Proxy small thick subcategories of derived categories

Let R be a commutative noetherian ring. Denote by $D^b\left(R\right)$ the bounded derived category of finitely generated R-modules. Extending the notion of a proxy small object of $D^b\left(R\right)$ in the sense of Dwyer, Greenlees, Iyengar and Pollitz, we introduce the notion of a proxy small thick subcategory of $D^b\left(R\right)$. When R is a locally dominant ring, we give a complete classification of the proxy small thick subcategories of $D^b\left(R\right)$ in terms of pairs of specialization-closed subsets of Spec R and Sing R.