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Go/NoGo/Gray Decision Probabilities for Two Continuous Endpoints

Source: R/pbayesdecisionprob2cont.R
pbayesdecisionprob2cont.Rd

Computes the operating characteristics (Go, NoGo, Gray, and optionally Miss probabilities) for a two-continuous-endpoint Bayesian Go/NoGo decision framework by Monte Carlo simulation over treatment scenarios.

Usage

pbayesdecisionprob2cont(
  nsim,
  prob,
  design,
  prior,
  GoRegions,
  NoGoRegions,
  gamma_go,
  gamma_nogo,
  theta_TV1 = NULL,
  theta_MAV1 = NULL,
  theta_TV2 = NULL,
  theta_MAV2 = NULL,
  theta_NULL1 = NULL,
  theta_NULL2 = NULL,
  n_t,
  n_c = NULL,
  m_t = NULL,
  m_c = NULL,
  mu_t,
  Sigma_t,
  mu_c = NULL,
  Sigma_c = NULL,
  kappa0_t = NULL,
  nu0_t = NULL,
  mu0_t = NULL,
  Lambda0_t = NULL,
  kappa0_c = NULL,
  nu0_c = NULL,
  mu0_c = NULL,
  Lambda0_c = NULL,
  r = NULL,
  ne_t = NULL,
  ne_c = NULL,
  alpha0e_t = NULL,
  alpha0e_c = NULL,
  bar_ye_t = NULL,
  bar_ye_c = NULL,
  se_t = NULL,
  se_c = NULL,
  nMC = NULL,
  CalcMethod = "MC",
  error_if_Miss = TRUE,
  Gray_inc_Miss = FALSE,
  seed
)

Arguments

nsim

A positive integer. Number of simulated datasets per scenario.

prob

A character string specifying the probability type. Must be 'posterior' or 'predictive'.

design

A character string specifying the trial design. Must be 'controlled', 'uncontrolled', or 'external'.

prior

A character string specifying the prior distribution. Must be 'vague' or 'N-Inv-Wishart'.

GoRegions

An integer vector specifying which of the nine posterior regions (R1–R9) or four predictive regions (R1–R4) constitute a Go decision. For prob = 'posterior', valid values are integers in 1–9; for prob = 'predictive', in 1–4. A common choice is GoRegions = 1 (both endpoints exceed TV or NULL for posterior/predictive, respectively).

NoGoRegions

An integer vector specifying which regions constitute a NoGo decision. A common choice is NoGoRegions = 9 (both endpoints below MAV) for posterior, or NoGoRegions = 4 for predictive. Must be disjoint from GoRegions.

gamma_go

A numeric scalar in (0, 1). Go threshold: a Go decision is made if \(P(\mathrm{GoRegions}) \ge \gamma_1\).

gamma_nogo

A numeric scalar in (0, 1). NoGo threshold: a NoGo decision is made if \(P(\mathrm{NoGoRegions}) \ge \gamma_2\). No ordering constraint on gamma_go and gamma_nogo is imposed; their combination determines the frequency of Miss outcomes.

theta_TV1

A numeric scalar giving the target value (TV) threshold for Endpoint 1. Required when prob = 'posterior'; must satisfy theta_TV1 > theta_MAV1. Set to NULL when prob = 'predictive'.

theta_MAV1

A numeric scalar giving the minimum acceptable value (MAV) threshold for Endpoint 1. Required when prob = 'posterior'; must satisfy theta_TV1 > theta_MAV1. Set to NULL when prob = 'predictive'.

theta_TV2

A numeric scalar giving the target value (TV) threshold for Endpoint 2. Required when prob = 'posterior'; must satisfy theta_TV2 > theta_MAV2. Set to NULL when prob = 'predictive'.

theta_MAV2

A numeric scalar giving the minimum acceptable value (MAV) threshold for Endpoint 2. Required when prob = 'posterior'; must satisfy theta_TV2 > theta_MAV2. Set to NULL when prob = 'predictive'.

theta_NULL1

A numeric scalar giving the null hypothesis threshold for Endpoint 1. Required when prob = 'predictive'; set to NULL when prob = 'posterior'.

theta_NULL2

A numeric scalar giving the null hypothesis threshold for Endpoint 2. Required when prob = 'predictive'; set to NULL when prob = 'posterior'.

n_t

A positive integer giving the number of patients in the treatment group in the proof-of-concept (PoC) trial.

n_c

A positive integer giving the number of patients in the control group in the PoC trial. For design = 'uncontrolled', this is the hypothetical control sample size (required for consistency with other designs).

m_t

A positive integer giving the number of patients in the treatment group for the future trial. Required when prob = 'predictive'; otherwise set to NULL.

m_c

A positive integer giving the number of patients in the control group for the future trial. Required when prob = 'predictive'; otherwise set to NULL.

mu_t

Numeric matrix with 2 columns. Each row gives the true treatment mean vector for one scenario. A length-2 vector is coerced to a 1-row matrix.

