Complete Random Assignment

complete_ra assigns exactly fixed numbers of units to each treatment condition. In the canonical two-arm case, exactly m of N units are assigned to treatment and N-m to control on every draw. This guarantee that the counts are fixed is the defining feature of complete random assignment, and it is what distinguishes it from simple random assignment (where counts vary from draw to draw).

Usage

complete_ra(
  N,
  m = NULL,
  m_unit = NULL,
  m_each = NULL,
  prob = NULL,
  prob_unit = NULL,
  prob_each = NULL,
  num_arms = NULL,
  conditions = NULL,
  check_inputs = TRUE
)

Arguments

N: The number of units. Must be a positive integer. (required)
m: Use for a two-arm design: exactly m units are assigned to treatment and N-m to control. (optional)
m_unit: Use for a two-arm design. unique(m_unit) units are assigned to treatment; must be the same for all units and of length N. (optional)
m_each: Use for a multi-arm design. A numeric vector giving the exact number of units assigned to each condition; must sum to N. (optional)
prob: Use for a two-arm design: either floor(N*prob) or ceiling(N*prob) units are assigned to treatment so that the marginal probability of assignment equals exactly prob. Must be between 0 and 1. One edge is deliberate: when ceiling(N*prob) == N (for instance N = 3, prob = 0.9), exactly floor(N*prob) units are treated, never all N, so the marginal probability is floor(N*prob)/N; complete_ra_probabilities() reports the probability actually used. (optional)
prob_unit: Use for a two-arm design. unique(prob_unit) will be passed to the prob argument; must be the same for all units. (optional)
prob_each: Use for a multi-arm design. A numeric vector giving the probability of assignment to each condition; entries must be nonnegative and sum to 1. Due to integer rounding the exact count assigned to each condition may differ slightly from draw to draw, but the overall probability of assignment is exactly prob_each. (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 counts sum to N, that probabilities lie between 0 and 1 and sum to 1, that vectors are of length N, 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)

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

Researchers can specify counts directly (via m or m_each) or target probabilities (via prob or prob_each). When probabilities are specified and the implied counts are not integers, complete_ra uses stochastic rounding to ensure that the overall probability of assignment exactly equals the target. In a two-arm design, either floor(N*prob) or ceiling(N*prob) units are assigned to treatment, with the draw between these two values chosen so that Pr(treatment) equals exactly prob. In a multi-arm design, the remaining units after floor allocation are assigned using a single round of simple random assignment calibrated to hit the exact target probabilities.

If only N is specified, a balanced two-arm trial (prob = 0.5) is assumed. When N is odd, either floor(N/2) or ceiling(N/2) units are assigned to treatment.

Examples

# Two-arm Designs
Z <- complete_ra(N = 100)
table(Z)
#> Z
#>  0  1 
#> 50 50 

Z <- complete_ra(N = 100, m = 50)
table(Z)
#> Z
#>  0  1 
#> 50 50 

Z <- complete_ra(N = 100, m_unit = rep(30, 100))
table(Z)
#> Z
#>  0  1 
#> 70 30 

Z <- complete_ra(N = 100, prob = 0.111)
table(Z)
#> Z
#>  0  1 
#> 89 11 

Z <- complete_ra(N = 100, prob_unit = rep(0.1, 100))
table(Z)
#> Z
#>  0  1 
#> 90 10 

Z <- complete_ra(N = 100, conditions = c("control", "treatment"))
table(Z)
#> Z
#>   control treatment 
#>        50        50 


# Multi-arm Designs
Z <- complete_ra(N = 100, num_arms = 3)
table(Z)
#> Z
#> T1 T2 T3 
#> 33 33 34 

Z <- complete_ra(N = 100, m_each = c(30, 30, 40))
table(Z)
#> Z
#> T1 T2 T3 
#> 30 30 40 

Z <- complete_ra(N = 100, prob_each = c(0.1, 0.2, 0.7))
table(Z)
#> Z
#> T1 T2 T3 
#> 10 20 70 

Z <- complete_ra(N = 100, conditions = c("control", "placebo", "treatment"))
table(Z)
#> Z
#>   control   placebo treatment 
#>        33        33        34 

# Special Cases
# Two-arm trial where the conditions are by default "T1" and "T2"
Z <- complete_ra(N = 100, num_arms = 2)
table(Z)
#> Z
#> T1 T2 
#> 50 50 

# If N = m, every unit is assigned to treatment with probability 1
complete_ra(N = 2, m = 2)
#> [1] 1 1

# The single-unit case works the same way: m = 1 out of N = 1 is treated
# with probability 1. Up through randomizr 0.12.0 this case was instead
# treated as a coin flip, so the unit was assigned to treatment only half of
# the time. The change is noted here because it silently alters the
# probabilities of assignment in code written against those versions.
complete_ra(N = 1, m = 1)
#> [1] 1

Usage

Arguments

Value

Details

See also

Examples