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Multiple-outcome confidence rectangle

Source: R/rectangles_multiple_outcomes.R
rectangle_multiple_outcomes.Rd

Construct an effective two-arm variance rectangle for multiple outcomes. For estimand = "index", outcomes are first combined using weights. For estimand = "coprimary", one rectangle is built per outcome and combined conservatively using the outcome weights.

Usage

rectangle_multiple_outcomes(
  y,
  d,
  weights = NULL,
  estimand = c("coprimary", "index"),
  alpha = 0.05,
  method = c("auto", "bounded", "bernoulli", "maurer_pontil", "mp", "bernoulli_exact",
    "martinez_taboada_ramdas", "mtr"),
  beta = NULL,
  na.rm = TRUE,
  tol = 1e-11
)

Arguments

y

Pilot outcomes as a numeric matrix, data frame, or vector. Rows are units and columns are outcomes.

d

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

weights

Optional nonnegative outcome weights. If NULL, equal weights are used.

estimand

Either "coprimary" or "index".

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 scalar endpoint error allocation.

na.rm

If TRUE, drop rows with missing y or d.

tol

Numerical tolerance for exact Bernoulli bound inversion.

Value

A list of class cmr_multiple_outcomes_rectangle. For estimand = "index", this wraps the ordinary two-arm rectangle for the weighted index. For estimand = "coprimary", it contains the effective two-arm rectangle, weights, outcome-specific bounds, pilot summaries, endpoint error allocation, 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_proxy(), rectangle_stratified(), rectangle_unbounded(), stratified_variance_objective(), variance_bounds_bernoulli_exact(), variance_bounds_maurer_pontil(), variance_bounds_unbounded_mom()

Examples

set.seed(9)
d <- rep(c(1, 0), each = 20)
y <- cbind(
  y1 = c(rbeta(20, 2, 6), rbeta(20, 4, 4)),
  y2 = c(rbeta(20, 5, 3), rbeta(20, 3, 5))
)
rectangle_multiple_outcomes(y, d, weights = c(0.6, 0.4))
#> $rectangle
#> v_l1 v_u1 v_l0 v_u0 
#> 0.00 0.25 0.00 0.25 
#> 
#> $estimand
#> [1] "coprimary"
#> 
#> $weights
#>  y1  y2 
#> 0.6 0.4 
#> 
#> $alpha
#> [1] 0.05
#> 
#> $beta
#> [1] 0.00625
#> 
#> $joint_error_bound
#> [1] 0.05
#> 
#> $method
#> [1] "bounded"
#> 
#> $n
#> n1 n0 
#> 20 20 
#> 
#> $vhat
#>      vhat1      vhat0 
#> 0.02317230 0.01787976 
#> 
#> $outcome_bounds
#> $outcome_bounds$y1
#> $outcome_bounds$y1$treatment
#> $outcome_bounds$y1$treatment$L
#> [1] 0
#> 
#> $outcome_bounds$y1$treatment$U
#> [1] 0.25
#> 
#> $outcome_bounds$y1$treatment$vhat
#> [1] 0.01749479
#> 
#> $outcome_bounds$y1$treatment$method
#> [1] "bounded"
#> 
#> $outcome_bounds$y1$treatment$n
#> [1] 20
#> 
#> $outcome_bounds$y1$treatment$statistic
#> $outcome_bounds$y1$treatment$statistic$vhat
#> [1] 0.01749479
#> 
#> $outcome_bounds$y1$treatment$statistic$projected_vhat
#> [1] 0.01749479
#> 
#> $outcome_bounds$y1$treatment$statistic$sdhat
#> [1] 0.1322679
#> 
#> $outcome_bounds$y1$treatment$statistic$beta_l
#> [1] 0.00625
#> 
#> $outcome_bounds$y1$treatment$statistic$beta_u
#> [1] 0.00625
#> 
#> 
#> 
#> $outcome_bounds$y1$control
#> $outcome_bounds$y1$control$L
#> [1] 0
#> 
#> $outcome_bounds$y1$control$U
#> [1] 0.25
#> 
#> $outcome_bounds$y1$control$vhat
#> [1] 0.01650368
#> 
#> $outcome_bounds$y1$control$method
#> [1] "bounded"
#> 
#> $outcome_bounds$y1$control$n
#> [1] 20
#> 
#> $outcome_bounds$y1$control$statistic
#> $outcome_bounds$y1$control$statistic$vhat
#> [1] 0.01650368
#> 
#> $outcome_bounds$y1$control$statistic$projected_vhat
#> [1] 0.01650368
#> 
#> $outcome_bounds$y1$control$statistic$sdhat
#> [1] 0.1284667
#> 
#> $outcome_bounds$y1$control$statistic$beta_l
#> [1] 0.00625
#> 
#> $outcome_bounds$y1$control$statistic$beta_u
#> [1] 0.00625
#> 
#> 
#> 
#> 
#> $outcome_bounds$y2
#> $outcome_bounds$y2$treatment
#> $outcome_bounds$y2$treatment$L
#> [1] 0
#> 
#> $outcome_bounds$y2$treatment$U
#> [1] 0.25
#> 
#> $outcome_bounds$y2$treatment$vhat
#> [1] 0.03168856
#> 
#> $outcome_bounds$y2$treatment$method
#> [1] "bounded"
#> 
#> $outcome_bounds$y2$treatment$n
#> [1] 20
#> 
#> $outcome_bounds$y2$treatment$statistic
#> $outcome_bounds$y2$treatment$statistic$vhat
#> [1] 0.03168856
#> 
#> $outcome_bounds$y2$treatment$statistic$projected_vhat
#> [1] 0.03168856
#> 
#> $outcome_bounds$y2$treatment$statistic$sdhat
#> [1] 0.1780128
#> 
#> $outcome_bounds$y2$treatment$statistic$beta_l
#> [1] 0.00625
#> 
#> $outcome_bounds$y2$treatment$statistic$beta_u
#> [1] 0.00625
#> 
#> 
#> 
#> $outcome_bounds$y2$control
#> $outcome_bounds$y2$control$L
#> [1] 0
#> 
#> $outcome_bounds$y2$control$U
#> [1] 0.25
#> 
#> $outcome_bounds$y2$control$vhat
#> [1] 0.01994388
#> 
#> $outcome_bounds$y2$control$method
#> [1] "bounded"
#> 
#> $outcome_bounds$y2$control$n
#> [1] 20
#> 
#> $outcome_bounds$y2$control$statistic
#> $outcome_bounds$y2$control$statistic$vhat
#> [1] 0.01994388
#> 
#> $outcome_bounds$y2$control$statistic$projected_vhat
#> [1] 0.01994388
#> 
#> $outcome_bounds$y2$control$statistic$sdhat
#> [1] 0.1412228
#> 
#> $outcome_bounds$y2$control$statistic$beta_l
#> [1] 0.00625
#> 
#> $outcome_bounds$y2$control$statistic$beta_u
#> [1] 0.00625
#> 
#> 
#> 
#> 
#> 
#> $outcome_vhat
#> $outcome_vhat$treatment
#> [1] 0.01749479 0.03168856
#> 
#> $outcome_vhat$control
#> [1] 0.01650368 0.01994388
#> 
#> 
#> attr(,"class")
#> [1] "cmr_multiple_outcomes_rectangle" "list"