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Two-arm confidence rectangles

Source: R/rectangles_bernoulli.R
rectangle_bernoulli_binary.Rd

Construct a two-arm variance confidence rectangle from pilot data. These are expert helpers used by cmr_two_arm() and related extension functions.

Usage

rectangle_bernoulli_binary(
  y,
  d,
  alpha = 0.05,
  beta = NULL,
  correction = c("bonferroni", "sidak_arms"),
  na.rm = TRUE,
  tol = 1e-11
)

rectangle_binary(
  y,
  d,
  alpha = 0.05,
  method = c("auto", "bounded", "bernoulli", "maurer_pontil", "mp", "bernoulli_exact",
    "martinez_taboada_ramdas", "mtr", "unbounded", "unbounded_mom", "median_of_means",
    "mom"),
  beta = NULL,
  correction = c("bonferroni", "sidak_arms"),
  normalize = FALSE,
  lower = NULL,
  upper = NULL,
  psi = NULL,
  na.rm = TRUE,
  tol = 1e-11
)

rectangle_two_arm(
  y,
  d,
  alpha = 0.05,
  method = c("auto", "bounded", "bernoulli", "maurer_pontil", "mp", "bernoulli_exact",
    "martinez_taboada_ramdas", "mtr", "unbounded", "unbounded_mom", "median_of_means",
    "mom"),
  beta = NULL,
  correction = c("bonferroni", "sidak_arms"),
  normalize = FALSE,
  lower = NULL,
  upper = NULL,
  psi = NULL,
  na.rm = TRUE,
  tol = 1e-11
)

rectangle_bernoulli_two_arm(
  y,
  d,
  alpha = 0.05,
  beta = NULL,
  correction = c("bonferroni", "sidak_arms"),
  na.rm = TRUE,
  tol = 1e-11
)

Arguments

y

Pilot outcomes.

d

Pilot treatment indicator; treatment is 1 and control is 0.

alpha

Target joint error level.

beta

Optional endpoint error allocation. If NULL, error is split according to correction.

correction

Endpoint error correction, either "bonferroni" or "sidak_arms" for two-arm workflows.

na.rm

If TRUE, drop rows with missing y or d.

tol

Numerical tolerance for exact Bernoulli bound inversion.

method

Confidence-set method. "auto" chooses exact Bernoulli bounds for 0/1 outcomes and bounded Maurer–Pontil bounds otherwise.

normalize

If TRUE, normalize bounded outcomes to [0, 1] before computing variances. For guarantee-bearing bounded CMR on a non-unit scale, provide known lower and upper bounds.

lower, upper

Optional lower and upper outcome bounds used when normalize = TRUE. If either is omitted, the pilot minimum and/or maximum is used with a warning; that data-dependent normalization is exploratory and does not carry the finite-sample bounded-outcome CMR guarantee.

psi

Bounded-kurtosis parameter used only when method is an unbounded-outcome method.

Value

A rectangle object. Bounded and Bernoulli methods return a cmr_binary_rectangle; unbounded methods return a cmr_unbounded_rectangle. The object contains the numeric rectangle, one-arm bound details, endpoint error allocation, pilot sample sizes and variance estimates, and method metadata.

See also

Other rectangle helpers: binary_rectangle_corners(), cmr_multiarm_from_rectangle(), cmr_stratified_from_rectangle(), cmr_unbounded_from_rectangle(), folded_binomial_pmf(), multiarm_variance_objective(), rectangle_bounded_two_arm(), rectangle_multiarm(), rectangle_multiple_outcomes(), rectangle_proxy(), rectangle_stratified(), rectangle_unbounded(), stratified_variance_objective(), variance_bounds_bernoulli_exact(), variance_bounds_maurer_pontil(), variance_bounds_unbounded_mom()

