  Weighting estimators based on propensity scores are widely used for causal
estimation in a variety of contexts, such as observational studies, marginal
structural models and interference. They enjoy appealing theoretical properties
such as consistency and possible efficiency under correct model specification.
However, this theoretical appeal may be diminished in practice by sensitivity
to misspecification of the propensity score model. To improve on this, we
borrow an idea from an alternative approach to causal effect estimation in
observational studies, namely subclassification estimators. It is well known
that compared to weighting estimators, subclassification methods are usually
more robust to model misspecification. In this paper, we first discuss an
intrinsic connection between the seemingly unrelated weighting and
subclassification estimators, and then use this connection to construct robust
propensity score weights via subclassification. We illustrate this idea by
proposing so-called full-classification weights and accompanying estimators for
causal effect estimation in observational studies. Our novel estimators are
both consistent and robust to model misspecification, thereby combining the
strengths of traditional weighting and subclassification estimators for causal
effect estimation from observational studies. Numerical studies show that the
proposed estimators perform favorably compared to existing methods.
