A new multivariate zero-adjusted Poisson model with applications to biomedicine.

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero-vectors; (ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases; (iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process.

We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.

A new multivariate t distribution with variant tail weights and its application in robust regression analysis.

In this paper, we propose a new kind of multivariate t distribution by allowing different degrees of freedom for each univariate component. Compared with the classical multivariate t distribution, it is more flexible in the model specification that can be used to deal with the variant amounts of tail weights on marginals in multivariate data modeling. In particular, it could include components following the multivariate normal distribution, and it contains the product of independent t-distributions as a special case. Subsequently, it is extended to the regression model as the joint distribution of the error terms. Important distributional properties are explored and useful statistical methods are developed. The flexibility of the specified structure in better capturing the characteristic of data is exemplified by both simulation studies and real data analyses.

The Association Between Coffee Consumption and Metabolic Syndrome in Adults: A Systematic Review and Meta-Analysis.

Previous meta-analyses that found an inverse association between coffee consumption and metabolic syndrome pooled data from cross-sectional and longitudinal studies, which could lead to potentially misleading conclusions. Hence, this work aimed to reassess this association by analyzing data from the 2 types of studies separately and including recent studies. Online databases including PubMed, Scopus, Embase, The Cumulative Index to Nursing and Allied Health Literature (CINAHL) Plus, and Science Direct were searched for relevant studies published up to July 2020. Both cross-sectional and longitudinal studies were included if published after 1999, reported both effect estimates and CIs, and presented results adjusted for confounding variables. Data of the highest coffee consumption level in each study, as well as those of medium consumption levels in studies with ≥3 consumption categories, were pooled using random-effect models, with sex-stratified and sex-adjusted results being analyzed separately. Results were obtained based on data from 13 cross-sectional studies involving 280,803 participants and 2 longitudinal studies involving 17,014 participants. The overall sex-adjusted association of the highest consumption level was not significant (n = 9 studies; OR: 0.88; 95% CI: 0.70, 1.10; I2: 91.5%) and the 2 longitudinal studies both yielded no association. Subgroup analysis revealed inverse associations in both males and females, as well as in Caucasians with medium coffee consumption (n = 4 studies, OR: 0.88; 95% CI: 0.84, 0.93; I2: 0%). Although residual confounding could affect the results of this meta-analysis, our findings suggested with a low certainty that coffee consumption may not be associated with metabolic syndrome, a finding that is different from those of previous meta-analyses and could be due to variation in characteristics of study participants. More longitudinal studies are also needed to further assess the temporal association between coffee consumption and metabolic syndrome. This meta-analysis was registered at https://www.crd.york.ac.uk/prospero as CRD42018110650.