A Fixed, Unblocked Cluster Randomized Design

A fixed-sample-size DesignFixed in which whole clusters of subjects (identified by cluster_col), rather than individual subjects, are the unit of randomization: every subject in a given cluster always receives the same treatment assignment. This is the unblocked analog of DesignFixedBlockedCluster — there is no stratification step here, so clusters are randomized to treatment as a single pool rather than within strata. Cluster-level randomization is required whenever individual-level randomization would create within-cluster interference/spillover that violates SUTVA (e.g. clusters are classrooms, clinics, villages, or households), at the cost of an effective sample size driven by the number of clusters, not subjects, and a corresponding need for cluster-aware inference.

Randomization mechanism. draw_ws_raw(r) extracts each subject's cluster ID from cluster_col (erroring if any are missing) and calls cluster_ra (randomizr) once per replicate, which performs complete random assignment at the cluster level: subject to rounding, prob_T of clusters are assigned to treatment, and all subjects sharing a cluster inherit that cluster's assignment. r independent replicate columns are generated via replicate() (one randomizr call per replicate).

Cluster-aware bootstrap. draw_bootstrap_indices() overrides the default subject-level bootstrap to resample whole clusters with replacement (via resample_group_rows_cpp()) rather than individual rows, since outcomes are correlated within a cluster (shared assignment plus, typically, shared context) and the exchangeable resampling unit for a valid bootstrap variance/interval estimate is therefore the cluster, not the subject.

References

Middleton, J. A., and Aronow, P. M. (2015). "Unbiased estimation of the average treatment effect in cluster-randomized experiments." Statistics, Politics and Policy, 6(1-2), 39-75, doi:10.1515/spp-2013-0002 . See also cluster randomized controlled trial for orientation, and DesignFixedBlockedCluster for the blocked variant of this design.

Super classes

Design -> DesignFixed -> DesignFixedCluster

Methods

Public methods

• DesignFixedCluster$is_a_cluster_capable()

• DesignFixedCluster$new()

• DesignFixedCluster$clone()

+ inherited public methods from DesignFixed

• DesignFixed$add_all_subject_responses()
• DesignFixed$add_all_subjects_to_experiment()
• DesignFixed$assign_w_to_all_subjects()
• DesignFixed$overwrite_all_subject_assignments()

+ inherited public methods from Design

• Design$add_one_subject_response()
• Design$any_censoring()
• Design$applicable_inference_class_names()
• Design$assert_all_responses_recorded()
• Design$assert_all_subjects_arrived()
• Design$assert_even_allocation()
• Design$assert_fixed_sample()
• Design$capabilities()
• Design$check_experiment_completed()
• Design$draw_ws_according_to_design()
• Design$duplicate()
• Design$get_X()
• Design$get_X_imp()
• Design$get_X_raw()
• Design$get_design_formula()
• Design$get_edi_version_created()
• Design$get_effective_dead()
• Design$get_effective_time()
• Design$get_missingness_method()
• Design$get_n()
• Design$get_ordinal_levels()
• Design$get_original_ordinal_levels()
• Design$get_prob_T()
• Design$get_response_type()
• Design$get_response_type_original()
• Design$get_t()
• Design$get_w()
• Design$get_y()
• Design$get_y_L()
• Design$get_y_R()
• Design$get_y_original()
• Design$has_general_censoring()
• Design$incompatible_inference_classes_due_to_design_structure()
• Design$is_a_bernoulli_capable()
• Design$is_a_kk_matching_capable()
• Design$is_blocking_design()
• Design$is_fixed_sample_size()
• Design$is_matching_design()
• Design$prepare_for_resampling_replay()
• Design$randomization_family()
• Design$supports()
• Design$supports_randomization_draw()
• Design$supports_resampling()
• Design$supports_resampling_replay()
• Design$transform_y()
• Design$unavailable_inference_classes_due_to_missing_packages()
• Design$warm_all_subject_data_cache()

---

DesignFixedCluster$is_a_cluster_capable()

Characterization: this design randomizes whole clusters (see class documentation), so it is cluster-structured by construction.

Usage

DesignFixedCluster$is_a_cluster_capable()

Returns

Always TRUE for this class.

---

DesignFixedCluster$new()

Initialize a cluster randomized fixed experimental design (no blocking/stratification; see DesignFixedBlockedCluster if stratification is also needed).

Usage

DesignFixedCluster$new(
  cluster_col,
  response_type,
  prob_T = 0.5,
  include_is_missing_as_a_new_feature = TRUE,
  n = NULL,
  verbose = FALSE,
  missingness_method = "impute",
  design_formula = ~.,
  seed = NULL
)

Arguments

cluster_col

The column name in the data that identifies the cluster for each subject.

response_type

The data type of response values.

prob_T

The target probability that a given cluster is assigned to treatment (subjects inherit their cluster's assignment).

include_is_missing_as_a_new_feature

Flag for missingness indicators.

n

The sample size.

verbose

Flag for verbosity.

missingness_method

How to handle missing values in covariates.

design_formula

A formula object.

seed

Integer seed for reproducibility.

Returns

A new `DesignFixedCluster` object

---

DesignFixedCluster$clone()

The objects of this class are cloneable with this method.

Usage

DesignFixedCluster$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

des = DesignFixedCluster$new(n = 20, response_type = 'continuous', cluster_col = 'cl')
X = data.frame(x = rnorm(20), cl = factor(rep(1:5, each = 4)))
des$add_all_subjects_to_experiment(X)
des$assign_w_to_all_subjects()