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Cluster Random Assignment

Source: R/cluster_ra.R
cluster_ra.Rd

cluster_ra assigns entire groups of units (clusters) to treatment conditions, so that all units within a cluster share the same treatment status. Cluster assignment is appropriate when the intervention can only be delivered at the group level (for example, a school-wide program that cannot be withheld from individual students), when spillovers within groups make individual-level assignment infeasible, or when the treatment is itself defined as a group-level condition. Because all units in a cluster move together, the effective sample size for estimating average effects is the number of clusters, not the number of units. Clustering therefore typically increases sampling variability relative to complete or block random assignment; the precision loss grows with the intra-cluster correlation in potential outcomes.

Usage

cluster_ra(
  clusters = NULL,
  m = NULL,
  m_unit = NULL,
  m_each = NULL,
  prob = NULL,
  prob_unit = NULL,
  prob_each = NULL,
  num_arms = NULL,
  conditions = NULL,
  simple = FALSE,
  check_inputs = TRUE
)

Arguments

clusters

A vector of length N indicating which cluster each unit belongs to. (required)

m

Use for a two-arm design in which exactly m clusters are assigned to treatment. (optional)

m_unit

Use for a two-arm design. unique(m_unit) clusters 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 number of clusters assigned to each condition; must sum to the total number of clusters. (optional)

prob

Use for a two-arm design in which either floor(N_clusters*prob) or ceiling(N_clusters*prob) clusters are assigned to treatment. Which of the two is used is itself random: the ceiling is drawn with probability equal to the fractional part of N_clusters*prob and the floor otherwise, so that each cluster's probability of assignment is exactly prob. When N_clusters*prob is a whole number the count is fixed. Must be between 0 and 1. (optional)

prob_unit

Use for a two-arm design. unique(prob_unit) will be passed to the prob argument and 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, sum to 1. Because of integer rounding, the exact number of clusters assigned to each condition may differ slightly from assignment to assignment, but the overall probability of assignment is exactly prob_each. (optional)

num_arms

The total number of treatment arms. If unspecified, determined from m_each or conditions. (optional)

conditions

A character vector giving the names of the treatment groups. If unspecified, groups will be named T1, T2, T3, etc. (optional)

simple

Logical, defaults to FALSE. If TRUE, clusters are assigned to conditions independently (simple random assignment at the cluster level), so the number of treated clusters varies from draw to draw. Do not specify m or m_each when simple = TRUE. (optional)

check_inputs

Logical. Whether to verify before assigning that the arguments are internally consistent: that counts sum to the number of clusters, that probabilities lie between 0 and 1 and sum to 1, 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. Every unit in a cluster receives the same value. Numeric in a two-arm trial; a factor (ordered by conditions) in a multi-arm trial.

Details

By default, cluster_ra conducts complete random assignment at the cluster level: a fixed number of clusters are assigned to each condition on every draw. Setting simple = TRUE switches to independent Bernoulli assignment of clusters.

See also

complete_ra(), block_and_cluster_ra(), cluster_rs(), cluster_ra_probabilities()

Examples

# Ten clusters, of sizes 1 through 10
clusters <- rep(letters[1:10], times = 1:10)

# Two Group Designs

Z <- cluster_ra(clusters = clusters)
table(Z, clusters)
#>    clusters
#> Z    a  b  c  d  e  f  g  h  i  j
#>   0  1  2  0  4  5  0  7  0  0  0
#>   1  0  0  3  0  0  6  0  8  9 10

Z <- cluster_ra(clusters = clusters, m = 4)
table(Z, clusters)
#>    clusters
#> Z    a  b  c  d  e  f  g  h  i  j
#>   0  1  2  3  4  0  0  0  8  0 10
#>   1  0  0  0  0  5  6  7  0  9  0

Z <- cluster_ra(clusters = clusters, m_each = c(6, 4),
                conditions = c("control", "treatment"))
table(Z, clusters)
#>            clusters
#> Z            a  b  c  d  e  f  g  h  i  j
#>   control    0  2  0  4  0  6  7  8  0 10
#>   treatment  1  0  3  0  5  0  0  0  9  0

# Multi-arm Designs
Z <- cluster_ra(clusters = clusters, num_arms = 3)
table(Z, clusters)
#>     clusters
#> Z     a  b  c  d  e  f  g  h  i  j
#>   T1  0  0  0  0  5  0  0  8  9  0
#>   T2  0  2  0  0  0  6  0  0  0 10
#>   T3  1  0  3  4  0  0  7  0  0  0

Z <- cluster_ra(clusters = clusters, m_each = c(3, 3, 4))
table(Z, clusters)
#>     clusters
#> Z     a  b  c  d  e  f  g  h  i  j
#>   T1  1  0  3  0  0  0  0  0  0 10
#>   T2  0  2  0  4  0  0  7  0  0  0
#>   T3  0  0  0  0  5  6  0  8  9  0

Z <- cluster_ra(clusters = clusters, m_each = c(3, 3, 4),
                conditions = c("control", "placebo", "treatment"))
table(Z, clusters)
#>            clusters
#> Z            a  b  c  d  e  f  g  h  i  j
#>   control    1  0  0  4  0  0  0  0  9  0
#>   placebo    0  2  0  0  5  6  0  0  0  0
#>   treatment  0  0  3  0  0  0  7  8  0 10

Z <- cluster_ra(clusters = clusters,
                conditions = c("control", "placebo", "treatment"))
table(Z, clusters)
#>            clusters
#> Z            a  b  c  d  e  f  g  h  i  j
#>   control    0  0  3  0  5  0  0  0  0 10
#>   placebo    0  0  0  4  0  6  0  8  0  0
#>   treatment  1  2  0  0  0  0  7  0  9  0