

Views of Preventing Borassus Aethiopum from Extinction among Four Communities in Ghana

An investigation into how Borassus aethiopum might be prevented from extinction among farmers was carried out in  four communities (Fiaso, Oforikrom, Nyamebekyere and Bayerenkwanta) in the transitional vegetation zone of  Ghana, from  April 2013 to July 2013.  The farmers were randomly selected from the communities. Data were collected from the farmers using questionnaire supplemented with interviews. In addition to the crops grown for food, farmers also obtained food from the wild/non domesticated plants of which Borassus aethiopum was one. Farmers also used Borassus aethiopum, as a timber source, for the production of wine, for roofing and for making fan,  as fire wood and as a medicinal plant. No education had been received on  the plant or even on any other non domesticated plant. All  the farmers agreed that the plant should be preserved, however, only few  (Fiaso – 44%; Oforikrom – 48%; Nyamebekyere – 40%; Bayerenkwanta – 20%) had some ideas on how the plant might  be preserved. The few farmers considered  cultivation (Fiaso – 40%; Oforikrom – 33%; Nyamebekyere – 50%; Bayerenkwanta – 60%)  as a means of preventing the extinction of the plant. Other preservation  methods were;  prevention of bush burning and indiscriminate felling of the tree, and enacting laws on the usage of the plant. It was recommended that all communities with the support of governments should create community forest reserves/parks made up  Borassus aethiopum/non domesticated plant food species, and  also  enact laws to preserve these plants. Keywords: Borassus aethiopum,  extinction, preservatio