oc {earlygating}

Single Arm Operating Characteristics

Description

Function for calculating the operating characteristics of the single arm Bayesian designs in setting 1 and 2 for early gating.

Usage

oc(
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  RR_h = NULL,
  N_h = NULL,
  hist_RR_c = NULL,
  trues = seq(0, 1, 0.01),
  adapt = 1,
  plot = T,
  legend = T,
  legend.pos = "topleft"
)

Arguments

N_e

Sample Size in the experimental group. Can be either a single value or a vector.

delta

Required superiority to make a "GO" decision. Corresponds to \delta.

delta_power

Superiority, at which decision power will be evaluated. Corresponds to \bar{\delta}.

confidence

Required confidence to make "GO" decision. Corresponds to \gamma.

e_a

Alpha parameter of Beta Prior Distribution for the experimental response rate. Corresponds to \alpha_e. Default is \frac{1}{2}.

e_b

Beta parameter of Beta Prior Distribution for the experimental response rate. Corresponds to \beta_e. Default is \frac{1}{2}.

h_a

Alpha parameter of Beta Prior Distribution for the historical control response rate. Corresponds to \alpha_h. Only needs to be specified, if RR_h and N_h are also specified. Default is \frac{1}{2}.

h_b

Beta parameter of Beta Prior Distribution for the historical control response rate. Corresponds to \beta_h. Only needs to be specified, if RR_h and N_h are also specified. Default is \frac{1}{2}.

RR_h

Historical control response rate. Corresponds to p_h. If specified together with N_h, function will use setting 2 from pdf.

N_h

Historical control sample size. Corresponds to n_h. If specified together with RR_h, function will use setting 2 from pdf.

hist_RR_c

Point estimate of historical control repsonse rate. Corresponds to \hat{p_h}. If specified, while RR_h and N_h are not specified, function will use setting 1 from pdf.

trues

Sequence of true control response rates and experimental response rates, at which the Probability to Go will be computed. Default is seq(0,1,0.01) to ensure continuous plots and accurate results.

adapt

Level of adapting of experimental control rate to account for patient selection bias from phase II to phase III. Corresponds to \xi. Default is 1, so no adapting.

plot

Plots yes or no. Default is TRUE.

legend

Logical; whether or not to include legend in plot. Default is TRUE.

legend.pos

Position of legend. Default is "topleft".

Value

A matrix containing the decision power and decision alpha with respect to the true control response rate.

Examples

# Setting 1
oc(
  N_e = 50, delta = 0.08, delta_power = 0.13,
  confidence = 0.6, hist_RR_c = 0.5
)

# Setting 2
oc(
  N_e = 50, delta = 0.08, delta_power = 0.13,
  confidence = 0.6, RR_h = 0.5, N_h = 50
)