Conditional probability and ratio-based approaches for mapping the coverage of multi-dose vaccines.

Many vaccines are often administered in multiple doses to boost their effectiveness. In the case of childhood vaccines, the coverage maps of the doses and the differences between these often constitute an evidence base to guide investments in improving access to vaccination services and health system performance in low and middle-income countries. A major problem often encountered when mapping the coverage of multi-dose vaccines is the need to ensure that the coverage maps decrease monotonically with successive doses. That is, for doses i $$ i $$ and j $$ j $$ , i < j ⇒ p i ( s ) ≥ p j ( s ) $$ i

Bayesian spatio-temporal joint disease mapping of Covid-19 cases and deaths in local authorities of England.

The overwhelming spatio-temporal nature of the spread of the ongoing Covid-19 pandemic demands urgent attention of data analysts and model developers. Modelling results obtained from analytical tool development are essential to understand the ongoing pandemic dynamics with a view to helping the public and policy makers. The pandemic has generated data on a huge number of interesting statistics such as the number of new cases, hospitalisations and deaths in many spatio-temporal resolutions for the analysts to investigate. The multivariate nature of these data sets, along with the inherent spatio-temporal dependencies, poses new challenges for modellers. This article proposes a two-stage hierarchical Bayesian model as a joint bivariate model for the number of cases and deaths observed weekly for the different local authority administrative regions in England. An adaptive model is proposed for the weekly Covid-19 death rates as part of the joint bivariate model. The adaptive model is able to detect possible step changes in death rates in neighbouring areas. The joint model is also used to evaluate the effects of several socio-economic and environmental covariates on the rates of cases and deaths. Inclusion of these covariates points to the presence of a north-south divide in both the case and death rates. Nitrogen dioxide, the only air pollution measure used in the model, is seen to be significantly positively associated with the number cases, even in the presence of the spatio-temporal random effects taking care of spatio-temporal dependencies present in the data. The proposed models provide excellent fits to the observed data and are seen to perform well for predicting the location specific number of deaths a week in advance. The structure of the models is very general and the same framework can be used for modelling other areally aggregated temporal statistics of the pandemics, e.g. the rate of hospitalisation.

Regional surface chlorophyll trends and uncertainties in the global ocean.

Changes in marine primary productivity are key to determine how climate change might impact marine ecosystems and fisheries. Satellite ocean color sensors provide coverage of global ocean chlorophyll with a combined record length of ~ 20 years. Coupled physical-biogeochemical models can inform on expected changes and are used here to constrain observational trend estimates and their uncertainty. We produce estimates of ocean surface chlorophyll trends, by using Coupled Model Intercomparison Project (CMIP5) models to form priors as a "first guess", which are then updated using satellite observations in a Bayesian spatio-temporal model. Regional chlorophyll trends are found to be significantly different from zero in 18/23 regions, in the range ± 1.8% year-1. A global average of these regional trends shows a net positive trend of 0.08 ± 0.35% year-1, highlighting the importance of considering chlorophyll changes at a regional level. We compare these results with estimates obtained with the commonly used "vague" prior, representing no independent knowledge; coupled model priors are shown to slightly reduce trend magnitude and uncertainties in most regions. The statistical model used here provides a robust framework for making best use of all available information and can be applied to improve understanding of global change.

Geographic coverage of demographic surveillance systems for characterising the drivers of childhood mortality in sub-Saharan Africa.

A major focus of international health and development goals is the reduction of mortality rates in children under 5 years of age. Achieving this requires understanding the drivers of mortality and how they vary geographically to facilitate the targeting and prioritisation of appropriate interventions. Much of our knowledge on the causes of, and trends in, childhood mortality come from longitudinal demographic surveillance sites, with a renewed focus recently on the establishment and growth of networks of sites from which standardised outputs can facilitate broader understanding of processes. To ensure that the collective outputs from surveillance sites can be used to derive a comprehensive understanding and monitoring system for driving policy on tackling childhood mortality, confidence is needed that existing and planned networks of sites are providing a reliable and representative picture of the geographical variation in factors associated with mortality. Here, we assembled subnational data on childhood mortality as well as key factors known to be associated with it from household surveys in 27 sub-Saharan African countries. We then mapped the locations of existing longitudinal demographic surveillance sites to assess the extent of current coverage of the range of factors, identifying where gaps exist. The results highlight regions with unique combinations of factors associated with childhood mortality that are poorly represented by the current distribution of sites, such as southern Mali, central Nigeria and southern Zambia. Finally, we determined where the establishment of new surveillance systems could improve coverage.

A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health.

In the United Kingdom, air pollution is linked to around 40000 premature deaths each year, but estimating its health effects is challenging in a spatio-temporal study. The challenges include spatial misalignment between the pollution and disease data; uncertainty in the estimated pollution surface; and complex residual spatio-temporal autocorrelation in the disease data. This article develops a two-stage model that addresses these issues. The first stage is a spatio-temporal fusion model linking modeled and measured pollution data, while the second stage links these predictions to the disease data. The methodology is motivated by a new five-year study investigating the effects of multiple pollutants on respiratory hospitalizations in England between 2007 and 2011, using pollution and disease data relating to local and unitary authorities on a monthly time scale.

Modelling macronutrient dynamics in the Hampshire Avon river: A Bayesian approach to estimate seasonal variability and total flux.

