Bayesian temporal and spatio-temporal Markov switching models for the detection of influenza outbreaks

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

Postnatal exposure to mercury and neuropsychological development among preschooler children

The objective of this study was to describe the postnatal exposure to Hg and to evaluate its association with neuropsychological development among preschool children. The study population are 4–5 years old children (n = 1252) participant in the Spanish INMA Project. Total Hg was measured in cord blood and in hair samples taken at 4 years of age (2008–2012). Neuropsychological development was assessed using the McCarthy Scales of Children’s Abilities (MSCA). Information on covariates and possible confounders was obtained by questionnaires during pregnancy and childhood. Generalized additive and linear regression models were built in order to assess the relationship between MSCA scores and Hg exposure. We also evaluated the magnitude of the possible bias generated from measurement error in seafood intake estimate from questionnaire and Hg determination. The geometric mean of hair Hg was 0.98 μg/g [95% confidence interval (CI) 0.94, 1.03]. In the regression analysis, the association between Hg and the MSCA scores was positive for all the scales and statistically significant for the verbal (β = 0.89; 95%CI 0.38, 1.39), memory (β = 0.42; 95%CI 0.09, 0.76) and general cognitive scales (β = 1.35; 95%CI 0.45, 2.25). However, these associations were clearly attenuated when we adjusted by the children’s fish intake variables or when took into account theoretical scenarios of low precision in fish intake and Hg measurements. Hg levels in this Spanish population were high in comparison with other European countries; however, we did not observe adverse effects on child neuropsychological development associated with this postnatal exposure to Hg

Selenium status during pregnancy: Influential factors and effects on neuropsychological development among Spanish infants

Selenium (Se) has been positively associated with neurodevelopment in early life. However, its margin of safety is rather narrow, and few prospective studies have evaluated its potential neurotoxic effects at intermediate levels. We aimed to explore the association between maternal Se concentrations and child neuropsychological development, including the genetic effect modification of the Se metabolizing gene INMT. Study subjects were 650 mother-child pairs from the Spanish Childhood and Environment Project (INMA, 2003–2005). Infant neuropsychological development was assessed around 12 months of age by the Bayley Scales of Infant Development. Sociodemographic and dietary characteristics were collected by questionnaire at the first and third trimester of gestation. Se was measured in serum samples at the first trimester. The mean serum Se concentration was 79.7 (standard deviation = 7.9) μg/L. In multivariate analysis, nonsignificant inverse linear associations were found between Se concentrations and standardized mental and psychomotor development scores (β (95% CI) = − 0.13 (− 0.29, 0.03) and β (95% CI) = − 0.08 (− 0.24, 0.07), respectively). Generalized additive models indicated inverted U-shaped relationships between Se concentrations and both scales. Using segmented regression, the turning point for the associations was estimated at 86 μg/L for both scales. The association between Se and neuropsychological development was inverted U-shaped for children with the AG + AA genotype for rs6970396 INMT but a descending curve was suggested for the GG genotype. Further studies would be necessary in order to disentangle the complex equilibrium between the toxicity and benefits of Se exposure during the prenatal period