Probabilities of assignment: Block Random Assignment

Returns the probability that each unit is assigned to each condition under block random assignment. Units in different blocks routinely have different probabilities, which is exactly when these numbers are needed.

Usage

block_ra_probabilities(
  blocks = NULL,
  prob = NULL,
  prob_unit = NULL,
  prob_each = NULL,
  m = NULL,
  m_unit = NULL,
  block_m = NULL,
  block_m_each = NULL,
  block_prob = NULL,
  block_prob_each = NULL,
  num_arms = NULL,
  conditions = NULL,
  check_inputs = TRUE
)

Arguments

blocks: A vector of length N indicating which block each unit belongs to. Can be character, factor, or numeric. (required)
prob: Use for a two-arm design in which either floor(N_block*prob) or ceiling(N_block*prob) units are assigned to treatment within each block. Which of the two is used is itself random: the ceiling is drawn with probability equal to the fractional part of N_block*prob and the floor otherwise, which makes each unit's probability of assignment exactly prob. When N_block*prob is a whole number the count is fixed. Must be a real number between 0 and 1. (optional)
prob_unit: Use for a two-arm design. Must be of length N. tapply(prob_unit, blocks, unique) will be passed to block_prob. (optional)
prob_each: Use for a multi-arm design in which the values of prob_each determine the probabilities of assignment to each treatment condition. Must be a numeric vector giving the probability of assignment to each condition. All entries must be nonnegative real numbers between 0 and 1 and the total must sum to 1. Because of integer rounding, the exact number of units assigned to each condition may differ slightly from assignment to assignment, but the overall probability of assignment is exactly prob_each. (optional)
m: Use for a two-arm design in which the scalar m gives the fixed number of units to assign to treatment within every block. This count does not vary across blocks. (optional)
m_unit: Use for a two-arm design. Must be of length N. tapply(m_unit, blocks, unique) will be passed to block_m. (optional)
block_m: Use for a two-arm design in which block_m gives the number of units to assign to treatment within each block. Must be a numeric vector as long as the number of blocks, in the same order as sort(unique(blocks)). (optional)
block_m_each: Use for a multi-arm design in which block_m_each gives the number of units assigned to each condition within each block. Must be a matrix with one row per block and one column per treatment arm. Rows should respect the ordering of blocks by sort(unique(blocks)); columns should be in the order of conditions, if specified. (optional)
block_prob: Use for a two-arm design in which the probability of assignment to treatment varies across blocks. Must be in the same order as sort(unique(blocks)). (optional)
block_prob_each: Use for a multi-arm design in which assignment probabilities vary across blocks. Must be a matrix with one row per block and one column per treatment arm. Each row must sum to 1. Rows respect the ordering of sort(unique(blocks)). (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, the treatment groups will be named 0 (for control) and 1 (for treatment) 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 the block sizes, that probabilities lie between 0 and 1 and sum to 1, that matrices have one row per block, 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


blocks <- rep(c("A", "B","C"), times = c(50, 100, 200))
prob_mat <- block_ra_probabilities(blocks = blocks)
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 <- block_ra_probabilities(blocks = blocks, m = 20)
head(prob_mat)
#>      prob_0 prob_1
#> [1,]    0.6    0.4
#> [2,]    0.6    0.4
#> [3,]    0.6    0.4
#> [4,]    0.6    0.4
#> [5,]    0.6    0.4
#> [6,]    0.6    0.4

block_m_each <- rbind(c(25, 25),
                 c(50, 50),
                 c(100, 100))

prob_mat <- block_ra_probabilities(blocks = blocks, block_m_each = block_m_each)
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

block_m_each <- rbind(c(10, 40),
                 c(30, 70),
                 c(50, 150))

prob_mat <- block_ra_probabilities(blocks = blocks,
                                   block_m_each = block_m_each,
                                   conditions = c("control", "treatment"))
head(prob_mat)
#>      prob_control prob_treatment
#> [1,]          0.2            0.8
#> [2,]          0.2            0.8
#> [3,]          0.2            0.8
#> [4,]          0.2            0.8
#> [5,]          0.2            0.8
#> [6,]          0.2            0.8

prob_mat <- block_ra_probabilities(blocks = blocks, 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

block_m_each <- rbind(c(10, 20, 20),
                 c(30, 50, 20),
                 c(50, 75, 75))
prob_mat <- block_ra_probabilities(blocks = blocks, block_m_each = block_m_each)
head(prob_mat)
#>      prob_T1 prob_T2 prob_T3
#> [1,]     0.2     0.4     0.4
#> [2,]     0.2     0.4     0.4
#> [3,]     0.2     0.4     0.4
#> [4,]     0.2     0.4     0.4
#> [5,]     0.2     0.4     0.4
#> [6,]     0.2     0.4     0.4

prob_mat <- block_ra_probabilities(blocks = blocks, block_m_each = block_m_each,
                       conditions = c("control", "placebo", "treatment"))
head(prob_mat)
#>      prob_control prob_placebo prob_treatment
#> [1,]          0.2          0.4            0.4
#> [2,]          0.2          0.4            0.4
#> [3,]          0.2          0.4            0.4
#> [4,]          0.2          0.4            0.4
#> [5,]          0.2          0.4            0.4
#> [6,]          0.2          0.4            0.4

prob_mat <- block_ra_probabilities(blocks = blocks, prob_each = c(0.1, 0.1, 0.8))
head(prob_mat)
#>      prob_T1 prob_T2 prob_T3
#> [1,]     0.1     0.1     0.8
#> [2,]     0.1     0.1     0.8
#> [3,]     0.1     0.1     0.8
#> [4,]     0.1     0.1     0.8
#> [5,]     0.1     0.1     0.8
#> [6,]     0.1     0.1     0.8

Usage

Arguments

Value

Details

See also

Examples