Sigma_t

A 2x2 positive-definite matrix. True treatment covariance.

mu_c

Numeric matrix with 2 columns or a length-2 vector. True control (or hypothetical control) mean vector(s).

Sigma_c

A 2x2 positive-definite matrix. True control covariance.

kappa0_t

A positive numeric scalar giving the NIW prior concentration parameter for the treatment group. Required when prior = 'N-Inv-Wishart'; otherwise set to NULL.

nu0_t

A numeric scalar giving the NIW prior degrees of freedom for the treatment group. Must be greater than 3. Required when prior = 'N-Inv-Wishart'; otherwise set to NULL.

mu0_t

A numeric vector of length 2 giving the NIW prior mean for the treatment group. Required when prior = 'N-Inv-Wishart'; otherwise set to NULL.

Lambda0_t

A 2x2 positive-definite numeric matrix giving the NIW prior scale matrix for the treatment group. Required when prior = 'N-Inv-Wishart'; otherwise set to NULL.

kappa0_c

A positive numeric scalar giving the NIW prior concentration parameter for the control group. Required when prior = 'N-Inv-Wishart' and design != 'uncontrolled'; otherwise set to NULL.

nu0_c

A numeric scalar giving the NIW prior degrees of freedom for the control group. Must be greater than 3. Required when prior = 'N-Inv-Wishart' and design != 'uncontrolled'; otherwise set to NULL.

mu0_c

A numeric vector of length 2 giving the NIW prior mean for the control group, or the hypothetical control location when design = 'uncontrolled'. Required when prior = 'N-Inv-Wishart'; otherwise set to NULL.

Lambda0_c

A 2x2 positive-definite numeric matrix giving the NIW prior scale matrix for the control group. Required when prior = 'N-Inv-Wishart' and design != 'uncontrolled'; otherwise set to NULL.

r

A positive numeric scalar giving the variance scaling factor for the hypothetical control distribution. Required when design = 'uncontrolled'; otherwise set to NULL.

ne_t

A positive integer giving the external treatment group sample size. Required when design = 'external' and external treatment data are used; otherwise set to NULL.

ne_c

A positive integer giving the external control group sample size. Required when design = 'external' and external control data are used; otherwise set to NULL.

alpha0e_t

A numeric scalar in (0, 1] giving the power prior weight for the external treatment data. Required when external treatment data are used; otherwise set to NULL.

alpha0e_c

A numeric scalar in (0, 1] giving the power prior weight for the external control data. Required when external control data are used; otherwise set to NULL.

bar_ye_t

A numeric vector of length 2 giving the external treatment group sample mean. Required when external treatment data are used; otherwise set to NULL.

bar_ye_c

A numeric vector of length 2 giving the external control group sample mean. Required when external control data are used; otherwise set to NULL.

se_t

A 2x2 numeric matrix giving the external treatment group sum-of-squares matrix. Required when external treatment data are used; otherwise set to NULL.

se_c

A 2x2 numeric matrix giving the external control group sum-of-squares matrix. Required when external control data are used; otherwise set to NULL.

nMC

A positive integer giving the number of Monte Carlo draws used to estimate region probabilities. Default is 10000. Required when CalcMethod = 'MC'. May be set to NULL when CalcMethod = 'MM' and \(\nu_k > 4\) (the MM method uses mvtnorm::pmvt analytically); if CalcMethod = 'MM' but \(\nu_k \le 4\) causes a fallback to MC, nMC must be a positive integer.

CalcMethod

A character string specifying the computation method. Must be 'MC' (Monte Carlo, default) or 'MM' (Moment-Matching via mvtnorm::pmvt). When CalcMethod = 'MM' and \(\nu_k \le 4\), a warning is issued and the function falls back to CalcMethod = 'MC'.

error_if_Miss

Logical. If TRUE (default), the function stops with an error when positive Miss probability is obtained. If FALSE, Miss probability is handled according to Gray_inc_Miss.

