Benjamin M. Taylor

Spatial and spatio-temporal log-gaussian cox processes: Extending the geostatistical paradigm

In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based inference. We then demonstrate the usefulness of the LGCP by describing four applications: estimating the intensity surface of a spatial point process; investigating spatial segregation in a multi-type process; constructing spatially continuous maps of disease risk from spatially discrete data; and real-time health surveillance. We argue that problems of this kind fit naturally into the realm of geostatistics, which traditionally is defined as the study of spatially continuous processes using spatially discrete observations at a finite number of locations. We suggest that a more useful definition of geostatistics is by the class of scientific problems that it addresses, rather than by particular models or data formats.

INLA or MCMC? A tutorial and comparative evaluation for spatial prediction in log-Gaussian Cox processes

We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We first describe the device of approximating a spatially continuous Gaussian field by a Gaussian Markov random field on a discrete lattice, and present a simulation study showing that, with careful choice of parameter values, small neighbourhood sizes can give excellent approximations. We then introduce the spatial log-Gaussian Cox process and describe MCMC and INLA methods for spatial prediction within this model class. We report the results of a simulation study in which we compare the Metropolis-adjusted Langevin Algorithm (MALA) and the technique of approximating the continuous latent field by a discrete one, followed by approximate Bayesian inference via INLA over a selection of 18 simulated scenarios. The results question the notion that the latter technique is both significantly faster and more robust than MCMC in this setting; 100,000 iterations of the MALA algorithm running in 20 min on a desktop PC delivered greater predictive accuracy than the default INLA strategy, which ran in 4 min and gave comparative performance to the full Laplace approximation which ran in 39 min.

An Adaptive Sequential Monte Carlo Sampler

Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state–space models, but offer an alternative to Markov chain Monte Carlo (MCMC) in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC method that uses adaptive MCMC kernels for particle dynamics. The proposed algorithm features an online stochastic optimization procedure to select the best MCMC kernel and simultaneously learn optimal tuning parameters. Theoretical results are presented that justify the approach and give guidance on how it should be implemented. Empirical results, based on analysing data from mixture models, show that the new adaptive SMC algorithm (ASMC) can both choose the best MCMC kernel, and learn an appropriate scaling for it. ASMC with a choice between kernels outperformed the adaptive MCMC algorithm of Haario et al. (1998) in 5 out of the 6 cases considered.

Mapping English GP prescribing data: a tool for monitoring health-service inequalities

Objective The aim of this paper was to show that easily interpretable maps of local and national prescribing data, available from open sources, can be used to demonstrate meaningful variations in prescribing performance. Design The prescription dispensing data from the National Health Service (NHS) Information Centre for the medications metformin hydrochloride and methylphenidate were compared with reported incidence data for the conditions, diabetes and attention deficit hyperactivity disorder, respectively. The incidence data were obtained from the open source general practitioner (GP) Quality and Outcomes Framework. These data were mapped using the Ordnance Survey CodePoint Open data and the data tables stored in a PostGIS spatial database. Continuous maps of spending per person in England were then computed by using a smoothing algorithm and areas whose local spending is substantially (at least fourfold) and significantly (p<0.05) higher than the national average are then highlighted on the maps. Setting NHS data with analysis of primary care prescribing. Population England, UK. Results The spatial mapping demonstrates that several areas in England have substantially and significantly higher spending per person on metformin and methyphenidate. North Kent and the Wirral have substantially and significantly higher spending per child on methyphenidate. Conclusions It is possible, using open source data, to use statistical methods to distinguish chance fluctuations in prescribing from genuine differences in prescribing rates. The results can be interactively mapped at a fine spatial resolution down to individual GP practices in England. This process could be automated and reported in real time. This can inform decision-making and could enable earlier detection of emergent phenomena.

Calculating Strength of Schedule, and Choosing Teams for March Madness

We propose a new way of quantifying a team’s strength of schedule for NCAA basketball. This strength of a schedule is defined as the number of games a team on the borderline of the annual national tournament would expect to win if they played that schedule. Our method gives a direct way of quantifying how well different teams have done relative to the schedules they have played. The motivation for constructing this strength of schedule is to help inform the choice of teams given bids to the national tournament: teams who have won more games than their strength of schedule have strongest evidence that they deserve such a bid. Estimating the strength of schedules is possible through fitting a simple statistical model to the results of all regular season matches. We are able to quantify the uncertainty in these estimates, which helps differentiate between teams with clear evidence for selection and those on the borderline. Our results suggest that St. Mary’s warranted a bid to the 2009 tournament, at the expense of Wisconsin; and that both Arizona State and Nebraska warranted bids to the 2008 tournament instead of South Alabama and St. Joseph’s. Supplementary material is available online.

