  Principal stratification is essential for revealing causal mechanisms
involving post-treatment intermediate variables. Principal stratification
analysis with continuous intermediate variables is increasingly common but
challenging due to the infinite principal strata and the nonidentifiability and
nonregularity of principal causal effects. Inspired by recent research, we
resolve these challenges by first using a flexible copula-based principal score
model to identify principal causal effect under weak principal ignorability. We
then target the local functional substitute of principal causal effect, which
is statistically regular and can accurately approximate principal causal effect
with vanishing bandwidth. We simplify the full efficient influence function of
the local functional substitute by considering its oracle-scenario alternative.
This leads to a computationally efficient and straightforward estimator for the
local functional substitute and principal causal effect with vanishing
bandwidth. We prove the double robustness and statistical optimality of our
proposed estimator, and derive its asymptotic normality for inferential
purposes. We illustrate the appealing statistical performance of our proposed
estimator in simulations, and apply it to two real datasets with intriguing
scientific discoveries.