Gray_inc_Miss

Logical. If TRUE, Miss probability is included in Gray probability. If FALSE (default), Miss probability is reported as a separate column. Active only when error_if_Miss = FALSE.

seed

A single numeric value. Seed for reproducible random number generation.

Value

A data frame of class c("pbayesdecisionprob2cont", "data.frame") with columns for the scenario parameters and Go, NoGo, Gray (and optionally Miss) probabilities. All input parameters are attached as attributes.

Details

The function follows the same structure as pbayesdecisionprob1cont:

  1. For each scenario \(s\), nsim datasets are simulated by generating treatment (and control) observations from \(N_2(\mu_k^{(s)}, \Sigma_k)\). To minimise overhead, raw standardised residuals are generated once (scenario- invariant) and shifted by the scenario mean.

  2. All nsim simulated sufficient statistics \((\bar{y}_{1,i}, S_{1,i})\) (and \((\bar{y}_{2,i}, S_{2,i})\) for controlled/external designs) are passed to pbayespostpred2cont in a single vectorised call, returning an \(nsim \times n_{\rm regions}\) matrix of region probabilities.

  3. Go/NoGo/Miss probabilities are obtained as the column means of indicator matrices derived from the region probability matrix.

Examples

# Example 1: Controlled design, posterior probability, vague prior
Sigma <- matrix(c(4.0, 0.8, 0.8, 1.0), 2, 2)
pbayesdecisionprob2cont(
  nsim = 100L, prob = 'posterior', design = 'controlled',
  prior = 'vague',
  GoRegions = 1L, NoGoRegions = 9L,
  gamma_go = 0.8, gamma_nogo = 0.8,
  theta_TV1 = 1.5, theta_MAV1 = 0.5,
  theta_TV2 = 1.0, theta_MAV2 = 0.3,
  theta_NULL1 = NULL, theta_NULL2 = NULL,
  n_t = 20L, n_c = 20L, m_t = NULL, m_c = NULL,
  mu_t = rbind(c(1.0, 0.5), c(2.5, 1.5), c(4.0, 2.5)),
  Sigma_t = Sigma,
  mu_c = rbind(c(0.0, 0.0), c(0.0, 0.0), c(0.0, 0.0)),
  Sigma_c = Sigma,
  kappa0_t = NULL, nu0_t = NULL, mu0_t = NULL, Lambda0_t = NULL,
  kappa0_c = NULL, nu0_c = NULL, mu0_c = NULL, Lambda0_c = NULL,
  r = NULL,
  ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
  bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
  nMC = 500L, CalcMethod = 'MC',
  error_if_Miss = TRUE, Gray_inc_Miss = FALSE, seed = 1L
)
#> Go/NoGo/Gray Decision Probabilities (Two Continuous Endpoints) 
#> ---------------------------------------------------------------- 
#>   Probability type : posterior 
#>   Design           : controlled 
#>   Prior            : vague 
#>   Method           : NULL 
#>   Simulations      : nsim = 100 
#>   MC draws         : nMC = 500 
#>   Seed             : 1 
#>   Threshold(s)     : TV1 = 1.5, MAV1 = 0.5 
#>                      TV2 = 1, MAV2 = 0.3 
#>   Go  threshold    : gamma_go = 0.8 
#>   NoGo threshold   : gamma_nogo = 0.8 
#>   Go  regions      : {1} 
#>   NoGo regions     : {9} 
#>   Sample size      : n_t = 20, n_c = 20 
#>   True cov (treat.): Sigma_t = [4, 0.8; 0.8, 1] 
#>   True cov (cont.) : Sigma_c = [4, 0.8; 0.8, 1] 
#>   Miss handling    : error_if_Miss = TRUE, Gray_inc_Miss = FALSE 
#> ---------------------------------------------------------------- 
#>  mu_t1 mu_t2 mu_c1 mu_c2     Go   Gray   NoGo
#>    1.0   0.5     0     0 0.0100 0.9800 0.0100
#>    2.5   1.5     0     0 0.5500 0.4500 0.0000
#>    4.0   2.5     0     0 1.0000 0.0000 0.0000
#> ---------------------------------------------------------------- 

