Probabilities of assignment: Complete Random Assignment

Returns the probability that each unit is assigned to each condition under complete random assignment. When the implied counts are not integers the probabilities account for the stochastic rounding complete_ra uses, so they equal the target exactly rather than approximately.

Usage

complete_ra_probabilities(
  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 matrix with N rows and one column per treatment condition, with columns named prob_<condition>. Entry (i, j) is the probability that unit i is assigned to condition j, and every row sums to 1.

Details

These are the quantities inverse-probability weights are built from: weight each unit by the reciprocal of the probability of the condition it landed in, which obtain_condition_probabilities() extracts for you.

Examples

# 2-arm designs
prob_mat <- complete_ra_probabilities(N = 100)
head(prob_mat)
#>      prob_0 prob_1
#> [1,]    0.5    0.5
#> [2,]    0.5    0.5
#> [3,]    0.5    0.5
#> [4,]    0.5    0.5
#> [5,]    0.5    0.5
#> [6,]    0.5    0.5

prob_mat <- complete_ra_probabilities(N = 100, m = 50)
head(prob_mat)
#>      prob_0 prob_1
#> [1,]    0.5    0.5
#> [2,]    0.5    0.5
#> [3,]    0.5    0.5
#> [4,]    0.5    0.5
#> [5,]    0.5    0.5
#> [6,]    0.5    0.5

prob_mat <- complete_ra_probabilities(N = 100, prob = 0.3)
head(prob_mat)
#>      prob_0 prob_1
#> [1,]    0.7    0.3
#> [2,]    0.7    0.3
#> [3,]    0.7    0.3
#> [4,]    0.7    0.3
#> [5,]    0.7    0.3
#> [6,]    0.7    0.3

prob_mat <- complete_ra_probabilities(N = 100, m_each = c(30, 70),
                          conditions = c("control", "treatment"))
head(prob_mat)
#>      prob_control prob_treatment
#> [1,]          0.3            0.7
#> [2,]          0.3            0.7
#> [3,]          0.3            0.7
#> [4,]          0.3            0.7
#> [5,]          0.3            0.7
#> [6,]          0.3            0.7

# Multi-arm Designs
prob_mat <- complete_ra_probabilities(N = 100, num_arms = 3)
head(prob_mat)
#>        prob_T1   prob_T2   prob_T3
#> [1,] 0.3333333 0.3333333 0.3333333
#> [2,] 0.3333333 0.3333333 0.3333333
#> [3,] 0.3333333 0.3333333 0.3333333
#> [4,] 0.3333333 0.3333333 0.3333333
#> [5,] 0.3333333 0.3333333 0.3333333
#> [6,] 0.3333333 0.3333333 0.3333333

prob_mat <- complete_ra_probabilities(N = 100, m_each = c(30, 30, 40))
head(prob_mat)
#>      prob_T1 prob_T2 prob_T3
#> [1,]     0.3     0.3     0.4
#> [2,]     0.3     0.3     0.4
#> [3,]     0.3     0.3     0.4
#> [4,]     0.3     0.3     0.4
#> [5,]     0.3     0.3     0.4
#> [6,]     0.3     0.3     0.4

prob_mat <- complete_ra_probabilities(N = 100, m_each = c(30, 30, 40),
                          conditions = c("control", "placebo", "treatment"))
head(prob_mat)
#>      prob_control prob_placebo prob_treatment
#> [1,]          0.3          0.3            0.4
#> [2,]          0.3          0.3            0.4
#> [3,]          0.3          0.3            0.4
#> [4,]          0.3          0.3            0.4
#> [5,]          0.3          0.3            0.4
#> [6,]          0.3          0.3            0.4

prob_mat <- complete_ra_probabilities(N = 100, conditions = c("control", "placebo", "treatment"))
head(prob_mat)
#>      prob_control prob_placebo prob_treatment
#> [1,]    0.3333333    0.3333333      0.3333333
#> [2,]    0.3333333    0.3333333      0.3333333
#> [3,]    0.3333333    0.3333333      0.3333333
#> [4,]    0.3333333    0.3333333      0.3333333
#> [5,]    0.3333333    0.3333333      0.3333333
#> [6,]    0.3333333    0.3333333      0.3333333

prob_mat <- complete_ra_probabilities(N = 100, prob_each = c(0.2, 0.7, 0.1))
head(prob_mat)
#>      prob_T1 prob_T2 prob_T3
#> [1,]     0.2     0.7     0.1
#> [2,]     0.2     0.7     0.1
#> [3,]     0.2     0.7     0.1
#> [4,]     0.2     0.7     0.1
#> [5,]     0.2     0.7     0.1
#> [6,]     0.2     0.7     0.1

Usage

Arguments

Value

Details

See also

Examples