Package 'earlygating' reference manual

Title:	Properties of Bayesian Early Gating Designs
Description:	Computes the most important properties of four 'Bayesian' early gating designs (two single arm and two randomized controlled designs), such as minimum required number of successes in the experimental group to make a GO decision, operating characteristics and average operating characteristics with respect to the sample size. These might aid in deciding what design to use for the early phase trial.
Authors:	Elias Laurin Meyer [aut, cre]
Maintainer:	Elias Laurin Meyer <[email protected]>
License:	GPL-3
Version:	1.1
Built:	2025-02-12 04:25:34 UTC
Source:	https://github.com/el-meyer/earlygating

Single Arm Average Operating Characteristics

Description

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.

Usage

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"
)
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
)

# 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
)

# 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
)

# 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
)

RCT Average Operating Characteristics

Description

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

Usage

avg_oc_wr_ne_rct(
  N_c,
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  c_a = 0.5,
  c_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  N_h = NULL,
  RR_h = NULL,
  w = NULL,
  alpha_c,
  beta_c,
  trues = seq(0, 1, 0.01),
  plot = T,
  coresnum = NULL,
  legend = T,
  legend.pos = "topleft"
)
avg_oc_wr_ne_rct(
  N_c,
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  c_a = 0.5,
  c_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  N_h = NULL,
  RR_h = NULL,
  w = NULL,
  alpha_c,
  beta_c,
  trues = seq(0, 1, 0.01),
  plot = T,
  coresnum = NULL,
  legend = T,
  legend.pos = "topleft"
)

Arguments

`N_c`	Sample Size in the control group. Can be either a single value or a vector, but needs to be the same length as N_e.
`N_e`	Sample Size in the experimental group. Can be either a single value or a vector, but needs to be the same length as N_c.
`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 $\frac{1}{2}$ .
`c_a`	Alpha parameter of Beta Prior Distribution for the control response rate. Corresponds to $\alpha_c$ . Default is $\frac{1}{2}$ .
`c_b`	Beta parameter of Beta Prior Distribution for the control response rate. Corresponds to $\beta_c$ . 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, N_h and w 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, N_h and w are also specified. Default is $\frac{1}{2}$ .
`N_h`	Historical control sample size. Corresponds to $n_h$ . If specified together with RR_h and w, function will use setting 4 from pdf.
`RR_h`	Historical control response rate. Corresponds to $p_h$ . If specified together with N_h and w, function will use setting 4 from pdf.
`w`	Level of dynmaic borrowing. Corresponds to $w$ .
`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.
`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 3
avg_oc_wr_ne_rct(
N_c = 25, N_e = 25, delta = 0.08,
delta_power = 0.13, confidence = 0.6,
alpha_c = 15, beta_c = 13
)



# Setting 4
avg_oc_wr_ne_rct(
N_c = 25, N_e = 25, delta = 0.08,
delta_power = 0.13, confidence = 0.6,
alpha_c = 15, beta_c = 13,
RR_h = 0.5, N_h = 100, w = 0.3
)

# Setting 3
avg_oc_wr_ne_rct(
N_c = 25, N_e = 25, delta = 0.08,
delta_power = 0.13, confidence = 0.6,
alpha_c = 15, beta_c = 13
)



# Setting 4
avg_oc_wr_ne_rct(
N_c = 25, N_e = 25, delta = 0.08,
delta_power = 0.13, confidence = 0.6,
alpha_c = 15, beta_c = 13,
RR_h = 0.5, N_h = 100, w = 0.3
)

Average operating characteristics with respect to historic target

Description

Function for calculating the average operating characteristics of a single arm Bayesian designs for early gating with respect to the historic target.

Usage

avg_oc_wr_ph(
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  alpha_c,
  beta_c,
  trues = seq(0, 1, 0.01),
  adapt = 1,
  plot = T,
  legend = T,
  legend.pos = "topleft"
)
avg_oc_wr_ph(
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  alpha_c,
  beta_c,
  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 $\frac{1}{2}$ .
`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.
`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 information about the decision power and the decision alpha with respect to p_h.

Examples


avg_oc_wr_ph(
  N_e = 50, delta = 0.08, delta_power = 0.13,
  confidence = 0.6, alpha_c = 15, beta_c = 13
)

avg_oc_wr_ph(
  N_e = 50, delta = 0.08, delta_power = 0.13,
  confidence = 0.6, alpha_c = 15, beta_c = 13
)

Parameters of Beta distribution given Historical Data

Description

Function for calculating the parameters of the beta distribution used to average the operating characteristics, given historical data.

