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An Additive Linear Mixed-effects Model (ALMM) with Kernel Smoothers and a Permutation Test on Temporal Heterogeneity of Geospatial Risk Patterns (307917)
*Yannan Tang, University of California, IrvinePublic health researchers often aim to quantify geospatial heterogeneity (spatial effects) in disease occurrence to identify potential health disparities, which are essential for policy makers. In these studies, spatial information is becoming increasingly available at the individual-level. Classic generalized additive models (GAMs) provide a framework for smoothing risk estimates over space while adjusting for confounding factors. As longitudinal studies that track disease indicators of individuals over time are becoming more prevalent, Wood (2017) describes a class of generalized additive mixed models (GAMMs) which incorporate individual-specific random effects into GAMs with spline smoothers. However, to our best knowledge, current GAMMs do not incorporate kernel smoothers. Given the fact that in various situations, kernel smoothers, locally estimated scatterplot smoothing (LOESS) in particular, are preferred by epidemiology researchers (Webster et al (2006) as an example) partly due to their robust estimation of spatial effects on irregular shaped maps. In this study, we propose a class of additive linear mixed-effects models (ALMMs) by incorporating kernel smoothers into additive model framework for continuous response. To fit ALMMs, we provide a backfitting procedure with within-cluster correlation adjustment. Furthermore, a modified permutation test for our ALMMs is developed to detect potential changes in spatial effects over time. Through simulation studies, we illustrate the advantage of ALMMs in spatial effects estimation when there are unbalanced clusters or random slopes. Our empirical results further suggest that the modified permutation test procedure yields relatively high power for detecting temporal heterogeneity in spatial effects under controlled type I error. Finally, we apply our ALMMs method on post-public-water-filtration serum perfluorooctanoic acid (PFOA) concentration data among residents in certain parts of West Virginia and Ohio, demonstrating the behavior of spatial effects on serum PFOA concentration after the filtration.