A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Bayesian Hierarchical Distributed Lag Models for Summer Ozone Exposure and Cardio-Respiratory Mortality

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994. At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP associated with short-term exposure to summer ozone. At the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by taking into account the variability within and across cities. We perform the calculations with respect to several random effects distributions (normal, t-student, and mixture of normal), thus relaxing the common assumption of a two-stage normal-normal hierarchical model. We assess the sensitivity of the results to: 1) lag structure for ozone exposure; 2) degree of adjustment for long-term trends; 3) inclusion of other pollutants in the model;4) heat waves; 5) random effects distributions; and 6) prior hyperparameters. On average across cities, we found that a 10ppb increase in summer ozone level for every day in the previous week is associated with 1.25 percent increase in CVDRESP mortality (95% posterior regions: 0.47, 2.03). The relative rate estimates are also positive and statistically significant at lags 0, 1, and 2. We found that associations between summer ozone and CVDRESP mortality are sensitive to the confounding adjustment for PM_10, but are robust to: 1) the adjustment for long-term trends, other gaseous pollutants (NO_2, SO_2, and CO); 2) the distributional assumptions at the second stage of the hierarchical model; and 3) the prior distributions on all unknown parameters. Bayesian hierarchical distributed lag models and their application to the NMMAPS data allow us estimation of an acute health effect associated with exposure to ambient air pollution in the last few days on average across several locations. The application of these methods and the systematic assessment of the sensitivity of findings to model assumptions provide important epidemiological evidence for future air quality regulations.

The impact of temperature on mortality in Tianjin, China : a case-crossover design with a distributed lag non-linear model

Background There has been increasing interest in assessing the impacts of temperature on mortality. However, few studies have used a case–crossover design to examine non-linear and distributed lag effects of temperature on mortality. Additionally, little evidence is available on the temperature-mortality relationship in China, or what temperature measure is the best predictor of mortality. Objectives To use a distributed lag non-linear model (DLNM) as a part of case–crossover design. To examine the non-linear and distributed lag effects of temperature on mortality in Tianjin, China. To explore which temperature measure is the best predictor of mortality; Methods: The DLNM was applied to a case¬−crossover design to assess the non-linear and delayed effects of temperatures (maximum, mean and minimum) on deaths (non-accidental, cardiopulmonary, cardiovascular and respiratory). Results A U-shaped relationship was consistently found between temperature and mortality. Cold effects (significantly increased mortality associated with low temperatures) were delayed by 3 days, and persisted for 10 days. Hot effects (significantly increased mortality associated with high temperatures) were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. Conclusions In Tianjin, extreme cold and hot temperatures increased the risk of mortality. Results suggest that the effects of cold last longer than the effects of heat. It is possible to combine the case−crossover design with DLNMs. This allows the case−crossover design to flexibly estimate the non-linear and delayed effects of temperature (or air pollution) whilst controlling for season.

Temperature variation between neighboring days and mortality: a distributed lag non-linear analysis

Objectives To investigate whether a sudden temperature change between neighboring days has significant impact on mortality. Methods A Poisson generalized linear regression model combined with a distributed lag non-linear models was used to estimate the association of temperature change between neighboring days with mortality in a subtropical Chinese city during 2008–2012. Temperature change was calculated as the current day’s temperature minus the previous day’s temperature. Results A significant effect of temperature change between neighboring days on mortality was observed. Temperature increase was significantly associated with elevated mortality from non-accidental and cardiovascular diseases, while temperature decrease had a protective effect on non-accidental mortality and cardiovascular mortality. Males and people aged 65 years or older appeared to be more vulnerable to the impact of temperature change. Conclusions Temperature increase between neighboring days has a significant adverse impact on mortality. Further health mitigation strategies as a response to climate change should take into account temperature variation between neighboring days.

