Adaptive geostatistical design and analysis for prevalence surveys

Non-adaptive geostatistical designs (NAGDs) offer standard ways of collecting and analysing geostatistical data in which sampling locations are fixed in advance of any data collection. In contrast, adaptive geostatistical designs (AGDs) allow collection of geostatistical data over time to depend on information obtained from previous information to optimise data collection towards the analysis objective. AGDs are becoming more important in spatial mapping, particularly in poor resource settings where uniformly precise mapping may be unrealistically costly and the priority is often to identify critical areas where interventions can have the most health impact. Two constructions are: singleton and batch adaptive sampling. In singleton sampling, locations xi are chosen sequentially and at each stage, xk+1 depends on data obtained at locations x1,…,xk. In batch sampling, locations are chosen in batches of size b>1, allowing each new batch, {x(k+1),…,x(k+b)}, to depend on data obtained at locations x1,…,xkb. In most settings, batch sampling is more realistic than singleton sampling. We propose specific batch AGDs and assess their efficiency relative to their singleton adaptive and non-adaptive counterparts using simulations. We then show how we are applying these findings to inform an AGD of a rolling Malaria Indicator Survey, part of a large-scale, five-year malaria transmission reduction project in Malawi

Geostatistical inference in the presence of geomasking:A composite-likelihood approach

In almost any geostatistical analysis, one of the underlying, often implicit, modelling assumptions is that the spatial locations, where measurements are taken, are recorded without error. In this study we develop geostatistical inference when this assumption is not valid. This is often the case when, for example, individual address information is randomly altered to provide privacy protection or imprecisions are induced by geocoding processes and measurement devices. Our objective is to develop a method of inference based on the composite likelihood that overcomes the inherent computational limits of the full likelihood method as set out in Fanshawe and Diggle (2011). Through a simulation study, we then compare the performance of our proposed approach with an N-weighted least squares estimation procedure, based on a corrected version of the empirical variogram. Our results indicate that the composite-likelihood approach outperforms the latter, leading to smaller root-mean-square-errors in the parameter estimates. Finally, we illustrate an application of our method to analyse data on malnutrition from a Demographic and Health Survey conducted in Senegal in 2011, where locations were randomly perturbed to protect the privacy of respondents. We conclude that our approach based on the composite likelihood is a feasible and computationally more efficient alternative option to existing likelihood-based methods that deal with positional error in a geostatistical context

Dynamic predictive probabilities to monitor rapid cystic fibrosis disease progression.

Cystic fibrosis (CF) is a progressive, genetic disease characterized by frequent, prolonged drops in lung function. Accurately predicting rapid underlying lung-function decline is essential for clinical decision support and timely intervention. Determining whether an individual is experiencing a period of rapid decline is complicated due to its heterogeneous timing and extent, and error component of the measured lung function. We construct individualized predictive probabilities for "nowcasting" rapid decline. We assume each patient's true longitudinal lung function, S(t), follows a nonlinear, nonstationary stochastic process, and accommodate between-patient heterogeneity through random effects. Corresponding lung-function decline at time t is defined as the rate of change, S'(t). We predict S'(t) conditional on observed covariate and measurement history by modeling a measured lung function as a noisy version of S(t). The method is applied to data on 30 879 US CF Registry patients. Results are contrasted with a currently employed decision rule using single-center data on 212 individuals. Rapid decline is identified earlier using predictive probabilities than the center's currently employed decision rule (mean difference: 0.65 years; 95% confidence interval (CI): 0.41, 0.89). We constructed a bootstrapping algorithm to obtain CIs for predictive probabilities. We illustrate real-time implementation with R Shiny. Predictive accuracy is investigated using empirical simulations, which suggest this approach more accurately detects peak decline, compared with a uniform threshold of rapid decline. Median area under the ROC curve estimates (Q1-Q3) were 0.817 (0.814-0.822) and 0.745 (0.741-0.747), respectively, implying reasonable accuracy for both. This article demonstrates how individualized rate of change estimates can be coupled with probabilistic predictive inference and implementation for a useful medical-monitoring approach

Modelling and Forecasting Spatio-temporal Variations in the Risk of Chronic Malnutrition Among Under-Five Children in Ghana

Background: Spatio-temporal variation in under-five-year-old children malnutrition remains unstudied in most developing countries like Ghana. This study explores and forecasts the spatio-temporal patterns in childhood chronic malnutrition among these children. We also investigate the effect of maternal education on childhood malnutrition. Methods: We analysed data on 10,036 children residing in 1,516 geographic locations. A spatio-temporal model was fitted to the data and was used to produce predictive maps of spatio-temporal variation in the probability of stunting. Results: The study found substantial spatio-temporal variation in the prevalence of stunting. Also, higher levels of mother's education were associated with decreased risk of being stunted. Conclusion: Our spatio-temporal model captured variations in childhood stunting over place and time. Our method facilitates and enriches modelling and forecasting of future stunting prevalence to identify areas at high risk. Improving maternal education could be given greater consideration within an overall strategy for addressing childhood malnutrition

