Clustered spatio-temporal varying coefficient regression model

Assessing and attenuating the impact of selection bias on spatial cluster detection studies

Spatial cluster analyses are commonly used in epidemiologic studies of case-control data to detect whether certain areas in a study region have an excess of disease risk. Case-control studies are susceptible to potential biases including selection bias, which can result from non-participation of eligible subjects in the study. However, there has been no systematic evaluation of the effects of non-participation on the findings of spatial cluster analyses. In this paper, we perform a simulation study assessing the effect of non-participation on spatial cluster analysis using the local spatial scan statistic under a variety of scenarios that vary the location and rates of study non-participation and the presence and intensity of a zone of elevated risk for disease for simulated case-control studies. We find that geographic areas of lower participation among controls than cases can greatly inflate false-positive rates for identification of artificial spatial clusters. Additionally, we find that even modest non-participation outside of a true zone of elevated risk can decrease spatial power to identify the true zone. We propose a spatial algorithm to correct for potentially spatially structured non-participation that compares the spatial distributions of the observed sample and underlying population. We demonstrate its ability to markedly decrease false positive rates in the absence of elevated risk and resist decreasing spatial sensitivity to detect true zones of elevated risk. We apply our method to a case-control study of non-Hodgkin lymphoma. Our findings suggest that greater attention should be paid to the potential effects of non-participation in spatial cluster studies.

Sparse spatially clustered coefficient model via adaptive regularization

Large spatial datasets with many spatial covariates have become ubiquitous in many fields in recent years. A question of interest is to identify which covariates are likely to influence a spatial response, and whether and how the effects of these covariates vary across space, including potential abrupt changes from region to region. To solve this question, a new efficient regularized spatially clustered coefficient (RSCC) regression approach is proposed, which could achieve variable selection and identify latent spatially heterogeneous covariate effects with clustered patterns simultaneously. By carefully designing the regularization term of RSCC as a chain graph guided fusion penalty plus a group lasso penalty, the RSCC model is computationally efficient for large spatial datasets while still achieving the theoretical guarantees for estimation. RSCC also adopts the idea of adaptive learning to allow for adaptive weights and adaptive graphs in its regularization terms and further improves the estimation performance. RSCC is applied to study the acceptance of COVID-19 vaccines using county-level data in the United States and discover the determinants of vaccination acceptance with varying effects across counties, revealing important within-state and across-state spatially clustered patterns of covariates effects.

VPint: value propagation-based spatial interpolation

Given the common problem of missing data in real-world applications from various fields, such as remote sensing, ecology and meteorology, the interpolation of missing spatial and spatio-temporal data can be of tremendous value. Existing methods for spatial interpolation, most notably Gaussian processes and spatial autoregressive models, tend to suffer from (a) a trade-off between modelling local or global spatial interaction, (b) the assumption there is only one possible path between two points, and (c) the assumption of homogeneity of intermediate locations between points. Addressing these issues, we propose a value propagation-based spatial interpolation method called VPint, inspired by Markov reward processes (MRPs), and introduce two variants thereof: (i) a static discount (SD-MRP) and (ii) a data-driven weight prediction (WP-MRP) variant. Both these interpolation variants operate locally, while implicitly accounting for global spatial relationships in the entire system through recursion. We evaluated our proposed methods by comparing the mean absolute error, root mean squared error, peak signal-to-noise ratio and structural similarity of interpolated grid cells to those of 8 common baselines. Our analysis involved detailed experiments on a synthetic and two real-world datasets, as well as experiments on convergence and scalability. Empirical results demonstrate the competitive advantage of VPint on randomly missing data, where it performed better than baselines in terms of mean absolute error and structural similarity, as well as spatially clustered missing data, where it performed best on 2 out of 3 datasets.