Sandwich Mixed Randomization for Allocation Sequence Generation

Generates allocation sequences for randomized controlled trials using the sandwich mixed randomization (SMR) scheme, together with verification, diagnostics, and release utilities.

sandwichrand

Allocation sequences by Sandwich Mixed Randomization (SMR) for randomized controlled trials.

sandwichrand generates treatment allocation sequences (randomization lists) with the Sandwich Mixed Randomization scheme described in Wang et al. (2026), BMC Medical Research Methodology 26(1), 152, doi:10.1186/s12874-026-02877-2.

The sandwich

An SMR sequence is a sandwich:

|<--- n1 --->|<-------- N - 2*n1 -------->|<--- n1 --->|
+------------+----------------------------+------------+
| block 1    | blocks 2 .. K              | block K+1  |
| imbalanced | permuted blocks of         | complement |
|            | varying sizes              | of block 1 |
+------------+----------------------------+------------+

The head block (size n1) is deliberately imbalanced: it is drawn by repeated complete randomization until its imbalance (the spread of the deviations from the target allocation) lies in [1, 4]. n1 is sampled at random from the admissible multiples of ratio_sum, so there is no need to pre-specify it.
The middle is filled with permuted blocks of varying sizes (the PBVB procedure).
The tail block (size n1) is the exact complement of the head block, so overall balance is guaranteed while the next allocation stays unpredictable.

Installation

# from the source tarball
install.packages("sandwichrand_1.0.0.tar.gz", repos = NULL, type = "source")

Quick start

library(sandwichrand)

## Two-arm 1:1 trial, N = 48 -- the illustration of the SMR paper
x <- smr_alloc(N = 48, arms = c("TestTrt", "Placebo"), seed = 84529052)
x
head(x$alloc)
x$balance

## Three-arm 2:2:1 trial, N = 150, released without the block structure
y <- smr_alloc(N = 150, arms = c("A", "A", "B", "B", "C"), seed = 123456,
               keep.blocks = FALSE)
smr_balance(y)

## Independent streams for high-frequency calling (simulation loops)
ss <- smr_streams(seed = 42, n = 3)
a <- smr_alloc(N = 48, arms = c("A", "B"), stream = ss[[1]])
b <- smr_alloc(N = 48, arms = c("A", "B"), stream = ss[[2]])

## Verify, document and release
smr_verify(x)
smr_write_csv(x, file = "randomization.csv")
smr_rtf(x, file = "randomization.rtf")

Evaluating the design

A randomization procedure is assessed on two performance metrics (Wang et al. 2026):

Allocation balance — the absolute imbalance E|D(i)|, D(i) = n_A(i) - n_B(i):

smr_balance(x)            # final arm counts and deviations
smr_imbalance(x)          # running |D(i)| at every allocation step

Allocation unpredictability — the Blackwell–Hodges proportion of correct guesses (PCG). Under the convergence strategy the next assignment is predicted to go to the arm with the fewer prior allocations (0.5 on ties):
```
smr_correct_guesses(x)    # per-step correct-guess indicators
smr_pcg(x)                # proportion of correct guesses (0.5 = CRD)
```

Both are summarised across replications by smr_simulate():

smr_simulate(N = 48, arms = c("A", "B"), reps = 1000, seed = 11)
# final imbalance (balance) and correct-guess PCG (unpredictability)

Design highlights

Random head-block size. n1 is always sampled at random, so the block structure is not revealed in advance and there is no n1 argument to specify.
Spread-based imbalance. The imbalance is the spread max_g(count_g - n*mult_g/ratio_sum) - min_g(...), which equals the between-group count difference for 1:1 and is zero for an exactly proportional block.
Independent streams. Each call draws from an independent L'Ecuyer-CMRG sub-stream; smr_streams() derives a family of non-overlapping streams up front so high-frequency loops never reuse the same random numbers.
Reproducible. Every sequence is a deterministic function of a single seed (or of a supplied stream); smr_reproduce() regenerates it.
ICH E9 / GCP aware. keep.blocks = FALSE releases a list without any block information, while the statistician's copy stays in $blocks.

Documentation

The package vignette (vignette("sandwichrand")) follows the structure recommended for a Journal of Statistical Software contribution: motivation → methods → implementation → usage → validation → reproducibility → computational details → summary.

Clinical use and validation disclaimer

sandwichrand is research software provided "AS IS", without warranty of any kind, express or implied. It has not been validated as a computerised system under Good Clinical Practice (GCP), Good Clinical/Manufacturing Practice (GxP), 21 CFR Part 11, EU GMP Annex 11, or any other regulatory framework.

Before using sandwichrand to generate allocation sequences for a registration trial, or for any trial whose results may support a regulatory submission, the sponsor is solely responsible for:

independently validating the software and the generated sequences under its own quality system;
maintaining allocation concealment (ICH E9), including keeping the seed, the block structure and any stream information confidential; and
ensuring compliance with all applicable regulations.

The authors accept no liability for any consequences arising from the use of this software.