Randomization of Intervention-control Pairs

 

Menu location: Analysis_Randomization_Intervention-control Pairs

 

This function provides random allocation into intervention or control arms of a trial for a paired/matched experimental design. Each subject will experience both intervention and control treatment at some stage during the trial, the paired randomization determines the treatment order.

 

Randomization reduces opportunities for bias and confounding in experimental designs, and leads to treatment groups which are random samples of the population sampled, thus helping to meet assumptions of subsequent statistical analysis (Bland, 2000). A particular bias in this design might be intervention having some carry-over effect on control treatment.

 

Example: randomization of 50 patients into treatment (intervention) and placebo (control) arms of a trial of a new drug. This would give 50 pairs of INTERVENTION - CONTROL or CONTROL - INTERVENTION. If this was a randomized crossover study then you would give drug first if the order was INTERVENTION - CONTROL and you would give placebo first if the order was CONTROL - INTERVENTION.

 

To reproduce this allocation in StatsDirect select Intervention-control Pairs from the Randomization section of the Analysis menu, enter 50 as the number of pairs, enter 10 as the seed and answer yes to 'Try balanced allocation'. A seed gives the same allocation each time it is used; leave it blank for a seed taken from the clock. Balanced allocation gives each order to exactly half of the pairs, in a random arrangement, and needs an even number of pairs; without it (or with an odd number of pairs) each pair's order is decided independently with an equal chance of either, and the report's heading then shows the seed alone.

 

For this example:

 

Randomized intervention-control pairs

Randomized with seed: 10, balanced allocation

1 Intervention - Control
2 Intervention - Control
3 Control - Intervention
4 Intervention - Control
5 Control - Intervention
6 Intervention - Control
7 Control - Intervention
8 Control - Intervention
9 Intervention - Control
10 Intervention - Control
11 Intervention - Control
12 Control - Intervention
13 Intervention - Control
14 Intervention - Control
15 Control - Intervention
16 Control - Intervention
17 Control - Intervention
18 Control - Intervention
19 Intervention - Control
20 Control - Intervention
21 Control - Intervention
22 Intervention - Control
23 Intervention - Control
24 Control - Intervention
25 Intervention - Control
26 Intervention - Control
27 Control - Intervention
28 Control - Intervention
29 Control - Intervention
30 Intervention - Control
31 Control - Intervention
32 Control - Intervention
33 Intervention - Control
34 Intervention - Control
35 Intervention - Control
36 Intervention - Control
37 Control - Intervention
38 Intervention - Control
39 Intervention - Control
40 Control - Intervention
41 Control - Intervention
42 Control - Intervention
43 Intervention - Control
44 Control - Intervention
45 Intervention - Control
46 Intervention - Control
47 Intervention - Control
48 Control - Intervention
49 Control - Intervention
50 Control - Intervention

 

Technical validation

Robust (pseudo-)random number generation is used, see random number generation.

This R code reproduces the illustration above with R's own random number generator, so the same seed gives a different arrangement of the pairs. It needs no packages and was checked with R 4.6.1. Paste it into R, or save it as a script and run it.

# Randomization of intervention-control pairs: the StatsDirect help example (50
# patients, each given both treatments, allocated to the order intervention then
# control or control then intervention, seed 10, balanced allocation) in R
pairs <- 50
seed <- 10
orders <- c("Intervention - Control", "Control - Intervention")

# StatsDirect and R each have their own random number generator, so the same seed
# gives a different sequence in each program: this script repeats its own
# allocation every time it is run, but it does not repeat the table above.
# Balanced allocation gives each order to exactly half of the pairs (so the
# number of pairs must be even) in a random arrangement: sample() without
# replacement returns the 25 copies of each order in a random permutation.
set.seed(seed)
balanced <- sample(rep(orders, pairs / 2))
cat("Randomized intervention-control pairs\n")
cat(paste0("Randomized with seed: ", seed, ", balanced allocation"), "\n")
print(data.frame(pair = seq_len(pairs), order = balanced), row.names = FALSE)
cat("Pairs allocated Intervention - Control =", sum(balanced == orders[1]), "\n")
cat("Pairs allocated Control - Intervention =", sum(balanced == orders[2]), "\n")

# Every arrangement of 25 of each order is equally likely: there are choose(50, 25)
cat("Equally likely balanced arrangements =",
    formatC(choose(pairs, pairs / 2), format = "f", digits = 0), "\n")

# Without balancing, each pair's order is decided independently, like a coin
# toss, so the two orders need not be equally frequent (with this seed they happen
# to be): sample() with replacement
set.seed(seed)
tossed <- sample(orders, pairs, replace = TRUE)
cat("Unbalanced: Intervention - Control =", sum(tossed == orders[1]),
    "  Control - Intervention =", sum(tossed == orders[2]), "\n")