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

 

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")