# Example 2: Uncontrolled design, posterior probability, NIW prior
Sigma <- matrix(c(4.0, 0.8, 0.8, 1.0), 2, 2)
L0    <- matrix(c(8.0, 0.0, 0.0, 2.0), 2, 2)
pbayesdecisionprob2cont(
  nsim = 100L, prob = 'posterior', design = 'uncontrolled',
  prior = 'N-Inv-Wishart',
  GoRegions = 1L, NoGoRegions = 9L,
  gamma_go = 0.8, gamma_nogo = 0.8,
  theta_TV1 = 1.5, theta_MAV1 = 0.5,
  theta_TV2 = 1.0, theta_MAV2 = 0.3,
  theta_NULL1 = NULL, theta_NULL2 = NULL,
  n_t = 20L, n_c = NULL, m_t = NULL, m_c = NULL,
  mu_t = rbind(c(1.0, 0.5), c(2.5, 1.5), c(4.0, 2.5)),
  Sigma_t = Sigma,
  mu_c = rbind(c(0.0, 0.0), c(0.0, 0.0), c(0.0, 0.0)),
  Sigma_c = Sigma,
  kappa0_t = 2.0, nu0_t = 5.0, mu0_t = c(2.0, 1.0), Lambda0_t = L0,
  kappa0_c = NULL, nu0_c = NULL, mu0_c = c(0.0, 0.0), Lambda0_c = NULL,
  r = 1.0,
  ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
  bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
  nMC = 500L, CalcMethod = 'MC',
  error_if_Miss = TRUE, Gray_inc_Miss = FALSE, seed = 3L
)
#> Go/NoGo/Gray Decision Probabilities (Two Continuous Endpoints) 
#> ---------------------------------------------------------------- 
#>   Probability type : posterior 
#>   Design           : uncontrolled 
#>   Prior            : N-Inv-Wishart 
#>   Method           : NULL 
#>   Simulations      : nsim = 100 
#>   MC draws         : nMC = 500 
#>   Seed             : 3 
#>   Threshold(s)     : TV1 = 1.5, MAV1 = 0.5 
#>                      TV2 = 1, MAV2 = 0.3 
#>   Go  threshold    : gamma_go = 0.8 
#>   NoGo threshold   : gamma_nogo = 0.8 
#>   Go  regions      : {1} 
#>   NoGo regions     : {9} 
#>   Sample size      : n_t = 20, n_c = NULL 
#>   True cov (treat.): Sigma_t = [4, 0.8; 0.8, 1] 
#>   Prior (treatment): kappa0_t = 2, nu0_t = 5, mu0_t = (2, 1) 
#>                      Lambda0_t = [8, 0; 0, 2] 
#>   Hyp. control     : mu0_c = (0, 0), r = 1 
#>   Miss handling    : error_if_Miss = TRUE, Gray_inc_Miss = FALSE 
#> ---------------------------------------------------------------- 
#>  mu_t1 mu_t2     Go   Gray   NoGo
#>    1.0   0.5 0.0000 1.0000 0.0000
#>    2.5   1.5 0.6100 0.3900 0.0000
#>    4.0   2.5 1.0000 0.0000 0.0000
#> ---------------------------------------------------------------- 

