tout (version 1.0.3)

tout_design: Find optimal sample size and progression criteria

Description

Given a null and alternative hypothesis, this function finds the lowest sample size such that a design with optimal progression criteria (as determined by the function opt_pc) satisfies upper constraints on three operating characteristics.

Usage

tout_design(
  rho_0,
  rho_1,
  alpha_nom,
  beta_nom,
  gamma_nom = 1,
  eta_0 = 0.5,
  eta_1 = eta_0,
  tau = c(0, 0),
  max_n = NULL,
  n = NULL,
  x = NULL,
  sigma = NULL
)

Value

An object of class tout, which is a list containing the following components:

valid

boolean indicating if the nominal constraints are met.

n

sample size.

thesholds

numeric vector of the two decision thresholds.

alpha

attained value of operating characteristic alpha.

beta

attained value of operating characteristic beta.

gamma

attained value of operating characteristic gamma.

Arguments

rho_0

null hypothesis.

rho_1

alternative hypothesis.

alpha_nom

nominal upper constraint on alpha.

beta_nom

nominal upper constraint on beta.

gamma_nom

nominal upper constraint on gamma. Defaults to 1.

eta_0

probability of an incorrect decision under the null hypothesis after an intermediate result. Defaults to 0.5.

eta_1

probability of an incorrect decision under the alternative hypothesis after an intermediate result. Defaults to eta_0.

tau

two element vector denoting lower and upper limits of the effect of adjustment.

max_n

optional upper limit to use in search over sample sizes.

n

optional sample size (optimised if left unspecified).

x

optional vector of decision thresholds (optimised if left unspecified).

sigma

standard deviation of outcome. If left unspecified, a binary outcome is assumed.

Examples

rho_0 <- 0.5
rho_1 <- 0.7
alpha_nom <- 0.05
beta_nom <- 0.2

tout_design(rho_0, rho_1, alpha_nom, beta_nom)

# Allowing for adjustment effects:

tout_design(rho_0, rho_1, alpha_nom, beta_nom, tau = c(0.08, 0.12))

# Allowing for different error probabilities following a pause decision

tout_design(rho_0, rho_1, alpha_nom, beta_nom, eta_0 = 0.3)

# Designs for continuous outcomes:

tout_design(rho_0 = 0, rho_1 = 0.4, alpha_nom, beta_nom, sigma = 1)