  Randomization, as a key technique in clinical trials, can eliminate sources
of bias and produce comparable treatment groups. In randomized experiments, the
treatment effect is a parameter of general interest. Researchers have explored
the validity of using linear models to estimate the treatment effect and
perform covariate adjustment and thus improve the estimation efficiency.
However, the relationship between covariates and outcomes is not necessarily
linear, and is often intricate. Advances in statistical theory and related
computer technology allow us to use nonparametric and machine learning methods
to better estimate the relationship between covariates and outcomes and thus
obtain further efficiency gains. However, theoretical studies on how to draw
valid inferences when using nonparametric and machine learning methods under
stratified randomization are yet to be conducted. In this paper, we discuss a
unified framework for covariate adjustment and corresponding statistical
inference under stratified randomization and present a detailed proof of the
validity of using local linear kernel-weighted least squares regression for
covariate adjustment in treatment effect estimators as a special case. In the
case of high-dimensional data, we additionally propose an algorithm for
statistical inference using machine learning methods under stratified
randomization, which makes use of sample splitting to alleviate the
requirements on the asymptotic properties of machine learning methods. Finally,
we compare the performances of treatment effect estimators using different
machine learning methods by considering various data generation scenarios, to
guide practical research.
