The objective of the study was to examine the associations between environmentally relevant low metal concentrations and semen quality parameters in men. The concentrations of zinc (Zn), copper (Cu), cadmium (Cd), arsenic (As), selenium (Se), and lead (Pb) in the seminal plasma and urine were measured from 196 male human subjects in Taiwan. Urinary Cd concentrations were negatively associated with sperm viability (p = 0.006). Seminal plasma Cu concentrations of the normal group (≥ 15 × 10⁶/ml) were significantly lower than those of the abnormal group (p = 0.023). However, the linear regression analysis showed a weak association between Cu concentration and sperm concentration, along with other semen parameters. No significant relationship between other metals (As, Pb, Zn, and Se) and semen quality was observed.

Count time series data are observed in several applied disciplines such as environmental science, biostatistics, economics, public health, and finance. In some cases, a specific count, usually zero, may occur more often than other counts. However, overlooking the frequent occurrence of zeros could result in misleading inferences. In this article, we develop a copula-based time series regression model for zero-inflated counts. Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP) distributed marginals will be considered, and the joint distribution is modeled under Gaussian copula with autoregression moving average (ARMA) errors. Sequential sampling likelihood inference is performed. Simulated and real-life data examples are provided and studied to evaluate the proposed method.

Count time series data with excess zeros are observed in several applied disciplines. When these zero-inflated counts are sequentially recorded, they might result in serial dependence. Ignoring the zero-inflation and the serial dependence might produce inaccurate results. In this paper, Markov zero-inflated count time series models based on a joint distribution on consecutive observations are proposed. The joint distribution function of the consecutive observations is constructed through copula functions. First- and second-order Markov chains are considered with the univariate margins of zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated Conway–Maxwell–Poisson (ZICMP) distributions. Under the Markov models, bivariate copula functions such as the bivariate Gaussian, Frank, and Gumbel are chosen to construct a bivariate distribution of two consecutive observations. Moreover, the trivariate Gaussian and max-infinitely divisible copula functions are considered to build the joint distribution of three consecutive observations. Likelihood-based inference is performed and asymptotic properties are studied. To evaluate the estimation method and the asymptotic results, simulated examples are studied. The proposed class of models are applied to sandstorm counts example. The results suggest that the proposed models have some advantages over some of the models in the literature for modeling zero-inflated count time series data.

Recent clinical research describes a subset of glioblastoma patients that exhibit REP prior to the start of radiation therapy. Current literature has thus far described this population using clinicopathologic features. To our knowledge, this study is the first to investigate the potential of conventional radiomics, sophisticated multi-resolution fractal texture features, and different molecular features (MGMT, IDH mutations) as a diagnostic and prognostic tool for prediction of REP from non-REP cases using computational and statistical modeling methods. The radiation-planning T1 post-contrast (T1C) MRI sequences of 70 patients are analyzed. An ensemble method with 5-fold cross-validation over 1000 iterations offers an AUC of 0.793 ± 0.082 for REP versus non-REP classification. In addition, copula-based modeling under dependent censoring (where a subset of the patients may not be followed up with until death) identifies significant features (p-value < 0.05) for survival probability and prognostic grouping of patient cases. The prediction of survival for the patients’ cohort produces a precision of 0.881 ± 0.056. The prognostic index (PI) calculated using the fused features shows that 84.62% of REP cases fall under the bad prognostic group, suggesting the potential of fused features for predicting a higher percentage of REP cases. The experimental results further show that multi-resolution fractal texture features perform better than conventional radiomics features for prediction of REP and survival outcomes.

Much research has been conducted over the last half century in developing stochastic processes, and their dynamical nature. Typically, for time indexed processes, the temporal distribution is restricted to those having marginal distributions of a specified and familiar lifetime family. Extensions of temporal models to the spatio-temporal setting can be challenging. We generalize the results from a spatial statistic that captures local correlation, Moran’s index, to the spatio-temporal frame and describe a model that can be applied to temporal dynamical phenomena. The proposed approach leads to novel statistical inference results. Ensuring a foundational Moran measure is critical in describing event occurrence and progression over time of the process from observed initial conditions. In this paper, we provide a descriptive form of discrete spatio-temporal Moran’s index statistics based on processes motivated by the spread of an infectious plant disease in an agricultural setting. This family possesses an underlying Poisson point process in space and time. Estimators are developed and applied to simulated data and the output are analyzed. Our results adds substantially to known results in the literature and elude to the description of the time dependent Moran’s values.