  Subclassification and matching are often used to adjust for observed
covariates in observational studies; however, they are largely restricted to
relatively simple study designs with a binary treatment. One important
exception is Lu et al.(2001), who considered optimal pair matching with a
continuous treatment dose. In this article, we propose two criteria for optimal
subclassification/full matching based on subclass homogeneity with a continuous
treatment dose, and propose an efficient polynomial-time algorithm that is
guaranteed to find an optimal subclassification with respect to one criterion
and serves as a 2-approximation algorithm for the other criterion. We discuss
how to incorporate treatment dose and use appropriate penalties to control the
number of subclasses in the design. Via extensive simulations, we
systematically examine the performance of our proposed method, and demonstrate
that combining our proposed subclassification scheme with regression adjustment
helps reduce model dependence for parametric causal inference with a continuous
treatment dose. We illustrate the new design and how to conduct
randomization-based statistical inference under the new design using Medicare
and Medicaid claims data to study the effect of transesophageal
echocardiography (TEE) during CABG surgery on patients' 30-day mortality rate.