Using community-level prevalence of Loa loa infection to predict the proportion of highly-infected individuals:statistical modelling to support Lymphatic Filariasis and Onchocerciasis elimination programs

Lymphatic Filariasis and Onchocerciasis (river blindness) constitute pressing public health issues in tropical regions. Global elimination programs, involving mass drug administration (MDA), have been launched by the World Health Organisation. Although the drugs used are generally well tolerated, individuals who are highly co-infected with Loa loa are at risk of experiencing serious adverse events. Highly infected individuals are more likely to be found in communities with high prevalence. An understanding of the relationship between individual infection and population-level prevalence can therefore inform decisions on whether MDA can be safely administered in an endemic community. Based on Loa loa infection intensity data from individuals in Cameroon, the Republic of the Congo and the Democratic Republic of the Congo we develop a statistical model for the distribution of infection levels in communities. We then use this model to make predictive inferences regarding the proportion of individuals whose parasite count exceeds policy-relevant levels. In particular we show how to exploit the positive correlation between community-level prevalence and intensity of infection in order to predict the proportion of highly infected individuals in a community given only prevalence data from the community in question. The resulting prediction intervals are not substantially wider, and in some cases narrower, than the corresponding binomial confidence intervals obtained from data that include measurements of individual infection levels. Therefore the model developed here facilitates the estimation of the proportion of individuals highly infected with Loa loa using only estimated community level prevalence. It can be used to assess the risk of rolling out MDA in a specific community, or to guide policy decisions

Geostatistical Methods for Disease Mapping and Visualisation Using Data from Spatio‐temporally Referenced Prevalence Surveys

In this paper, we set out general principles and develop geostatistical methods for the analysis of data from spatio‐temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram‐based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood‐based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio‐temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualisation of spatio‐temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1 334 surveys conducted in Senegal between 1905 and 2014

Inhibitory geostatistical designs for spatial prediction taking account of uncertain covariance structure

The problem of choosing spatial sampling designs for investigating an unobserved spatial phenomenon S arises in many contexts, for example, in identifying households to select for a prevalence survey to study disease burden and heterogeneity in a study region D. We studied randomized inhibitory spatial sampling designs to address the problem of spatial prediction while taking account of the need to estimate covariance structure. Two specific classes of design are inhibitory designs and inhibitory designs plus close pairs. In an inhibitory design, any pair of sample locations must be separated by at least an inhibition distance δ. In an inhibitory plus close pairs design, n − k sample locations in an inhibitory design with inhibition distance δ are augmented by k locations each positioned close to one of the randomly selected n − k locations in the inhibitory design, uniformly distributed within a disk of radius ζ. We present simulation results for the Matérn class of covariance structures. When the nugget variance is non-negligible, inhibitory plus close pairs designs demonstrate improved predictive efficiency over designs without close pairs. We illustrate how these findings can be applied to the design of a rolling Malaria Indicator Survey that forms part of an ongoing large-scale, 5-year malaria transmission reduction project in Malawi

Modeling of spatio-temporal variation in plague incidence in Madagascar from 1980 to 2007

Plague is an infectious disease caused by the bacterium Yersinia pestis, which, during the fourteenth century, caused the deaths of an estimated 75–200 million people in Europe. Plague epidemics still occur in Africa, Asia and South America. Madagascar is today one of the most endemic countries, reporting nearly one third of the human cases worldwide from 2004 to 2009. The persistence of plague in Madagascar is associated with environmental and climatic conditions. In this paper we present a case study of the spatio-temporal analysis of plague incidence in Madagascar from 1980 to 2007. We study the relationship of plague with temperature and precipitation anomalies, and with elevation. A joint spatio-temporal analysis of the data proves to be computationally intractable. We therefore develop a spatio-temporal log-Gaussian Cox process model, but then carry out marginal temporal and spatial analyses. We also introduce a spatially discrete approximation for Gaussian processes, whose parameters retain a spatially continuous interpretation. We find evidence of a cumulative effect, over time, of temperature anomalies on plague incidence, and of a very high relative risk of plague occurrence for locations above 800 m in elevation. Our approach provides a useful modeling framework to assess the relationship between exposures and plague risk, irrespective of the spatial resolution at which the latter has been recorded