Multilevel modeling of spatially nested functional data: Spatiotemporal patterns of hospitalization rates in the US dialysis population

Abstract

End-stage renal disease patients on dialysis experience frequent hospitalizations. In addition to known temporal patterns of hospitalizations over the life span on dialysis, where poor outcomes are typically exacerbated during the first year on dialysis, variations in hospitalizations among dialysis facilities across the US contribute to spatial variation. Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multilevel spatiotemporal functional model to study spatiotemporal patterns of hospitalization rates among dialysis facilities. Hospitalization rates of dialysis facilities are considered as spatially nested functional data (FD) with longitudinal hospitalizations nested in dialysis facilities and dialysis facilities nested in geographic regions. A multilevel Karhunen-Loéve expansion is utilized to model the two-level (facility and region) FD, where spatial correlations are induced among region-specific principal component scores accounting for regional variation. A new efficient algorithm based on functional principal component analysis and Markov Chain Monte Carlo is proposed for estimation and inference. We report a novel application using USRDS data to characterize spatiotemporal patterns of hospitalization rates for over 400 health service areas across the US and over the posttransition time on dialysis. Finite sample performance of the proposed method is studied through simulations.

Multilevel varying coefficient spatiotemporal model

“…The residuals from this initial fit, denoted by E ij ( t ), capture the remaining spatiotemporal variation in the data after adjusting for the time‐varying effects of multilevel covariates and are used in targeting the between‐ ( G B ( t , t ′ )) and within‐facility covariances ( G W ( t , t ′ )) in Steps 2 and 3. FPCA is employed on the between‐ and within‐facility covariances to target the region‐ and facility‐level eigenfunctions { $$$ {\psi}_{\ell}^{(1)}(t),\ell =1,2,\dots, L $$$} and { $$$ {\psi}_m^{(2)}(t),m=1,2,\dots, M $$$} in Step 4, similar to Li et al (2021). The number of eigenfunctions ( L and M ) included in the decompositions of the region‐ ( U i ( t )) and facility‐specific deviations ( V ij ( t )) are selected by FVE.…”

“…For multilevel functional data that are spatially correlated, spatial correlations have typically been modelled across lower level units that are nested within independent subjects (Baladandayuthapani et al 2008; Hasenstab et al 2017; Staicu et al 2010; Scheffler et al 2020). For multilevel functional data where spatial correlation is at the highest level of the hierarchy (e.g., longitudinal hospitalizations nested in dialysis facilities and facilities nested in spatially correlated geographic regions), Li et al (2021) considered a multilevel spatiotemporal functional model with a focus on drawing valid multilevel inference accounting for spatiotemporal correlations. However, these models do not include potentially time‐varying effects of multilevel covariates.…”

Spatiotemporal factor models for functional data with application to population map forecast

“…The FDA framework for spatiotemporal data has been addressed in several previous studies (Zhang et al, 2023;Li et al, 2021;Wakayama and Sugasawa, 2021;Romano et al, 2011;Giraldo et al, 2011;Jiang and Serban, 2012). However, most of them have taken the approach of using time as the argument of the function and incorporating it into the analysis of spatial function data, ignoring the temporal structure.…”

Geospatial Modeling Methods in Epidemiological Kidney Research: An Overview and Practical Example

“… 2 , 6 , 7 , 8 , 9 , 10 Most existing epidemiological spatial studies of kidney disease, transplantation, and outcomes use descriptive spatial methods, such as disease mapping and cluster analyses with only a handful of studies applying associative methods. 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 Many previous reviews have described in depth the importance of geography and strengths of spatial analysis in epidemiology, and the central concept is that health conditions and outcomes are heavily influenced by where individuals live and/or work. 22 , 23 , 24 Without adjusting for the inherent spatial distribution of the population and risk factors linked to geographic location, traditional (nonspatial) associative modeling becomes biased due to violation of model assumptions, potentially resulting in bias via misrepresentations of coefficient direction and magnitude of effects and underestimation of standard errors.…”