spatsurv: An R Package for Bayesian Inference with Spatial Survival Models

Survival methods are used for the statistical modelling of time-to-event data. Survival data are characterized by a set of complete records, in which the time of the event is known; and a set of censored records, in which the event was known to have occurred in an interval. When survival data are spatially referenced, the spatial variation in survival times may be of scientific interest. In this article, we introduce a new R package, spatsurv, for inference with spatially referenced survival data. The specific type of model fitted by this package is a parametric proportional hazards model in which the spatially correlated frailties are modelled by a log-Gaussian stochastic process. The package is extensible in that it allows the user to easily create new models for the baseline hazard function and spatial covariance function. The package implements an advanced adaptive Markov chain Monte Carlo algorithm to deliver Bayesian inference with minimal input from the user. A particular feature of the new package is the ability to handle large datasets via the use of auxiliary frailties on a regular grid and the technique of circulant embedding for fast matrix computations. We demonstrate the new package on a real-life dataset.

Who are the patients that default tuberculosis treatment? - space matters!

The goals of this article are: (i) to understand how individual characteristics affect the likelihood of patients defaulting their pulmonary tuberculosis (PTB) treatment regimens; (ii) to quantify the predictive capacity of these risk factors; and (iii) to quantify and map spatial variation in the risk of defaulting. We used logistic regression models and generalized additive models with a spatial component to determine the odds of default across continental Portugal. We focused on new PTB cases, diagnosed between 2000 and 2013, and included some individual information (sex, age, residence area, alcohol abuse, intravenous drug use, homelessness, HIV, imprisonment status). We found that the global default rate was 4·88%, higher in individuals with well-known risk profiles (males, immigrants, HIV positive, homeless, prisoners, alcohol and drug users). Of specific epidemiological interest was that our geographical analysis found that Portugals main urban areas (the two biggest cities) and one tourist region have higher default rates compared to the rest of the country, after adjusting for the previously mentioneded risk factors. The challenge of treatment defaulting, either due to other individual non-measured characteristics, healthcare system failure or patient recalcitrance requires further analysis in the spatio-temporal domain. Our findings suggest the presence of significant within-country variation in the risk of defaulting that cannot be explained by these classical individual risk factors alone. The methods we advocate are simple to implement and could easily be applied to other diseases.

Modelling the time to detection of urban tuberculosis in two big cities in Portugal : a spatial survival analysis

SETTING Portuguese National Tuberculosis Control Programme. OBJECTIVE To examine delays in tuberculosis (TB) diagnosis using a spatial component in two high-incidence cities, Lisbon and Oporto, in Portugal, a low-incidence country. DESIGN A retrospective nationwide study was conducted based on official TB data between 2010 and 2013 to analyse diagnostic delays at the lowest administrative level (freguesias) using spatial survival analyses, taking into account individual level covariates. RESULTS Median diagnostic delays in Lisbon (n = 2706 cases) and Oporto (n = 1883) were respectively 62 (range 1-359, mean 81.01) and 60 days (range 1-3544, mean 79.5). In both cities, case detection rates initially rose until 50 days, then stabilised, but rose again at about 200 days. Diagnostic delay was significantly shorter among males and human immunodeficiency virus positive individuals in both cities, but was significantly longer among migrants in Lisbon. There is evidence of spatial correlation between freguesias; different spatial patterns were observed in diagnostic delays and in likelihood of case detection. CONCLUSION These results are concordant with existing literature. The two study areas present considerable spatial variations in diagnostic delay, highlighting the fact that large cities should not be treated as homogeneous entities. The potential of spatial survival methods in spatial epidemiology is highlighted.

Modelling and forecasting spatio-temporal variation in the risk of chronic malnutrition among under-five children in Ghana

BACKGROUND Spatio-temporal variation in under-5-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 1516 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 mothers 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.

Differences in survival among adults with HIV-associated Kaposi's sarcoma during routine HIV treatment initiation in Zomba district, Malawi: a retrospective cohort analysis

Background The HIV epidemic is a major public health concern throughout Africa. Malawi is one of the worst affected countries in sub-Saharan Africa with a 2014 national HIV prevalence currently estimated at 10% (9.3-10.8%) by UNAIDS. Study reports, largely in the African setting comparing outcomes in HIV patients with and without Kaposis sarcoma (KS) indicate poor prognosis and poor health outcomes amongst HIV+KS patients. Understanding the mortality risk in this patient group could help improve patient management and care. Methods Using data for the 559 adult HIV+KS patients who started ART between 2004 and September 2011 at Zomba clinic in Malawi, we estimated relative hazard ratios for all-cause mortality by controlling for age, sex, TB status, occupation, date of starting treatment and distance to the HIV+KS clinic. Results Patients with tuberculosis (95% CI: 1.05-4.65) and patients who started ART before 2008 (95% CI: 0.34-0.81) were at significantly greater risk of dying. A random-effects Cox model with Log-Gaussian frailties adequately described the variation in the hazard for mortality. Conclusion The year of starting ART and TB status significantly affected survival among HIV+KS patients. A sub-population analysis of this kind can inform an efficient triage system for managing vulnerable patients.