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Disease mapping ha recibido un gran interés durante las tres últimas décadas. Esta área de investigación persigue el estudio de la distribución geográfica de eventos relacionados con la salud, tales como la mortalidad o la incidencia de enfermedades, agregados en unidades geográficas, con el fin de identificar principalmente aquellas localizaciones que presentan un mayor riesgo. La aplicación de métodos estadísticos avanzados para llevar a cabo las estimaciones de los riesgos resulta fundamental para obtener estimaciones precisas y profundizar en el entendimiento de la distribución geográfica de las enfermedades. En esta tesis nos centramos en la aplicación y evaluación de varias propuestas de modelización relevantes surgidas en la literatura del mapeo de enfermedades para la estimación de la distribución geográfica de la mortalidad considerando diferentes escenarios con datos reales. Específicamente, estudiamos la distribución de la mortalidad a nivel de sección censal en las principales ciudades de la Comunitat Valenciana y a nivel municipal en la Comunitat Valenciana y en el conjunto de toda España. La evaluación de dichas propuestas ha evidenciado algunos problemas estadísticos en su implementación por lo que nos planteamos como objetivo principal el desarrollo de nuevas propuestas metodológicas que permitan resolver los problemas encontrados en cada uno de los escenarios considerados. Así mismo, nos planteamos también como objetivo el desarrollo de un atlas nacional de mortalidad avanzado que permita visualizar de forma interactiva la distribución geográfica y la evolución temporal de la mortalidad por un gran número de causas y a lo largo de un gran periodo de estudio en el conjunto de toda España. La tesis que aquí presentamos es un compendio de tres artículos y se estructura de la siguiente forma. En el Capítulo 1 presentamos una introducción general, incluyendo una descripción de los objetivos, de los datos analizados en cada proyecto y del software utilizado. En el Capítulo 2 describimos el marco general de modelización en los estudios de mapeo de enfermedades así como las propuestas de modelización que han sido evaluadas en cada escenario. Resumimos también las limitaciones encontradas en dichas propuestas y las nuevas propuestas de modelización desarrolladas en esta tesis para resolverlas. El Capítulo 3 resume los principales resultados obtenidos en cada proyecto. Los Capítulos 4, 5 y 6 contienen los tres artículos de investigación publicados que componen este compendio. En el Capítulo 7 describimos la metodología utilizada en el desarrollo del atlas nacional de mortalidad de España y sus principales características y resultados. Por último, en el Capítulo 8 presentamos algunas conclusiones y posibles líneas de trabajo futuro. Disease mapping has received great interest for the past three decades. This research area pursues the study of the geographical distribution of health-related events, such as mortality or the incidence of diseases, aggregated in geographic units, in order to mainly identify those locations that show a higher risk. The application of advanced statistical methods to carry risk estimates out is essential to obtain accurate estimates and to improve the understanding of the geographical distribution of diseases. In this thesis, we focus on the application and evaluation of several relevant modeling proposals, emerged in the disease mapping literature, to estimate the mortality geographic distribution, considering different scenarios with real data. Specifically, we study the distribution of mortality at the census tract level in the main cities of the Valencian Region and at the municipal level in the Valencian Region and in the whole of Spain. The evaluation of these previously published proposals reveals some statistical problems in their implementations. Therefore, our main goal with this thesis is the development of new methodological proposals that allow solving the problems of these previously published proposals. Likewise, we also pursue the development of an advanced national mortality atlas that allows to interactively visualize the geographical distribution, and the temporal evolution, of mortality for a large number of causes and throughout a long period of study in the whole of Spain. This thesis is a compendium of three articles and an additional work, which are structured as follows. In Chapter 1, we present a general introduction, including a description of the objectives, the data analyzed in each work and the software used. In Chapter 2, we introduce the general problem of disease mapping, as well as the modeling proposals that have been improved in each of our works. We also summarize the limitations found in these proposals and the new modeling proposals developed in this thesis. Chapter 3 summarizes the main results obtained in each of the subsequent works. Chapters 4, 5 and 6 contain the three published research articles that make up this compendium. In Chapter 7, we describe the methodology used in the development of the Spanish National Atlas of Mortality and its main characteristics and results. Finally, in Chapter 8, we present some conclusions and possible lines of future work.

