A Sequential Bernoulli (Independent-Coin-Flip) Randomized Design

A DesignSeqOneByOne in which each arriving subject's treatment assignment is drawn independently as \(w_t \stackrel{iid}{\sim} \mathrm{Bernoulli}(prob\_T)\), with no dependence on covariates or on prior assignments — the direct sequential-enrollment analog of DesignFixedBernoulli. As in the fixed-sample version, the realized number of treated subjects after \(t\) arrivals is random (\(\mathrm{Binomial}(t, prob\_T)\)), in contrast to sequential designs that actively balance assignment counts or covariates (e.g. DesignSeqOneByOneAtkinson).

Super classes

Design -> DesignSeqOneByOne -> DesignSeqOneByOneBernoulli

Methods

Public methods

• DesignSeqOneByOneBernoulli$is_a_bernoulli_capable()

• DesignSeqOneByOneBernoulli$new()

• DesignSeqOneByOneBernoulli$assign_wt()

• DesignSeqOneByOneBernoulli$clone()

+ inherited public methods from DesignSeqOneByOne

• DesignSeqOneByOne$add_one_subject()
• DesignSeqOneByOne$add_one_subject_to_experiment_and_assign()
• DesignSeqOneByOne$print_current_subject_assignment()

+ 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$is_a_cluster_capable()
• Design$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()

---

DesignSeqOneByOneBernoulli$is_a_bernoulli_capable()

Characterization: this design draws each subject's treatment assignment as an independent \(\mathrm{Bernoulli}(prob\_T)\) coin flip (see class documentation), so it is Bernoulli-capable by construction.

Usage

DesignSeqOneByOneBernoulli$is_a_bernoulli_capable()

Returns

Always TRUE for this class.

---

DesignSeqOneByOneBernoulli$new()

Initialize a Bernoulli (independent-coin-flip) sequential experimental design.

Usage

DesignSeqOneByOneBernoulli$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

The data type of response values which must be one of the following: "continuous", "incidence", "proportion", "count", "survival", "ordinal".

prob_T

The probability of the treatment assignment. This defaults to 0.5.

include_is_missing_as_a_new_feature

If missing data is present in a variable, should we include another dummy variable for its missingness? The default is TRUE.

n

The sample size (if fixed). Default is NULL.

verbose

A flag indicating whether messages should be displayed.

missingness_method

How to handle missing values in covariates.

design_formula

A formula object.

seed

Integer seed for reproducibility.

Returns

A new `DesignSeqOneByOneBernoulli` object

---

DesignSeqOneByOneBernoulli$assign_wt()

Draw the next subject's treatment assignment as a single independent \(\mathrm{Bernoulli}(prob\_T)\) coin flip (see class documentation); does not consult covariates or prior assignments.

Usage

DesignSeqOneByOneBernoulli$assign_wt()

Returns

The treatment assignment (0 or 1) for the next subject.

---

DesignSeqOneByOneBernoulli$clone()

The objects of this class are cloneable with this method.

Usage

DesignSeqOneByOneBernoulli$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

seq_des = DesignSeqOneByOneBernoulli$new(n = 6, response_type = 'continuous')
seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
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