Single Arm Average Operating Characteristics — avg_oc_wr

Function for calculating the average operating characteristics of two single arm bayesian designs for early gating with respect to the sample size in the experimental group and possible historical data.

avg_oc_wr_ne(
  N_e,
  true_RR_c = NULL,
  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,
  alpha_c,
  beta_c,
  trues = seq(0, 1, 0.001),
  adapt = 1,
  plot = T,
  coresnum = NULL,
  legend = T,
  legend.pos = "topleft"
)

Arguments

N_e	Sample Size in the experimental group. Can be either a single value or a vector.
true_RR_c	Default value is NULL. If specified, will be used in the generated plots, indicating the true achieved decision power and decision type 1 error. If not specified, will be set to either RR_h or hist_RR_c, depending on which was specified by the user.
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.
alpha_c	Alpha parameter of Beta Distribution for the control response rate used to calculate average operating characteristics. Corresponds to \(\alpha_c\).
beta_c	Beta parameter of Beta Distribution for the control response rate used to calculate average operating characteristics. Corresponds to \(\beta_c\).
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.
coresnum	Number of cores used for parallel computing, in case N_e is a vector. Default is the number of total cores - 1.
legend	Logical; whether or not to include legend in plot. Default is TRUE.
legend.pos	Position of legend. Default is "topleft".

Value

Either a vector containing the average decision power and average alpha (if N_e has length 1), or a matrix containing the average decision power and average decision alpha (if N_e has length > 1), where every row corresponds to one value of N_e.

Examples


# Setting 1
avg_oc_wr_ne(
  N_e = 50, delta = 0.08, delta_power = 0.13,
  confidence = 0.6, hist_RR_c = 0.5,
  alpha_c = 15, beta_c = 13
)
#> Avg. Dec. Alpha Avg. Dec. Power 
#>       0.3259171       0.7469275 

# Setting 2
avg_oc_wr_ne(
  N_e = 50, delta = 0.08, delta_power = 0.13,
  confidence = 0.6, RR_h = 0.5, N_h = 50,
  alpha_c = 15, beta_c = 13
)
#> Avg. Dec. Alpha Avg. Dec. Power 
#>       0.2667679       0.6905401