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Proxy or delayed-outcome confidence rectangle

Source: R/rectangles_proxy.R
rectangle_proxy.Rd

Construct a primary-outcome variance rectangle by estimating a proxy-outcome rectangle and widening each arm's standard-deviation interval by zeta.

Usage

rectangle_proxy(
  proxy_y,
  d,
  zeta,
  alpha = 0.05,
  method = c("auto", "bounded", "bernoulli", "maurer_pontil", "mp", "bernoulli_exact",
    "martinez_taboada_ramdas", "mtr"),
  beta = NULL,
  correction = c("bonferroni", "sidak_arms"),
  normalize = FALSE,
  lower = NULL,
  upper = NULL,
  na.rm = TRUE,
  tol = 1e-11
)

rectangle_delayed_outcome(
  proxy_y,
  d,
  zeta,
  alpha = 0.05,
  method = c("auto", "bounded", "bernoulli", "maurer_pontil", "mp", "bernoulli_exact",
    "martinez_taboada_ramdas", "mtr"),
  beta = NULL,
  correction = c("bonferroni", "sidak_arms"),
  normalize = FALSE,
  lower = NULL,
  upper = NULL,
  na.rm = TRUE,
  tol = 1e-11
)

Arguments

proxy_y

Pilot proxy or delayed primary outcomes.

d

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

zeta

Nonnegative standard-deviation bridge radius. Provide a scalar shared across arms or a treatment/control pair.

alpha

Target joint error level.

method

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

beta

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

correction

Endpoint error correction, either "bonferroni" or "sidak_arms".

normalize

If TRUE, normalize bounded proxy 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.

na.rm

If TRUE, drop rows with missing proxy_y or d.

tol

Numerical tolerance for exact Bernoulli bound inversion.

Value

A list of class cmr_proxy_rectangle and cmr_binary_rectangle with the widened primary-outcome rectangle, the underlying proxy confidence set, zeta, bridge metadata, endpoint error allocation, pilot summaries, 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_bernoulli_binary(), rectangle_bounded_two_arm(), rectangle_multiarm(), rectangle_multiple_outcomes(), rectangle_stratified(), rectangle_unbounded(), stratified_variance_objective(), variance_bounds_bernoulli_exact(), variance_bounds_maurer_pontil(), variance_bounds_unbounded_mom()

Examples

set.seed(11)
d <- rep(c(1, 0), each = 30)
proxy_y <- c(rbeta(30, 2, 6), rbeta(30, 4, 4))
rectangle_proxy(proxy_y, d, zeta = 0.05)
#> $rectangle
#> v_l1 v_u1 v_l0 v_u0 
#> 0.00 0.25 0.00 0.25 
#> 
#> $treatment
#> $treatment$L
#> [1] 0
#> 
#> $treatment$U
#> [1] 0.25
#> 
#> $treatment$vhat
#> [1] 0.01197773
#> 
#> $treatment$method
#> [1] "bounded"
#> 
#> $treatment$n
#> [1] 30
#> 
#> $treatment$statistic
#> $treatment$statistic$vhat
#> [1] 0.01197773
#> 
#> $treatment$statistic$projected_vhat
#> [1] 0.01197773
#> 
#> $treatment$statistic$sdhat
#> [1] 0.1094428
#> 
#> $treatment$statistic$beta_l
#> [1] 0.0125
#> 
#> $treatment$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> $treatment$L_proxy
#> [1] 0
#> 
#> $treatment$U_proxy
#> [1] 0.25
#> 
#> 
#> $control
#> $control$L
#> [1] 0
#> 
#> $control$U
#> [1] 0.25
#> 
#> $control$vhat
#> [1] 0.02927848
#> 
#> $control$method
#> [1] "bounded"
#> 
#> $control$n
#> [1] 30
#> 
#> $control$statistic
#> $control$statistic$vhat
#> [1] 0.02927848
#> 
#> $control$statistic$projected_vhat
#> [1] 0.02927848
#> 
#> $control$statistic$sdhat
#> [1] 0.1711096
#> 
#> $control$statistic$beta_l
#> [1] 0.0125
#> 
#> $control$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> $control$L_proxy
#> [1] 0
#> 
#> $control$U_proxy
#> [1] 0.25
#> 
#> 
#> $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] "proxy_bounded"
#> 
#> $n
#> n1 n0 
#> 30 30 
#> 
#> $vhat
#>      vhat1      vhat0 
#> 0.01197773 0.02927848 
#> 
#> $normalization
#> NULL
#> 
#> $proxy_confidence_set
#> $rectangle
#> v_l1 v_u1 v_l0 v_u0 
#> 0.00 0.25 0.00 0.25 
#> 
#> $treatment
#> $treatment$L
#> [1] 0
#> 
#> $treatment$U
#> [1] 0.25
#> 
#> $treatment$vhat
#> [1] 0.01197773
#> 
#> $treatment$method
#> [1] "bounded"
#> 
#> $treatment$n
#> [1] 30
#> 
#> $treatment$statistic
#> $treatment$statistic$vhat
#> [1] 0.01197773
#> 
#> $treatment$statistic$projected_vhat
#> [1] 0.01197773
#> 
#> $treatment$statistic$sdhat
#> [1] 0.1094428
#> 
#> $treatment$statistic$beta_l
#> [1] 0.0125
#> 
#> $treatment$statistic$beta_u
#> [1] 0.0125
#> 
#> 
#> 
#> $control
#> $control$L
#> [1] 0
#> 
#> $control$U
#> [1] 0.25
#> 
#> $control$vhat
#> [1] 0.02927848
#> 
#> $control$method
#> [1] "bounded"
#> 
#> $control$n
#> [1] 30
#> 
#> $control$statistic
#> $control$statistic$vhat
#> [1] 0.02927848
#> 
#> $control$statistic$projected_vhat
#> [1] 0.02927848
#> 
#> $control$statistic$sdhat
#> [1] 0.1711096
#> 
#> $control$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] "bounded"
#> 
#> $n
#> n1 n0 
#> 30 30 
#> 
#> $vhat
#>      vhat1      vhat0 
#> 0.01197773 0.02927848 
#> 
#> $normalization
#> NULL
#> 
#> attr(,"class")
#> [1] "cmr_binary_rectangle" "list"                
#> 
#> $zeta
#>    1    0 
#> 0.05 0.05 
#> 
#> $bridge
#> $bridge$assumption
#> [1] "abs(primary_sd - proxy_sd) <= zeta by arm"
#> 
#> $bridge$proxy_rectangle
#> v_l1 v_u1 v_l0 v_u0 
#> 0.00 0.25 0.00 0.25 
#> 
#> $bridge$primary_rectangle
#> v_l1 v_u1 v_l0 v_u0 
#> 0.00 0.25 0.00 0.25 
#> 
#> 
#> attr(,"class")
#> [1] "cmr_proxy_rectangle"  "cmr_binary_rectangle" "list"