Reducing selection bias risk to enhance RCT validity: sandwich mixed randomization outperforms permuted block design

Random allocation is essential in randomized controlled trials (RCTs) to ensure impartial treatment allocation and minimize selection bias. Despite permuted block design (PBD) is used in approximately 75% of RCTs, it has long been criticized for its predictable allocation sequences-due to periodic rebalancing of group sizes-which compromises allocation concealment and undermines randomization integrity. Although numerous proposed alternatives, few have achieved widespread adoption. There remains a pressing need for a simple, intuitive, and universally applicable alternative to PBD that preserves its treatment balance and operational simplicity while dramatically improving allocation unpredictability.

We propose a novel approach-Sandwich Mixed Randomization (SMR)-a conceptually simple and operationally feasible method that integrates complete randomization with PBD within a "sandwich" framework to enhance allocation unpredictability while preserving group size balance. Using Monte Carlo simulations of 1:1 two-arm open-label RCTs under strict allocation concealment (per Good Clinical Practice), we evaluated SMR across small (n = 48), medium (n = 240), and large (n = 1,200) trials. SMR was compared with fixed- and variable-sized PBD using the well-established metrics: treatment imbalance (absolute group size difference), allocation predictability (proportion of correct guesses), and a newly introduced metric-the relative excess risk of selection bias-benchmarked against the ideal performance of complete randomization.

While PBD ensures perfect treatment balance, it exhibits high allocation predictability. Under pre-randomization guessing during enrollment, correct guess proportions reached 70.83% for fixed block size 4 and exceeded 68% for variable block sizes (4, 6, 8) and fixed size 6-far above the 50% benchmark of complete randomization. In contrast, SMR maintains balanced group sizes while reducing correct guess proportions to ~56% in small trials and ~53% in larger ones. Compared to variable-sized PBD, SMR reduces the risk of selection bias by >66% in small trials and >81% in larger ones. Across all sample sizes, the PBD-to-SMR risk ratio for selection bias consistently exceeds 3, underscoring the substantial bias risk associated with conventional PBD.

The inherent predictability of PBD, regardless of fixed or variable block size, significantly increases the risk of selection bias, warranting caution in interpreting results from PBD-based trials. SMR substantially reduces this risk and offers a universally applicable, low-effort alternative to PBD across all RCT settings, including open-label, single-blinded, and multi-center designs. Its benefits remain meaningful even in double-blind RCTs with imperfect masking. Transitioning from conventional PBD to SMR enhances randomization integrity, strengthens internal validity, and reinforces the RCT as the gold standard for generating reliable, unbiased clinical evidence.