Continuous Inference for Aggregated Point Process Data

Abstract

Summary The paper introduces new methods for inference with count data registered on a set of aggregation units. Such data are omnipresent in epidemiology because of confidentiality issues: it is much more common to know the county in which an individual resides, say, than to know their exact location in space. Inference for aggregated data has traditionally made use of models for discrete spatial variation, e.g. conditional auto‐regressive models. We argue that such discrete models can be improved from both a scientific and an inferential perspective by using spatiotemporally continuous models to model the aggregated counts directly. We introduce methods for delivering (limiting) continuous inference with spatiotemporal aggregated count data in which the aggregation units might change over time and are subject to uncertainty. We illustrate our methods by using two examples: from epidemiology, spatial prediction of malaria incidence in Namibia, and, from politics, forecasting voting under the proposed changes to parliamentary boundaries in the UK.

Using the intrinsic growth rate of the mosquito population improves spatio-temporal dengue risk estimation

“…We evaluated if any spatio-temporal association exists between the incidence of dengue cases and the mosquito intrinsic growth rate and abundance. To model dengue cases at the pixel level across our study region we assumed that the locations of the cases follow a spatiotemporal log-Gaussian Cox process ( Taylor et al., 2018 ; Taylor 2019 ). This model assumes the number of cases, Y( s; t ) follows a Poisson distribution: where P ( s; t ) is a known component of the intensity function (the 2010 number of people per grid-cell from WORLDPOP project ( Tatem 2017 ), which is provided at a resolution of 3 ′onds, meaning approximately 100 m), X ( s; t ) is a vector of covariates (mosquito abundance and/or IGR), β is a vector of parameter effects to be estimated and G is a spatiotemporal Gaussian process where covariance is modelled as in Eq.…”

“…Secondly, we evaluated whether the intrinsic growth rate is significantly associated with dengue spatio-temporal incidence and how it compares with a mosquito abundance model and a null model (intercept+spatio-temporal random effect). This section of the analysis is based on a spatio-temporal log-Gaussian Cox model ( Taylor et al., 2018 ).…”

Model ensembles with different response variables for base and meta models: malaria disaggregation regression combining prevalence and incidence data

“…These predictions were finally inverse logit transformed so that they are on the linear predictor scale of the top level model. The top level model was a disaggregation regression model (Sturrock et al, 2014;Wilson and Wakefield, 2017;Law et al, 2018;Taylor et al, 2017;Li et al, 2012). This model is defined by a likelihood at the level of the polygon with covariates and a spatial random field at the pixel-level.…”

“…High-resolution maps of malaria risk are vital for elimination but mapping malaria in low burden countries presents new challenges as traditional mapping of prevalence from cluster-level surveys (Gething et al, 2011;Bhatt et al, 2017;Gething et al, 2012;Bhatt et al, 2015) is often not effective because, firstly, so few individuals are infected that most surveys will detect zero cases, and secondly, because of the lack of nationally representative prevalence surveys in low burden countries (Sturrock et al, 2016(Sturrock et al, , 2014. Routine surveillance data of malaria case counts, often aggregated over administrative regions defined by geographic polygons, is becoming more reliable and more widely available (Sturrock et al, 2016) and recent work has focussed on methods for estimating high-resolution malaria risk from these data (Sturrock et al, 2014;Wilson and Wakefield, 2017;Law et al, 2018;Taylor et al, 2017;Li et al, 2012). However, the aggregation of cases over space means that the data may be relatively uninformative, especially if the case counts are aggregated over large or heterogeneous areas, because it is unclear where within the polygon, and in which environments, the cases occurred.…”

Mapping malaria by sharing spatial information between incidence and prevalence datasets

“…Disaggregation regression methods have been proposed as a way to model malaria burden using polygon-level, routine surveillance records of incidence (Sturrock et al, 2014; Wilson and Wakefield, 2018; Law et al, 2018; Taylor et al, 2017; Li et al, 2012; Johnson et al, 2019). Disaggregation regression requires an aggregation step in which the high-resolution estimates of disease incidence are summed to match the level of the administitive unit at which the incidence data are observed.…”