Influenza is a disease which affects millions of people every year and causes hundreds of thousends of deads every year. This disease causes substantial direct and indirect costs every year. The influenza epidemic have a particular behavior which shapes the statistical methods for their detection. Seasonal epidemics happen virtually every year in the temperate parts of the globe during the cold months and extend throughout whole regions, countries and even continents. Besides the seasonal epidemics, some nonseasonal epidemics can be observed at unexpected times, usually caused by strains which jump the barrier between animals and humans, as happened with the well known Swine Flu epidemic, which caused great alarm in 2009. Several statistical methods have been proposed for the detection of outbreaks of diseases and, in particular, for influenza outbreaks. A reduced version of the review present in this thesis has been published in REVSTAT-Statistical Journal by Amorós et al. in 2015. An interesting tool for the modeling of statistical methods for the detection of influenza outbreaks is the use of Markov switching models, where latent variables are paired with the observations, indicating the epidemic or endemic phase. Two different models are applied to the data according to the value of the latent variable. The latent variables are temporally linked through a Markov chain. The observations are also conditionally dependent on their temporal or spatio-temporal neighbors. Models using this tool can offer a probability of being in epidemic as an outcome instead of just a ‘yes’ or ‘no’. Bayesian paradigm offers an interesting framework where the outcomes can be interpreted as probability distributions. Also, inference can be done over complex hierarchical models, as usually the Markov switching models are. This research offer two extensions of the model proposed by Martinez-Beneito et al. in 2008, published in Statistics in Medicine. The first proposal is a framework of Poison Markov switching models over the counts. This proposal has been published in Statistical Methods in Medical Research by Conesa et al. in 2015. In this proposal, the counts are modeled through a Poisson distribution, and the mean of these counts is related to the rates through the population. Then, the rates are modeled through a Normal distribution. The the mean and variance of the rates depend on whether we are in the epidemic or nonepidemic phase for each week. The latent variables which determine the epidemic phase are modeled through a hidden Markov chain. The mean and the variance on the epidemic phase is considered to be larger than the ones on the endemic phase. Different degrees of temporal dependency of the mean of the data can be defined. A first option is be to consider the rates conditionally independent. A second option is to consider that every observation is conditionally dependent on the previous observation through an autoregressive process of order 1. Higher orders of dependency can be defined, but we limited our framework of models to an autoregressive process of order 2 to avoid unnecessary complexity, as no big changes in the outcome were appreciated using higher orders of autocorrelation. The application of this framework of methods over several data bases showed that this proposal outperforms other methodologies present in the literature. It also stresses several difficulties in the process of evaluation of statistical methods for the detection of influenza outbreaks. The second proposal of this research is a spatio-temporal Markov switching model over the differentiated rates, which are considered to follow a normal distribution, with mean and variance parameters dependent on the epidemic state. The latent variables are modeled in the same way as in the temporal proposal, but having one conditionally independent hidden Markov chain for each of the locations. The variance of the endemic phase is also considered to be lower than that of the epidemic phase. Three components are defined for the mean of the differentiated rates: First of all, a common term for all the regions for each time is set in both the endemic and epidemic mean. These terms are defined as two random effects, with mean zero and a higher variance for the epidemic phase. The variances of these random effects are linked to those of the likelihood to avoid problems of identifiability. An autoregressive term for each location is also defined for the epidemic term, as it is expected that from the begining of the epidemic until the peak we observe similar positive jumps and from the peak to the end of the epidemic we observe similar negative jumps. An intrinsic CAR structure is also defined for the epidemic mean, considering that the epidemic can spread to neighbor regions which will have similar epidemic increases of the rates. This proposal has been applied over the United States Google Flu Trends data from 2007 to 2013 for the 48 spatially connected states plus Washington D.C. The comparison of the model with several simplifications and variations has stressed the necessity of several of the assumptions made during the modeling process.

En los últimos años han ido surgiendo numerosos estudios de áreas pequeñas en los que se analiza la asociación entre una variable respuesta y una covariable en varias ciudades de forma independiente. En este trabajo se pretende implementar y explorar las posibles ventajas de un estudio conjunto de regresión ecológica para todas las regiones que tenga en cuenta la estructura espacial tanto dentro como entre ciudades. El modelo propuesto se basa en conceptos del "disease mapping" y de la geoestadística, y tiene en cuenta la estructura espacial de los datos. Además, permite predecir riesgos relativos (y evaluar su significación) en localizaciones geográficas donde no se dispone de datos. Este modelo se compara con dos alternativas. La regresión ecológica propuesta se ilustra mediante un ejemplo en el que se pretende analizar la asociación entre el desempleo y la mortalidad por cáncer de pulmón en 31 ciudades españolas.

Esta tesis tiene dos objetivos principales. El primero es proponer métodos multivariantes para el estudio de las desigualdades socioeconómicas en la mortalidad en áreas pequeñas. El segundo es estudiar estas desigualdades en la práctica en varias ciudades españolas. En consecuencia, se han realizado cuatro estudios diferentes: dos de ellos más metodológicos y los otros dos más aplicados al estudio de las desigualdades. El primer estudio metodológico propone usar Análisis Factorial Bayesiano para el cálculo de índices de privación. Además, en este estudio se concluye que ignorar la variabilidad en la estimación del índice puede conducir a un sesgo cuando las áreas se agrupan según cuantiles del índice. En el segundo estudio se ha reformulado el modelo SANOVA de modo que es posible introducir una covariable dentro de este modelo. Asimismo, dicha reformulación permite la descomposición de la varianza de los patrones estudiados como suma de varianzas de todas las componentes del modelo. Finalmente, los estudios restantes evidencian la existencia de desigualdades socioeconómicas en la mortalidad total y en la mortalidad por las principales causas específicas en once ciudades españolas. Además, para las enfermedades isquémicas del corazón estas desigualdades parecen aumentar ligeramente en el tiempo., This thesis has two main objectives. The first is to propose multivariate methods for the study of socioeconomic inequalities in mortality in small areas. The second is to study socioeconomic inequalities in mortality in small areas of several Spanish cities. Four different studies were conducted to attain these objectives: two of them focussed on the methodological aspects and the other two being empirical studies focussed on the study of inequalities. The first methodological study proposes the Bayesian factor analysis to calculate a deprivation index. Additionally, this study concludes that ignoring the uncertainty obtained in the estimation of the index may result in a misclassification bias when the areas are grouped according to quantiles of the index. In the second methodological study the SANOVA model has been reformulated enabling the introduction of a covariate in the model. Also, this reformulation permits the decomposition of the variance of the studied patterns into the sum of variances of all the model components. Finally, the other studies show the existence of socioeconomic inequalities in total mortality and mortality by specific causes in eleven major Spanish cities. In addition, for ischemic heart disease these inequalities appear to increase slightly over time.