Usage

beta_par(
  mu_cov,
  phi_cov = NULL,
  orr,
  data,
  newdata,
  link = NULL,
  weights = NULL,
  plot = T
)
beta_par(
  mu_cov,
  phi_cov = NULL,
  orr,
  data,
  newdata,
  link = NULL,
  weights = NULL,
  plot = T
)

Arguments

`mu_cov`	A character vector containing the names of covariates in data that should be used to model the parameter $\mu$ in the pdf.
`phi_cov`	A character vector containing the names of covariates in data that should be used to model the parameter $\phi$ in the pdf. Default is NULL, so $\phi$ will not be modelled with respect to the covariates.
`orr`	Character containing the name of the variable in data that represents the objective response rate.
`data`	Data frame containing all the covariates and the ORR.
`newdata`	Data frame containing a single value for each of the specified covariates that will be used to estimate the parameters of the Beta distribution.
`link`	Link function for $\mu$ . Corresponds to $g$ . Default is NULL, which means the link function will be automatically chosen as the one yielding the highest log-likelihood for the given data and covariates.
`weights`	Weights that should be used for regression. Default is NULL, so no weights.
`plot`	Plots yes or no. Default is TRUE.

Examples


mu_cov <- c("date", "Phase")
orr <- "ORR"
newdata <- data.frame(
  "date" = 2017,
  "Phase" = factor(3)
  )
studs <- data.frame(
  "ORR"= c(0.693, 0.580, 0.693, 0.477, 0.609,
           0.727, 0.727, 0.591, 0.362, 0.593,
           0.792, 0.620, 0.550, 0.690, 0.776),
  "date" = c(2011, 2008.5, 2009, 1996, 2001,
             2003.5, 2002.5, 2008, 2000,
             2006, 2005, 2007.5, 2009.5,
             2010.5, 2010),
   "Phase" = factor(c(3, 2, 3, 3, 2, 2, 3, 3,
                      3, 3, 2, 3, 3, 3, 2)),
   "N" = c(293, 69, 336, 235, 92, 110, 131,
           208, 94, 123, 53, 182, 267, 239, 237)
 )

beta_par(
  mu_cov = mu_cov,
  orr = orr,
  data = studs,
  newdata = newdata,
  weights = studs$N/mean(studs$N)
)

mu_cov <- c("date", "Phase")
orr <- "ORR"
newdata <- data.frame(
  "date" = 2017,
  "Phase" = factor(3)
  )
studs <- data.frame(
  "ORR"= c(0.693, 0.580, 0.693, 0.477, 0.609,
           0.727, 0.727, 0.591, 0.362, 0.593,
           0.792, 0.620, 0.550, 0.690, 0.776),
  "date" = c(2011, 2008.5, 2009, 1996, 2001,
             2003.5, 2002.5, 2008, 2000,
             2006, 2005, 2007.5, 2009.5,
             2010.5, 2010),
   "Phase" = factor(c(3, 2, 3, 3, 2, 2, 3, 3,
                      3, 3, 2, 3, 3, 3, 2)),
   "N" = c(293, 69, 336, 235, 92, 110, 131,
           208, 94, 123, 53, 182, 267, 239, 237)
 )

beta_par(
  mu_cov = mu_cov,
  orr = orr,
  data = studs,
  newdata = newdata,
  weights = studs$N/mean(studs$N)
)

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"
)
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
)

# 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
)

RCT Operating Characteristics

Description

Function for calculating the operating characteristics of the RCT Bayesian designs in setting 3 and 4 for early gating.

Usage

oc_rct(
  N_c,
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  c_a = 0.5,
  c_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  RR_h = NULL,
  N_h = NULL,
  w = NULL,
  trues = seq(0, 1, 0.01),
  plot = T,
  legend = T,
  legend.pos = "topleft"
)
oc_rct(
  N_c,
  N_e,
  delta,
  delta_power,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  c_a = 0.5,
  c_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  RR_h = NULL,
  N_h = NULL,
  w = NULL,
  trues = seq(0, 1, 0.01),
  plot = T,
  legend = T,
  legend.pos = "topleft"
)

Arguments

`N_c`	Sample Size in the control group. Can be either a single value or a vector, but needs to be the same length as N_e.
`N_e`	Sample Size in the experimental group. Can be either a single value or a vector, but needs to be the same length as N_c.
`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 $\frac{1}{2}$ .
`c_a`	Alpha parameter of Beta Prior Distribution for the control response rate. Corresponds to $\alpha_c$ . Default is $\frac{1}{2}$ .
`c_b`	Beta parameter of Beta Prior Distribution for the control response rate. Corresponds to $\beta_c$ . 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, N_h and w 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, N_h and w are also specified. Default is $\frac{1}{2}$ .
`RR_h`	Historical control response rate. Corresponds to $p_h$ . If specified together with N_h and w, function will use setting 4 from pdf.
`N_h`	Historical control sample size. Corresponds to $n_h$ . If specified together with RR_h and w, function will use setting 4 from pdf.
`w`	Level of dynmaic borrowing. Corresponds to $w$ .
`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.
`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 3
oc_rct(
  N_c = 25, N_e = 25, delta = 0.08,
  delta_power = 0.13, confidence = 0.6
)

