**1. Introduction**

The term spatial statistics is used to describe a wide range of statistical models and methods for the analysis of geo-referenced data [1]. Its rapid use has been increasing in various fields of science, such as biology, image processing, environmental and earth sciences, ecology, epidemiology, agronomy, forestry, among others [2]. In epidemiology, spatial statistics are used to study the occurrence of health-disease events or deaths in a region of interest. It is now known that several public health problems tend to exhibit spatial dependence (spatial autocorrelation, spatial variability), and that sometimes these problems are related to climatic factors that are generally of a spatially continuous nature or with factors specific to the study region. The use of classical statistical techniques to model spatial data generally leads to an overestimation of model parameters [1]; and although they may eventually help, these models, lacking adequate structure, will not be able to model the spatial variability of the data; valuable information that will be sent to model error and cannot be used to explain the nature of the phenomenon under study.

Recent studies have shown that spatial models can help identify spatial patterns in infectious and non-infectious diseases. These models also help determine the factors that favor them, such as sociodemographic, environmental, etc.; as well as generate maps to visualize the distribution of morbidity or mortality of infectious and noninfectious diseases, and identify critical points in the spatial distribution [3, 4].

Generalized linear spatial models (GLSM), which are a particular class of multilevel or hierarchical models, have been used for the study of certain diseases (infectious and non-infectious). The estimation of GLSM parameters can be done under the frequentist or Bayesian approach [1], some examples are given below. A spatial Poisson regression model, where parameter estimation was performed under the frequentist approach, was used to study esophageal cancer incidence rates [5] and the sociodemographic risk factors for diabetes [6]. Under the Bayesian approach, these models have been used to study the relationship between Visceral Leishmaniasis incidence rates and climatological variables [7], as well as to identify risk factors associated with nontuberculous mycobacterial infections [8]. Spatial Binomial regression models, under the Bayesian approach, have been used to describe patterns of occurrence of dengue and chikungunya [9], and filariasis [10]. Under the classical approach, spatial binomial regression models have been used to investigate environmental and sociodemographic factors associated with leptoserosis disease [11]; are also used to study risk factors associated with HIV infection among drug users [12].

On the other hand, survival analysis under the spatial approach has also received great attention in recent years, because geographic location can play a relevant role in predicting disease survival [13]. Fragility models (spatial survival models) can be an option to analyze the heterogeneity of the data when it cannot be explained by the covariates in a classical survival model. In spatial survival models, in addition to covariates, a random effect known as *frailty* is added, which modifies the hazard function of an individual, or of spatially correlated individuals [14]. Generally, the random factor, which is assigned a multivariate normal distribution, plays an important role in modeling survival times; since in this term the differences that exist in the socioeconomic level, access to medical care, population density, weather conditions, among others, can be taken into account. It is worth mentioning that spatial survival models have been applied in studies such as: recovery time in patients with COVID-19 [15], hospitalization time in dengue patients [16], HIV/AIDS survival [17] and breast cancer [18] to name a few. In all these works, the estimation of the model parameters was under the Bayesian approach.

Extreme events in public health (for example, the saturation of hospitals) are generally analyzed through measures of central tendency or time series, however, these approaches are not the most appropriate to understand extreme events (unusual events); that when they occur they strongly impact the health care network, thus often collapsing the system [19]. The extreme value theory (EVT) aims to study the probability of occurrence of extreme events (values) of a phenomenon of interest over time, generally these values only occur when they exceed a threshold. Although the applications of EVT in public health are scarce, if they exist at all; an application was presented when predicting extreme events of annual seasonal influenza mortality and the number of emergency department visits in a network of hospitals [20], another application was presented when modeling elevated cholesterol levels using the spikes-over-threshold model [21]. In both cases, the parameters were estimated under the frequentist approach. Given the advantages they have with the application of a spatial model, it would be convenient to study the extreme events of the health sector in space, for which there is already a methodology known as spatial modeling of extreme values [22].

The objective of this work is to provide a general review of the theoretical framework of spatial statistical models developed in the area of geostatistics, which have been used in the area of epidemiology to analyze, model and predict the phenomena of interest. Some of the packages that exist in the statistical software R [23] to carry out said spatial analyzes are also mentioned.
