  Covariate-adjusted randomization (CAR) can reduce the risk of covariate
imbalance and, when accounted for in analysis, increase the power of a trial.
Despite CAR advances, stratified randomization remains the most common CAR
method. Matched Randomization (MR) randomizes treatment assignment within
optimally identified matched pairs based on covariates and a distance matrix.
When participants enroll sequentially, Sequentially Matched Randomization (SMR)
randomizes within matches found "on-the-fly" to meet a pre-specified matching
threshold. However, pre-specifying the ideal threshold can be challenging and
SMR yields less-optimal matches than MR. We extend SMR to allow multiple
participants to be randomized simultaneously, to use a dynamic threshold, and
to allow matches to break and rematch if a better match later enrolls
(Sequential Rematched Randomization; SRR). In simplified settings and a
real-world application, we assess whether these extensions improve covariate
balance, estimator/study efficiency, and optimality of matches. We investigate
whether adjusting for more covariates can be detrimental upon covariate balance
and efficiency as is the case of traditional stratified randomization. As
secondary objectives, we use the case study to assess how SMR schemes compare
side-by-side with common and related CAR schemes and whether adjusting for
covariates in the design can be as powerful as adjusting for covariates in a
parametric model. We find each SMR extension, individually and collectively, to
improve covariate balance, estimator efficiency, study power, and quality of
matches. We provide a case-study where CAR schemes with randomization-based
inference can be as and more powerful than Non-CAR schemes with parametric
adjustment for covariates.
