An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach -- the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the SLA-based and grid-based approaches perform equally well for spatially dense data.

The choice of spatial scales and spatial smoothness priors for various spatial patterns

Given the drawbacks for using geo-political areas in mapping outcomes unrelated to geo-politics, a compromise is to aggregate and analyse data at the grid level. This has the advantage of allowing spatial smoothing and modelling at a biologically or physically relevant scale. This article addresses two consequent issues: the choice of the spatial smoothness prior and the scale of the grid. Firstly, we describe several spatial smoothness priors applicable for grid data and discuss the contexts in which these priors can be employed based on different aims. Two such aims are considered, i.e., to identify regions with clustering and to model spatial dependence in the data. Secondly, the choice of the grid size is shown to depend largely on the spatial patterns. We present a guide on the selection of spatial scales and smoothness priors for various point patterns based on the two aims for spatial smoothing.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

Heat-related morbidity in Brisbane, Australia : spatial variation and area-level predictors

Background: Extreme heat is a leading weather-related cause of illness and death in many locations across the globe, including subtropical Australia. The possibility of increasingly frequent and severe heat waves warrants continued efforts to reduce this health burden, which could be accomplished by targeting intervention measures toward the most vulnerable communities. Objectives: We sought to quantify spatial variability in heat-related morbidity in Brisbane, Australia, to highlight regions of the city with the greatest risk. We also aimed to find area-level social and environmental determinants of high risk within Brisbane. Methods: We used a series of hierarchical Bayesian models to examine city-wide and intracity associations between temperature and morbidity using a 2007–2011 time series of geographically referenced hospital admissions data. The models accounted for long-term time trends, seasonality, and day of week and holiday effects. Results: On average, a 10°C increase in daily maximum temperature during the summer was associated with a 7.2% increase in hospital admissions (95% CI: 4.7, 9.8%) on the following day. Positive statistically significant relationships between admissions and temperature were found for 16 of the city’s 158 areas; negative relationships were found for 5 areas. High-risk areas were associated with a lack of high income earners and higher population density. Conclusions: Geographically targeted public health strategies for extreme heat may be effective in Brisbane, because morbidity risk was found to be spatially variable. Emergency responders, health officials, and city planners could focus on short- and long-term intervention measures that reach communities in the city with lower incomes and higher population densities, including reduction of urban heat island effects.

What is the apparent angle of a Kelvin ship wave pattern?

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Spatial analysis of risk factors for transmission of the Barmah forest virus in Queensland, Australia

Barmah Forest virus (BFV) disease is the second most common mosquito-borne disease in Australia but few data are available on the risk factors. We assessed the impact of spatial climatic, socioeconomic and ecological factors on the transmission of BFV disease in Queensland, Australia, using spatial regression. All our analyses indicate that spatial lag models provide a superior fit to the data compared to spatial error and ordinary least square models. The residuals of the spatial lag models were found to be uncorrelated, indicating that the models adequately account for spatial and temporal autocorrelation. Our results revealed that minimum temperature, distance from coast and low tide were negatively and rainfall was positively associated with BFV disease in coastal areas, whereas minimum temperature and high tide were negatively and rainfall was positively associated with BFV disease (all P-value.

Triphasic pattern in the ex vivo response of human proliferative phase endometrium to oestrogens

The aim of this study was to evaluate the ex vivo oestrogen responsiveness of human proliferative phase endometrium using short-term explant cultures. The effects of oestrogen (17beta-E2) on proliferation and the expression of oestrogen-responsive genes known to be involved in regulating endometrial function were evaluated. Three distinct response patterns could be distinguished: (1) the menstrual (M) phase pattern (cycle days 2-5), which is characterised by a complete lack in the proliferative response to 17beta-E2, while an increased expression of AR (2.6-fold, P<0.01), PR (2.7-fold, P<0.01) and COX-2 (3.5-fold, P<0.01) at the mRNA level was observed and a similar upregulation was also found for AR, PR and COX-2 at the protein level; (2) the early proliferative (EP) phase pattern (cycle days 6-10) with 17beta-E2 enhanced proliferation in the stroma (1.7-fold, P<0.05), whereas the expression of AR, PR and COX-2 were not affected at the mRNA and protein levels and ER-a mRNA and protein levels were significantly reduced by 17beta-E2; (3) the late proliferative (LP) phase pattern (cycle days 11-14), which is characterised by a moderate stimulation of proliferation (1.4-fold, P<0.05) and PR mRNA expression (1.7-fold, P<0.01) by 17beta-E2. In conclusion, three distinct response patterns to 17beta-E2 could be identified with respect to proliferation and the expression of known oestrogen-responsive genes in human proliferative phase endometrium explant cultures.

Did Brisbane grow smartly? Drivers of city growth 1991-2001 and lessons for current policies

Urban areas are growing unsustainably around the world; however, the growth patterns and their associated drivers vary between contexts. As a result, research has highlighted the need to adopt case study based approaches to stimulate the development of new theoretic understandings. Using land-cover data sets derived from Landsat images (30 m × 30 m), this research identifies both patterns and drivers of urban growth in a period (1991-2001) when a number of policy acts were enacted aimed at fostering smart growth in Brisbane, Australia. A linear multiple regression model was estimated using the proportion of lands that were converted from non-built-up (1991) to built-up usage (2001) within a suburb as a dependent variable to identify significant drivers of land-cover changes. In addition, the hot spot analysis was conducted to identify spatial biases of land-cover changes, if any. Results show that the built-up areas increased by 1.34% every year. About 19.56% of the non-built-up lands in 1991 were converted into built-up lands in 2001. This conversion pattern was significantly biased in the northernmost and southernmost suburbs in the city. This is due to the fact that, as evident from the regression analysis, these suburbs experienced a higher rate of population growth, and had the availability of habitable green field sites in relatively flat lands. The above findings suggest that the policy interventions undertaken between the periods were not as effective in promoting sustainable changes in the environment as they were aimed for.