A Sequential Design Guaranteeing Exact Terminal Balance (Random Allocation Rule)
Source:R/design_seq_one_by_one_ibcrd.R
DesignSeqOneByOneiBCRD.RdA DesignSeqOneByOne implementing the "random
allocation rule" (a sequential realization of complete randomization): treatment is
assigned to each arriving subject with probability equal to the fraction of
remaining treatment slots among all remaining slots,
\(\Pr(w_t = 1) = n_{T,\mathrm{rem}} / (n_{T,\mathrm{rem}} + n_{C,\mathrm{rem}})\),
where \(n_{T,\mathrm{rem}} = \mathrm{round}(n \cdot prob\_T) - n_T\) and
\(n_{C,\mathrm{rem}} = (n - \mathrm{round}(n \cdot prob\_T)) - n_C\) are the
treatment/control slots not yet used, given the running counts \(n_T\), \(n_C\).
This guarantees the realized sequence, once all \(n\) subjects have arrived, has
exactly \(\mathrm{round}(n \cdot prob\_T)\) treated subjects — the same
terminal allocation-count guarantee as
DesignFixediBCRD's complete randomization, but
realized online as subjects arrive one at a time rather than all at once, and with
every prefix of the sequence itself drawn from the correct conditional (hypergeometric)
distribution given the slots used so far. If a slot type is exhausted
(\(n_{T,\mathrm{rem}} \le 0\) or \(n_{C,\mathrm{rem}} \le 0\)), the remaining
subjects are deterministically assigned to whichever type still has open slots.
No target \(n\): falls back to Bernoulli. If n was not supplied at
construction (private$n is NULL), there is no terminal target to
balance toward, so assign_wt() falls back to an unbiased
\(\mathrm{Bernoulli}(prob\_T)\) draw for every subject instead (equivalent to
DesignSeqOneByOneBernoulli).
Single implicit block. add_one_subject_to_experiment_and_assign()
overrides the inherited method only to additionally set private$m to a
constant vector of 1s (a single block containing every subject enrolled so far)
after each assignment, mirroring the fixed-sample
DesignFixediBCRD's single-block convention for
shared blocking/matching machinery.
References
Rosenberger, W. F., and Lachin, J. M. (2016). Randomization in
Clinical Trials: Theory and Practice (2nd ed.), Wiley, for the random allocation
rule as a sequential implementation of complete randomization. See also
DesignFixediBCRD for the fixed-sample (all-at-once)
version of the same terminal randomization law.
Super classes
Design -> DesignSeqOneByOne -> DesignSeqOneByOneiBCRD
Methods
+ inherited public methods from DesignSeqOneByOne
+ inherited public methods from Design
Design$add_all_subject_responses()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$is_a_cluster_capable()Design$is_a_kk_matching_capable()Design$is_blocking_design()Design$is_fixed_sample_size()Design$is_matching_design()Design$overwrite_all_subject_assignments()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$warm_all_subject_data_cache()
DesignSeqOneByOneiBCRD$new()
Initialize a sequential design targeting exact terminal
treatment/control balance (see class documentation for the assignment
rule and the no-fixed-n fallback).
Usage
DesignSeqOneByOneiBCRD$new(
response_type,
prob_T = 0.5,
include_is_missing_as_a_new_feature = TRUE,
n = NULL,
verbose = FALSE,
missingness_method = "impute",
design_formula = ~.,
seed = NULL
)Arguments
response_type"continuous", "incidence", "proportion", "count", "survival", or "ordinal".
prob_TTarget probability of treatment assignment; the terminal number of treated subjects is fixed at
round(n * prob_T)whennis known (see class documentation).include_is_missing_as_a_new_featureFlag for missingness indicators.
nThe planned (target) sample size; if
NULL, there is no terminal balance target and assignment falls back to an unbiased Bernoulli coin (see class documentation).verboseA flag for verbosity.
missingness_methodHow to handle missing values in covariates.
design_formulaA formula object.
seedInteger seed for reproducibility.
DesignSeqOneByOneiBCRD$add_one_subject_to_experiment_and_assign()
Add one subject to the experiment and assign treatment via
assign_wt() (delegating to the inherited
DesignSeqOneByOne$add_one_subject_to_experiment_and_assign()),
then set private$m to a single-block vector of 1s covering every
subject enrolled so far (see class documentation), overwritten on every
call rather than only once all subjects have arrived.
DesignSeqOneByOneiBCRD$assign_wt()
Draw the next subject's treatment assignment via the random
allocation rule (see class documentation): with probability equal to the
fraction of remaining treatment slots among all remaining slots, or a
deterministic assignment if one slot type is exhausted; falls back to an
unbiased Bernoulli coin if no fixed n was supplied.
Examples
seq_des = DesignSeqOneByOneiBCRD$new(n = 6, response_type = 'continuous')
seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
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