Examples

d <- rep(c(1, 0), each = 6)
y <- c(1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1)
rectangle_two_arm(y, d, method = "bernoulli")
#> $rectangle
#>       v_l1       v_u1       v_l0       v_u0 
#> 0.02915219 0.25000000 0.02915219 0.25000000 
#> 
#> $treatment
#> $treatment$L
#> [1] 0.02915219
#> 
#> $treatment$U
#> [1] 0.25
#> 
#> $treatment$vhat
#> [1] 0.25
#> 
#> $treatment$method
#> [1] "bernoulli"
#> 
#> $treatment$n
#> [1] 6
#> 
#> $treatment$statistic
#> $treatment$statistic$j
#> [1] 2
#> 
#> $treatment$statistic$x
#> [1] 4
#> 
#> $treatment$statistic$m
#> [1] 6
#> 
#> $treatment$statistic$raw_sample_variance
#> [1] 0.2666667
#> 
#> $treatment$statistic$beta_l
#> [1] 0.0125
#> 
#> $treatment$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> 
#> $control
#> $control$L
#> [1] 0.02915219
#> 
#> $control$U
#> [1] 0.25
#> 
#> $control$vhat
#> [1] 0.25
#> 
#> $control$method
#> [1] "bernoulli"
#> 
#> $control$n
#> [1] 6
#> 
#> $control$statistic
#> $control$statistic$j
#> [1] 2
#> 
#> $control$statistic$x
#> [1] 2
#> 
#> $control$statistic$m
#> [1] 6
#> 
#> $control$statistic$raw_sample_variance
#> [1] 0.2666667
#> 
#> $control$statistic$beta_l
#> [1] 0.0125
#> 
#> $control$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> 
#> $alpha
#> [1] 0.05
#> 
#> $beta
#> beta_l1 beta_u1 beta_l0 beta_u0 
#>  0.0125  0.0125  0.0125  0.0125 
#> 
#> $correction
#> [1] "bonferroni"
#> 
#> $joint_error_bound
#> [1] 0.05
#> 
#> $method
#> [1] "bernoulli"
#> 
#> $n
#> n1 n0 
#>  6  6 
#> 
#> $vhat
#> vhat1 vhat0 
#>  0.25  0.25 
#> 
#> $normalization
#> NULL
#> 
#> attr(,"class")
#> [1] "cmr_binary_rectangle" "list"                
rectangle_binary(y, d, method = "auto")
#> $rectangle
#>       v_l1       v_u1       v_l0       v_u0 
#> 0.02915219 0.25000000 0.02915219 0.25000000 
#> 
#> $treatment
#> $treatment$L
#> [1] 0.02915219
#> 
#> $treatment$U
#> [1] 0.25
#> 
#> $treatment$vhat
#> [1] 0.25
#> 
#> $treatment$method
#> [1] "bernoulli"
#> 
#> $treatment$n
#> [1] 6
#> 
#> $treatment$statistic
#> $treatment$statistic$j
#> [1] 2
#> 
#> $treatment$statistic$x
#> [1] 4
#> 
#> $treatment$statistic$m
#> [1] 6
#> 
#> $treatment$statistic$raw_sample_variance
#> [1] 0.2666667
#> 
#> $treatment$statistic$beta_l
#> [1] 0.0125
#> 
#> $treatment$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> 
#> $control
#> $control$L
#> [1] 0.02915219
#> 
#> $control$U
#> [1] 0.25
#> 
#> $control$vhat
#> [1] 0.25
#> 
#> $control$method
#> [1] "bernoulli"
#> 
#> $control$n
#> [1] 6
#> 
#> $control$statistic
#> $control$statistic$j
#> [1] 2
#> 
#> $control$statistic$x
#> [1] 2
#> 
#> $control$statistic$m
#> [1] 6
#> 
#> $control$statistic$raw_sample_variance
#> [1] 0.2666667
#> 
#> $control$statistic$beta_l
#> [1] 0.0125
#> 
#> $control$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> 
#> $alpha
#> [1] 0.05
#> 
#> $beta
#> beta_l1 beta_u1 beta_l0 beta_u0 
#>  0.0125  0.0125  0.0125  0.0125 
#> 
#> $correction
#> [1] "bonferroni"
#> 
#> $joint_error_bound
#> [1] 0.05
#> 
#> $method
#> [1] "bernoulli"
#> 
#> $n
#> n1 n0 
#>  6  6 
#> 
#> $vhat
#> vhat1 vhat0 
#>  0.25  0.25 
#> 
#> $normalization
#> NULL
#> 
#> attr(,"class")
#> [1] "cmr_binary_rectangle" "list"