# Setting 4
oc_rct(
  N_c = 25, N_e = 25, delta = 0.08,
  delta_power = 0.13, confidence = 0.6,
  RR_h = 0.5, N_h = 50, w = 0.3
)

# Setting 3
oc_rct(
  N_c = 25, N_e = 25, delta = 0.08,
  delta_power = 0.13, confidence = 0.6
)

# Setting 4
oc_rct(
  N_c = 25, N_e = 25, delta = 0.08,
  delta_power = 0.13, confidence = 0.6,
  RR_h = 0.5, N_h = 50, w = 0.3
)

Required Responders for GO decision Single Arm

Description

Function for calculating the minimum required number of responders in the experimental group to make a GO decision in Settings 1 and 2.

Usage

req_resp(
  N_e,
  delta,
  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,
  adapt = 1
)
req_resp(
  N_e,
  delta,
  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,
  adapt = 1
)

Arguments

`N_e`	Sample Size in the experimental group.
`delta`	Required superiority to make a "GO" decision. Corresponds to $\delta$ .
`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.
`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.

Value

Integer.

Examples


# Setting 1
req_resp(
  N_e = 50, delta = 0.08,
  confidence = 0.6, hist_RR_c = 0.5
)

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

# Setting 1
req_resp(
  N_e = 50, delta = 0.08,
  confidence = 0.6, hist_RR_c = 0.5
)

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

Required Responders for GO decision RCT

Description

Function for calculating the minimum required number of responders in the experimental group to make a GO decision in Settings 3 and 4.

Usage

req_resp_rct(
  N_c,
  N_e,
  delta,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  c_a = 0.5,
  c_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  RR_h = NULL,
  N_h = NULL,
  w = NULL,
  plot = T
)
req_resp_rct(
  N_c,
  N_e,
  delta,
  confidence,
  e_a = 0.5,
  e_b = 0.5,
  c_a = 0.5,
  c_b = 0.5,
  h_a = 0.5,
  h_b = 0.5,
  RR_h = NULL,
  N_h = NULL,
  w = NULL,
  plot = T
)

Arguments

`N_c`	Sample Size in the control group.
`N_e`	Sample Size in the experimental group.
`delta`	Required superiority to make a "GO" decision. Corresponds to $\delta$ .
`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 $\frac{1}{2}$ .
`c_a`	Alpha parameter of Beta Prior Distribution for the control response rate. Corresponds to $\alpha_c$ . Default is $\frac{1}{2}$ .
`c_b`	Beta parameter of Beta Prior Distribution for the control response rate. Corresponds to $\beta_c$ . 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, N_h and w 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, N_h and w are also specified. Default is $\frac{1}{2}$ .
`RR_h`	Historical control response rate. Corresponds to $p_h$ . If specified together with N_h and w, function will use setting 4 from pdf.
`N_h`	Historical control sample size. Corresponds to $n_h$ . If specified together with RR_h and w, function will use setting 4 from pdf.
`w`	Level of dynmaic borrowing. Corresponds to $w$ .
`plot`	Plots yes or no. Default is TRUE.

Value

Matrix containing pairs of successes in control group and respective required successes in experimental group.

Examples


# Setting 3
req_resp_rct(
  N_c = 25, N_e = 25,
  delta = 0.08, confidence = 0.6
)

# Setting 4
req_resp_rct(
  N_c = 25, N_e = 25,
  delta = 0.08, confidence = 0.6,
  RR_h = 0.5, N_h = 50, w = 0.3
)

# Setting 3
req_resp_rct(
  N_c = 25, N_e = 25,
  delta = 0.08, confidence = 0.6
)

# Setting 4
req_resp_rct(
  N_c = 25, N_e = 25,
  delta = 0.08, confidence = 0.6,
  RR_h = 0.5, N_h = 50, w = 0.3
)

Package 'earlygating'

Help Index

Single Arm Average Operating Characteristics

Description

Usage

Arguments

Value

Examples

RCT Average Operating Characteristics

Description

Usage

Arguments

Value

Examples

Average operating characteristics with respect to historic target

Description

Usage

Arguments

Value

Examples

Parameters of Beta distribution given Historical Data

Description

Usage

Arguments

Examples

Single Arm Operating Characteristics

Description

Usage

Arguments

Value

Examples

RCT Operating Characteristics

Description

Usage

Arguments

Value

Examples

Required Responders for GO decision Single Arm

Description

Usage

Arguments

Value

Examples

Required Responders for GO decision RCT

Description

Usage

Arguments

Value

Examples