# Example 3: External design (control only), posterior probability, NIW prior
Sigma  <- matrix(c(4.0, 0.8, 0.8, 1.0), 2, 2)
L0     <- matrix(c(8.0, 0.0, 0.0, 2.0), 2, 2)
se_mat <- matrix(c(7.0, 1.2, 1.2, 1.8), 2, 2)
pbayesdecisionprob2cont(
  nsim = 100L, prob = 'posterior', design = 'external',
  prior = 'N-Inv-Wishart',
  GoRegions = 1L, NoGoRegions = 9L,
  gamma_go = 0.8, gamma_nogo = 0.8,
  theta_TV1 = 1.5, theta_MAV1 = 0.5,
  theta_TV2 = 1.0, theta_MAV2 = 0.3,
  theta_NULL1 = NULL, theta_NULL2 = NULL,
  n_t = 20L, n_c = 20L, m_t = NULL, m_c = NULL,
  mu_t = rbind(c(1.0, 0.5), c(2.5, 1.5), c(4.0, 2.5)),
  Sigma_t = Sigma,
  mu_c = rbind(c(0.0, 0.0), c(0.0, 0.0), c(0.0, 0.0)),
  Sigma_c = Sigma,
  kappa0_t = 2.0, nu0_t = 5.0, mu0_t = c(2.0, 1.0), Lambda0_t = L0,
  kappa0_c = 2.0, nu0_c = 5.0, mu0_c = c(0.0, 0.0), Lambda0_c = L0,
  r = NULL,
  ne_t = NULL, ne_c = 15L, alpha0e_t = NULL, alpha0e_c = 0.5,
  bar_ye_t = NULL, bar_ye_c = c(0.2, 0.1), se_t = NULL, se_c = se_mat,
  nMC = 500L, CalcMethod = 'MC',
  error_if_Miss = TRUE, Gray_inc_Miss = FALSE, seed = 5L
)
#> Go/NoGo/Gray Decision Probabilities (Two Continuous Endpoints) 
#> --------------------------------------------------------------------- 
#>   Probability type : posterior 
#>   Design           : external 
#>   Prior            : N-Inv-Wishart 
#>   Method           : NULL 
#>   Simulations      : nsim = 100 
#>   MC draws         : nMC = 500 
#>   Seed             : 5 
#>   Threshold(s)     : TV1 = 1.5, MAV1 = 0.5 
#>                      TV2 = 1, MAV2 = 0.3 
#>   Go  threshold    : gamma_go = 0.8 
#>   NoGo threshold   : gamma_nogo = 0.8 
#>   Go  regions      : {1} 
#>   NoGo regions     : {9} 
#>   Sample size      : n_t = 20, n_c = 20 
#>   True cov (treat.): Sigma_t = [4, 0.8; 0.8, 1] 
#>   True cov (cont.) : Sigma_c = [4, 0.8; 0.8, 1] 
#>   Prior (treatment): kappa0_t = 2, nu0_t = 5, mu0_t = (2, 1) 
#>                      Lambda0_t = [8, 0; 0, 2] 
#>   Prior (control)  : kappa0_c = 2, nu0_c = 5, mu0_c = (0, 0) 
#>                      Lambda0_c = [8, 0; 0, 2] 
#>   External (treat.): ne_t = NULL, alpha0e_t = NULL 
#>   External (cont.) : ne_c = 15, alpha0e_c = 0.5 
#>                      bar_ye_c = (0.2, 0.1), se_c = (7, 1.2, 1.2, 1.8) 
#>   Miss handling    : error_if_Miss = TRUE, Gray_inc_Miss = FALSE 
#> --------------------------------------------------------------------- 
#>  mu_t1 mu_t2 mu_c1 mu_c2     Go   Gray   NoGo
#>    1.0   0.5     0     0 0.0000 1.0000 0.0000
#>    2.5   1.5     0     0 0.7000 0.3000 0.0000
#>    4.0   2.5     0     0 1.0000 0.0000 0.0000
#> --------------------------------------------------------------------- 

# Example 4: Controlled design, predictive probability, NIW prior
Sigma <- matrix(c(4.0, 0.8, 0.8, 1.0), 2, 2)
L0    <- matrix(c(8.0, 0.0, 0.0, 2.0), 2, 2)
pbayesdecisionprob2cont(
  nsim = 100L, prob = 'predictive', design = 'controlled',
  prior = 'N-Inv-Wishart',
  GoRegions = 1L, NoGoRegions = 4L,
  gamma_go = 0.8, gamma_nogo = 0.8,
  theta_TV1 = NULL, theta_MAV1 = NULL,
  theta_TV2 = NULL, theta_MAV2 = NULL,
  theta_NULL1 = 0.5, theta_NULL2 = 0.3,
  n_t = 20L, n_c = 20L, m_t = 60L, m_c = 60L,
  mu_t = rbind(c(1.0, 0.5), c(2.5, 1.5), c(4.0, 2.5)),
  Sigma_t = Sigma,
  mu_c = rbind(c(0.0, 0.0), c(0.0, 0.0), c(0.0, 0.0)),
  Sigma_c = Sigma,
  kappa0_t = 2.0, nu0_t = 5.0, mu0_t = c(2.0, 1.0), Lambda0_t = L0,
  kappa0_c = 2.0, nu0_c = 5.0, mu0_c = c(0.0, 0.0), Lambda0_c = L0,
  r = NULL,
  ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
  bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
  nMC = 500L, CalcMethod = 'MC',
  error_if_Miss = TRUE, Gray_inc_Miss = FALSE, seed = 4L
)
#> