Simple Random Assignment

simple_ra assigns units to treatment conditions independently, with each unit's assignment drawn as a separate Bernoulli trial. Because units are assigned independently, the number of units assigned to each condition varies from draw to draw. For most experimental applications in which the number of units is known in advance, complete_ra() is preferable because it fixes the counts in each condition and thereby reduces sampling variability.

Usage

simple_ra(
  N,
  prob = NULL,
  prob_unit = NULL,
  prob_each = NULL,
  num_arms = NULL,
  conditions = NULL,
  check_inputs = TRUE,
  simple = TRUE
)

Arguments

N

The number of units. Must be a positive integer. (required)

prob

Use for a two-arm design. The probability of assignment to treatment; must be a real number between 0 and 1 and of length 1. (optional)

prob_unit

Use for a two-arm design. The probability of assignment to treatment for each unit; must be a real number between 0 and 1 and of length N. (optional)

prob_each

Use for a multi-arm design. A numeric vector or N-by-conditions matrix giving the probability of assignment to each condition; entries must be nonnegative and sum to 1. (optional)

num_arms

The number of treatment arms. If unspecified, determined from the other arguments. (optional)

conditions

A character vector giving the names of the treatment groups. If unspecified, groups will be named 0 and 1 in a two-arm trial and T1, T2, T3, in a multi-arm trial. A two-group design in which num_arms is set to 2 will use condition names T1 and T2. (optional)

check_inputs

Logical. Whether to verify before assigning that the arguments are internally consistent: that probabilities lie between 0 and 1 and sum to 1, that vectors are of length N, that only one of prob, prob_unit, and prob_each is supplied, and so on. Defaults to TRUE. FALSE skips the checking only: num_arms and conditions are still derived from the other arguments, so the same call draws the same assignment either way. What goes is the verification, and an impossible design is then no longer refused. block_m larger than a block, for instance, quietly treats the whole block. Declaring the design once with declare_ra() and drawing from it with conduct_ra() is the usual way to avoid re-checking the same arguments in a simulation. (optional)

simple

Logical. Internal use only; leave at its default. simple_ra always assigns units independently, and this argument exists so that the argument checker knows as much. Setting it to FALSE does not change how units are assigned, but it will cause a prob_unit that varies across units to be rejected. (optional)

Value

A vector of length N indicating the treatment condition of each unit. Numeric in a two-arm trial; a factor (ordered by conditions) in a multi-arm trial.

Details

Simple random assignment is appropriate when units arrive sequentially and the total sample size is not known in advance, or when the assignment must proceed without coordinating across units. If only N is specified, a two-arm trial with prob = 0.5 is assumed.

See also

complete_ra(), block_ra(), simple_rs(), simple_ra_probabilities()

Examples

# Two Group Designs

Z <- simple_ra(N = 100)
table(Z)
#> Z
#>  0  1 
#> 52 48 

Z <- simple_ra(N = 100, prob = 0.5)
table(Z)
#> Z
#>  0  1 
#> 56 44 

Z <- simple_ra(N = 100, prob_each = c(0.3, 0.7),
               conditions = c("control", "treatment"))
table(Z)
#> Z
#>   control treatment 
#>        26        74 

# A probability of assignment that varies unit by unit
Z <- simple_ra(N = 100, prob_unit = seq(0.1, 0.9, length.out = 100))
table(Z)
#> Z
#>  0  1 
#> 52 48 

# Skipping the input checks. The checks are also what fill in defaults, so
# conditions has to be given explicitly once they are skipped. In a
# simulation, declare_ra() and conduct_ra() are the tidier way to check the
# arguments once and then draw many assignments from them.
Z <- simple_ra(N = 100, prob = 0.3, conditions = c(0, 1), check_inputs = FALSE)
table(Z)
#> Z
#>  0  1 
#> 72 28 

# Multi-arm Designs
Z <- simple_ra(N = 100, num_arms = 3)
table(Z)
#> Z
#> T1 T2 T3 
#> 27 32 41 

Z <- simple_ra(N = 100, prob_each = c(0.3, 0.3, 0.4))
table(Z)
#> Z
#> T1 T2 T3 
#> 32 30 38 

Z <- simple_ra(N = 100, prob_each = c(0.3, 0.3, 0.4),
               conditions = c("control", "placebo", "treatment"))
table(Z)
#> Z
#>   control   placebo treatment 
#>        33        36        31 

Z <- simple_ra(N = 100, conditions = c("control", "placebo", "treatment"))
table(Z)
#> Z
#>   control   placebo treatment 
#>        30        41        29