Check asymptotic feasibility of a ROPE-based design

Computes the asymptotic (n -> Inf) ceiling on Bayesian predictive power under H1 and the asymptotic floor on Bayesian predictive type-I error under H0, implied by the specified beta design priors and decision boundary. These quantities provide a necessary (but not sufficient) condition for the feasibility of a calibrated design, and can be used to diagnose "No feasible design found" results from design_singlearm_onestage_rope before running the full numerical root-finding search. See Lemma 1 (non-inferiority / superiority) and Lemma 2 (equivalence) in the accompanying manuscript.

Usage

check_feasibility_rope(
  p0,
  delta,
  da0,
  db0,
  da1,
  db1,
  direction = c("equivalence", "noninferiority", "superiority"),
  target_power = NULL,
  target_type1 = NULL,
  verbose = TRUE
)

Arguments

p0

Benchmark response probability.

delta

ROPE half-width (equivalence), NI margin, or superiority margin.

da0, db0

Design prior parameters under H0, Beta(da0, db0).

da1, db1

Design prior parameters under H1, Beta(da1, db1).

direction

Decision type: "equivalence", "noninferiority", or "superiority".

target_power

Target Bayesian predictive power under H1 (optional).

target_type1

Target Bayesian predictive type-I error under H0 (optional).

verbose

Logical; if TRUE (default), prints a human-readable feasibility report.

Value

A list with components power_ceiling, type1_floor, power_feasible (logical or NA if no target given), and type1_feasible (logical or NA if no target given).

Examples

check_feasibility_rope(
  p0 = 0.30, delta = 0.10,
  da0 = 45, db0 = 105, da1 = 44, db1 = 36,
  direction = "superiority",
  target_power = 0.80, target_type1 = 0.10
)
#> ROPE design feasibility check (asymptotic n -> Inf)
#> Direction: superiority 
#> Power ceiling: 0.9966 (target 0.80) -> OK
#> Type-I floor: 0.0052 (target 0.10) -> OK