Background: Breast cancer is one of the most common diseases in women and causes more deaths rather than other cancers. The increasing trend of breast cancer in Iran makes clear the need of extensive breast cancer research in this area. Some studies showed that in the variety countries and even in the different areas in one country has different risk of breast cancer incidence and this is a reason that there is a correlation between region of life and risk of breast cancer. The purpose of this study was to determine the Spatial structure associated with the incidence of breast cancer based on statistical models and identification of areas with high incidence of breast cancer in Iran. Methods: This ecological study was conducted in Kermanshah University of Medical Sciences, Iran, from February to July 2018. Data on breast cancer patients in all provinces of Iran (30 provinces) were investigated since 2004 to 2009. Risk factors in this study included fruit and vegetable consumption, physical activity, overweight or obesity, and human development index. In this study, we have used routine and Spatial Poisson's generalized linear mixed models for data analysis. Results: In both routine and Spatial models, direct and significant correlation was found between the incidence of breast cancer and the human development index (P<0. 05). In addition to human development index, overweight or obesity factors were also had direct and significant relationship to the incidence of breast cancer in the Spatial Poisson's generalized linear mixed model (P<0. 05). In the Spatial Poisson's generalized linear mixed model with correlation structure of Besag Yorg Molie (BYM), two provinces of Gilan and East Azerbaijan had the highest risk of breast cancer incidence and province of Kohgiluyeh and Boyer Ahmad had the lowest risk of breast cancer incidence. Conclusion: The results showed that the distribution of breast cancer incidence in Iran has a Spatial structure. That is, the adjacent provinces have similar incidences of this disease.

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symmetric and skewed families. In this paper, a beta generalized linear mixed model with Spatial random effect is proposed emphasizing on small values of the Spatial range parameter and small sample sizes. Then some models with both fixed and varying precision parameter and different combinations of priors and sample sizes are discussed. Next, the Bayesian estimation of the model parameters is evaluated in an intensive simulation study. Selected priors improved the Bayesian estimation of the parameters, especially for small sample sizes and small values of range parameter. Finally, an application of the proposed model on data provided by Household Income and Expenditure Survey (HIES) of Tehran city is presented.

When discussing non-Gaussian Spatially correlated variables, generalized linear mixed models have enough flexibility for modeling various data types. However, the maximum likelihood methods are plagued with substantial calculations for large data sets, resulting in long waiting times for estimating the model parameters. To alleviate this drawback, composite likelihood functions obtained from the product of the likelihoods of subsets of observations are used. The current paper uses the pairwise likelihood method to study the parameter estimations of Spatial generalized linear mixed models. Then, we use the weighted pairwise and penalized likelihood functions to estimate the parameters of the mentioned models. The accuracy of estimates based on these likelihood functions is evaluated and compared with full likelihood function-based estimation using simulation studies. Based on our results, the penalized likelihood function improved parameter estimation. Prediction using penalized likelihood functions is applied. Ultimately, pairwise and penalized pairwise likelihood methods are applied to analyze count real data sets.

Background: Depression is one of the most common mental disorders and it has the third rank of the cause of disability and has been considered to increase the years of life with disability in Iran. Objectives: The purpose of this study was to map the geographical distribution and find hot spots of depression and its relation to demographic and socioeconomic factors in Mashhad. Methods: A population-based cross-sectional study was conducted in Mashhad in 2010. In this study, 9704 individuals aged 35 to 65 years old were evaluated using Beck’ s depression inventory-II. A generalized linear mixed model with a logit link was fitted for the Spatial modeling of depression. R and GIS software was used for Spatial analysis and disease mapping, respectively. Results: The prevalence of depression was different in geographical areas, ranging from 13. 29% to 26. 67%. The Spatial correlation in the prevalence of depression was significant. The fitted Spatial model showed that the Spatial adjusted associations between gender (P < 0. 001), marital status (P < 0. 001), socioeconomic status (P < 0. 001), and depression were significant. Conclusions: The significant Spatial correlation shows that depression is Spatially contagious and it is important to find its hot spots in the population. Thus developing health policy for prevention, early diagnostics, and treatment programs is preferred in these resource-limited areas.

Spatial generalized linear mixed models are used for modeling geostatistical discrete Spatial responses and Spatial correlation of the data is considered via latent variables. The most important interest in these models is estimation of the parameters and prediction of the latent variables. In this paper, first, a prediction method is presented. Then a Bayesian approach and MCMC algorithms are proposed. Since these models are complicated and Monte Carlo sampling is used in the Bayesian inference of these models, computation time is long. In order to resolve this problem, the Approximate Bayesian methods are considered. Finally, the proposed methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 1391.

Statistical process control methods for monitoring processes with univariate or multivariate measurements are used widely when the quality variables fit to known probability distributions. Some processes, however, are better characterized by a profile or a function of quality variables. For each profile, it is assumed that a collection of data on the response variable along with the values of the corresponding quality variables is measured. While the linear function is the simplest, it occurs frequently that many of the nonlinear functions may be transferred to linear functions easily. This paper proposes a control chart based on the generalized linear test (GLT) to monitor coefficients of the linear profiles and an R-chart to monitor the error variance, the combination of which is called GLT/R chart. While fixed values of the explanatory variables are cornerstones in other control charts proposed to monitor profiles, in GLT/R chart, it is not a necessary condition. In order to illustrate the robustness of the GLT/R chart a simulation study has been done in two different cases, i.e. fixed and non-fixed values of the explanatory variables. Then, the results obtained from GLT/R charts are compared to the ones from a multivariate T2 and Exponentially Weighted Moving Average/R (EWMA/R) control charts.

Spatial generalized linear mixed models are usually used for modeling non-Gaussian and discrete Spatial responses. In these models, Spatial correlation of the data can be considered via latent variables. Estimation of the latent variables at the sampled locations, the model parameters and the prediction of the latent variables at un-sampled locations are of the most important interest in SGLMM. Often the normal assumption for latent variables is considered just for convenient in practice. Although this assumption simplifies the calculations, in practice, it is not necessarily true or possible to be tested. In this paper, a closed skew normal distribution is proposed for the Spatial latent variables. This distribution includes the normal distribution and also remains closed under linear conditioning and marginalization. In these models, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, for maximum likelihood estimation of the model parameters and predictions of latent variables, an approximate algorithm is introduced that is faster than the former method. The performance of the proposed model and algorithm are illustrated through a simulation study.

Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete Spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the Spatial correlation structure of data is carried out by random effects or latent variables. In most Spatial analysis, it is assumed that random effects have Gaussian distribution, but the assumption is questionable. This assumption is replaced in the present work, using a skew Gaussian distribution for the latent variables, which is more flexible and includes Gaussian distribution. We examine the proposed method using a real discrete data set.