The macronutrients nitrate and phosphate are aquatic pollutants that arise naturally, however, in excess concentrations they can be harmful to human health and ecosystems. These pollutants are driven by river currents and show dynamics that are affected by weather patterns and extreme rainfall events. As a result, the nutrient budget in the receiving estuaries and coasts can change suddenly and seasonally, causing ecological damage to resident wildlife and fish populations. In this paper, we propose a statistical change-point model with interactions between time and river flow, to capture the macronutrient dynamics and their responses to river flow threshold behaviour. It also accounts for the nonlinear effect of water quality properties via nonparametric penalised splines. This model enables us to estimate the daily levels of riverine macronutrient fluxes and their seasonal and annual totals. In particular, we present a study of macronutrient dynamics on the Hampshire Avon River, which flows to the southern coast of the UK through the Christchurch Harbour estuary. We model daily data for more than a year during 2013-14 in which period there were multiple severe meteorological conditions leading to localised flooding. Adopting a Bayesian inference framework, we have quantified riverine macronutrient fluxes based on input river flow values. Out of sample empirical validation methods justify our approach, which captures also the dependencies of macronutrient concentrations with water body characteristics.

A Bayesian network for modelling blood glucose concentration and exercise in type 1 diabetes.

This article presents a new statistical approach to analysing the effects of everyday physical activity on blood glucose concentration in people with type 1 diabetes. A physiologically based model of blood glucose dynamics is developed to cope with frequently sampled data on food, insulin and habitual physical activity; the model is then converted to a Bayesian network to account for measurement error and variability in the physiological processes. A simulation study is conducted to determine the feasibility of using Markov chain Monte Carlo methods for simultaneous estimation of all model parameters and prediction of blood glucose concentration. Although there are problems with parameter identification in a minority of cases, most parameters can be estimated without bias. Predictive performance is unaffected by parameter misspecification and is insensitive to misleading prior distributions. This article highlights important practical and theoretical issues not previously addressed in the quest for an artificial pancreas as treatment for type 1 diabetes. The proposed methods represent a new paradigm for analysis of deterministic mathematical models of blood glucose concentration.

A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution.

Estimation of the long-term health effects of air pollution is a challenging task, especially when modeling spatial small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial autocorrelation structure in these data, which is accounted for using random effects modeled by a globally smooth conditional autoregressive model. These smooth random effects confound the effects of air pollution, which are also globally smooth. To avoid this collinearity a Bayesian localized conditional autoregressive model is developed for the random effects. This localized model is flexible spatially, in the sense that it is not only able to model areas of spatial smoothness, but also it is able to capture step changes in the random effects surface. This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models. These results are established using a simulation study, and are then illustrated with our motivating study on air pollution and respiratory ill health in Greater Glasgow, Scotland in 2011. The model shows substantial health effects of particulate matter air pollution and nitrogen dioxide, whose effects have been consistently attenuated by the currently available globally smooth models.

On the Effect of Preferential Sampling in Spatial Prediction.

The choice of the sampling locations in a spatial network is often guided by practical demands. In particular, many locations are preferentially chosen to capture high values of a response, for example, air pollution levels in environmental monitoring. Then, model estimation and prediction of the exposure surface become biased due to the selective sampling. Since prediction is often the main utility of the modeling, we suggest that the effect of preferential sampling lies more importantly in the resulting predictive surface than in parameter estimation. Our contribution is to offer a direct simulation-based approach to assessing the effects of preferential sampling. We compare two predictive surfaces over the study region, one originating from the notion of an 'operating' intensity driving the selection of monitoring sites, the other under complete spatial randomness. We can consider a range of response models. They may reflect the operating intensity, introduce alternative informative covariates, or just propose a flexible spatial model. Then, we can generate data under the given model. Upon fitting the model and interpolating (kriging), we will obtain two predictive surfaces to compare. It is important to note that we need suitable metrics to compare the surfaces and that the predictive surfaces are random, so we need to make expected comparisons.

High Resolution Space-Time Ozone Modeling for Assessing Trends.

The assessment of air pollution regulatory programs designed to improve ground level ozone concentrations is a topic of considerable interest to environmental managers. To aid this assessment, it is necessary to model the space-time behavior of ozone for predicting summaries of ozone across spatial domains of interest and for the detection of long-term trends at monitoring sites. These trends, adjusted for the effects of meteorological variables, are needed for determining the effectiveness of pollution control programs in terms of their magnitude and uncertainties across space. This paper proposes a space-time model for daily 8-hour maximum ozone levels to provide input to regulatory activities: detection, evaluation, and analysis of spatial patterns of ozone summaries and temporal trends. The model is applied to analyzing data from the state of Ohio which has been chosen because it contains a mix of urban, suburban, and rural ozone monitoring sites in several large cities separated by large rural areas. The proposed space-time model is auto-regressive and incorporates the most important meteorological variables observed at a collection of ozone monitoring sites as well as at several weather stations where ozone levels have not been observed. This problem of misalignment of ozone and meteorological data is overcome by spatial modeling of the latter. In so doing we adopt an approach based on the successive daily increments in meteorological variables. With regard to modeling, the increment (or change-in-meteorology) process proves more attractive than working directly with the meteorology process, without sacrificing any desired inference. The full model is specified within a Bayesian framework and is fitted using MCMC techniques. Hence, full inference with regard to model unknowns is available as well as for predictions in time and space, evaluation of annual summaries and assessment of trends.