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Probabilities of assignment: Simple Random Assignment

Source: R/simple_ra.R
simple_ra_probabilities.Rd

Returns the probability that each unit is assigned to each condition under simple random assignment. Every unit is assigned independently, so the probabilities do not depend on how the other units came out.

Usage

simple_ra_probabilities(
  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 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.

See also

simple_ra()

Examples

# Two Group Designs
prob_mat <- simple_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 <- simple_ra_probabilities(N = 100, prob = 0.5)
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 <- simple_ra_probabilities(N = 100, prob_each = c(0.3, 0.7),
                        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 <- simple_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 <- simple_ra_probabilities(N = 100, prob_each = c(0.3, 0.3, 0.4))
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 <- simple_ra_probabilities(N = 100, prob_each = c(0.3, 0.3, 0.4),
                        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 <- simple_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