Unusual scene detection using distributed behaviour model and sparse representation

The ability to detect unusual events in surviellance footage as they happen is a highly desireable feature for a surveillance system. However, this problem remains challenging in crowded scenes due to occlusions and the clustering of people. In this paper, we propose using the Distributed Behavior Model (DBM), which has been widely used in computer graphics, for video event detection. Our approach does not rely on object tracking, and is robust to camera movements. We use sparse coding for classification, and test our approach on various datasets. Our proposed approach outperforms a state-of-the-art work which uses the social force model and Latent Dirichlet Allocation.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Calibration of structure in a distributed forecasting model for a semiarid flash flood: dynamic surface storage and channel roughness

Flash floods pose a significant danger for life and property. Unfortunately, in arid and semiarid environment the runoff generation shows a complex non-linear behavior with a strong spatial and temporal non-uniformity. As a result, the predictions made by physically-based simulations in semiarid areas are subject to great uncertainty, and a failure in the predictive behavior of existing models is common. Thus better descriptions of physical processes at the watershed scale need to be incorporated into the hydrological model structures. For example, terrain relief has been systematically considered static in flood modelling at the watershed scale. Here, we show that the integrated effect of small distributed relief variations originated through concurrent hydrological processes within a storm event was significant on the watershed scale hydrograph. We model these observations by introducing dynamic formulations of two relief-related parameters at diverse scales: maximum depression storage, and roughness coefficient in channels. In the final (a posteriori) model structure these parameters are allowed to be both time-constant or time-varying. The case under study is a convective storm in a semiarid Mediterranean watershed with ephemeral channels and high agricultural pressures (the Rambla del Albujón watershed; 556 km 2 ), which showed a complex multi-peak response. First, to obtain quasi-sensible simulations in the (a priori) model with time-constant relief-related parameters, a spatially distributed parameterization was strictly required. Second, a generalized likelihood uncertainty estimation (GLUE) inference applied to the improved model structure, and conditioned to observed nested hydrographs, showed that accounting for dynamic relief-related parameters led to improved simulations. The discussion is finally broadened by considering the use of the calibrated model both to analyze the sensitivity of the watershed to storm motion and to attempt the flood forecasting of a stratiform event with highly different behavior.

Assessing the sensitivities of a distributed snow model to forcing data resolution

Highly heterogeneous mountain snow distributions strongly affect soil moisture patterns; local ecology; and, ultimately, the timing, magnitude, and chemistry of stream runoff. Capturing these vital heterogeneities in a physically based distributed snow model requires appropriately scaled model structures. This work looks at how model scale—particularly the resolutions at which the forcing processes are represented—affects simulated snow distributions and melt. The research area is in the Reynolds Creek Experimental Watershed in southwestern Idaho. In this region, where there is a negative correlation between snow accumulation and melt rates, overall scale degradation pushed simulated melt to earlier in the season. The processes mainly responsible for snow distribution heterogeneity in this region—wind speed, wind-affected snow accumulations, thermal radiation, and solar radiation—were also independently rescaled to test process-specific spatiotemporal sensitivities. It was found that in order to accurately simulate snowmelt in this catchment, the snow cover needed to be resolved to 100 m. Wind and wind-affected precipitation—the primary influence on snow distribution—required similar resolution. Thermal radiation scaled with the vegetation structure (~100 m), while solar radiation was adequately modeled with 100–250-m resolution. Spatiotemporal sensitivities to model scale were found that allowed for further reductions in computational costs through the winter months with limited losses in accuracy. It was also shown that these modeling-based scale breaks could be associated with physiographic and vegetation structures to aid a priori modeling decisions.

Weather variability, tides, and Barmah Forest Virus Disease in the Gladstone region, Australia

In this study we examined the impact of weather variability and tides on the transmission of Barmah Forest virus (BFV) disease and developed a weather-based forecasting model for BFV disease in the Gladstone region, Australia. We used seasonal autoregressive integrated moving-average (SARIMA) models to determine the contribution of weather variables to BFV transmission after the time-series data of response and explanatory variables were made stationary through seasonal differencing. We obtained data on the monthly counts of BFV cases, weather variables (e.g., mean minimum and maximum temperature, total rainfall, and mean relative humidity), high and low tides, and the population size in the Gladstone region between January 1992 and December 2001 from the Queensland Department of Health, Australian Bureau of Meteorology, Queensland Department of Transport, and Australian Bureau of Statistics, respectively. The SARIMA model shows that the 5-month moving average of minimum temperature (β = 0.15, p-value < 0.001) was statistically significantly and positively associated with BFV disease, whereas high tide in the current month (β = −1.03, p-value = 0.04) was statistically significantly and inversely associated with it. However, no significant association was found for other variables. These results may be applied to forecast the occurrence of BFV disease and to use public health resources in BFV control and prevention.