Spatio-Temporal Methods in Environmental Epidemiology

Why spatio-temporal epidemiology? Overview Health-exposure models Dependencies over space and time Examples of spatio-temporal epidemiological analyses Bayesian hierarchical models Spatial data Good spatio-temporal modelling approaches Modelling health risks Overview Types of epidemiological study Measures of risk Standardised mortality ratios (SMRs) Generalised linear models Generalised additive models Generalised estimating equations Poisson models for count data Estimating relative risks in relation to exposures Modelling the cumulative effects of exposure Logistic models for case-controls studies The importance of uncertainty Overview The wider world of uncertainty Quantitative uncertainty Methods for assessing uncertainty Quantifying uncertainty Embracing uncertainty: the Bayesian approach Overview Introduction to Bayesian inference Exchangeability Using the posterior for inference Predictions Transformations of parameters Prior formulation The Bayesian approach in practice Overview Analytical approximations Markov chain Monte Carlo (MCMC) Using samples for inference WinBUGS INLA Strategies for modelling Overview Contrasts Hierarchical models Generalised linear mixed models Linking exposure and health models Model selection and comparison What about the p-value? Comparison of models-Bayes factors Bayesian model averaging Is 'real' data always quite so real? Overview Missing Values Measurement error Preferential sampling Spatial patterns in disease Overview The Markov random field (MRF) The conditional autoregressive (CAR) model Spatial models for disease mapping From points to fields: modelling environmental hazards over space Overview A brief history of spatial modelling Exploring spatial data Modelling spatial data Spatial trend Spatial prediction Stationary and isotropic spatial processes Variograms Fitting variogram models Kriging Extensions of simple kriging A hierarchical model for spatially varying exposures INLA and spatial modelling in a continuous domain Non-stationary random fields Why time also matters Overview Time series epidemiology Time series modelling Modelling the irregular components The spectral representation theorem and Bochner's lemma Forecasting State space models A hierarchical model for temporally varying exposures The interplay between space and time in exposure assessment Overview Strategies Spatio-temporal models Dynamic linear models for space and time An empirical Bayes approach A hierarchical model for spatio-temporal exposure data Approaches to modelling non-separable processes Roadblocks on the way to causality: exposure pathways, aggregation and other sources of bias Overview Causality Ecological bias Acknowledging ecological bias Exposure pathways Personal exposure models Better exposure measurements through better design Overview Design objectives? Design paradigms Geometry-based designs Probability-based designs Model-based An entropy-based approach Implementation challenges New frontiers Overview Non-stationary fields Physical-statistical modelling The problem of extreme values Appendix 1: Distribution theory Appendix 2: Entropy decomposition References Index Author index A Summary and Exercises appear at the end of each chapter.