  Understanding longitudinally changing associations between Social
determinants of health (SDOH) and stroke mortality is crucial for timely stroke
management. Previous studies have revealed a significant regional disparity in
the SDOH -- stroke mortality associations. However, they do not develop
data-driven methods based on these longitudinal associations for regional
division in stroke control. To fill this gap, we propose a novel clustering
method for SDOH -- stroke mortality associations in the US counties. To enhance
interpretability and statistical efficiency of the clustering outcomes, we
introduce a new class of smoothness-sparsity pursued penalties for simultaneous
clustering and variable selection in the longitudinal associations. As a
result, we can identify important SDOH that contribute to longitudinal changes
in the stroke mortality, facilitating clustering of US counties into several
regions based on how these SDOH relate to stroke mortality. The effectiveness
of our proposed method is demonstrated through extensive numerical studies. By
applying our method to a county-level SDOH and stroke mortality longitudinal
data, we identify 18 important SDOH for stroke mortality and divide the US
counties into two clusters based on these selected SDOH. Our findings unveil
complex regional heterogeneity in the longitudinal associations between SDOH
and stroke mortality, providing valuable insights in region-specific SDOH
adjustments for mitigating stroke mortality.
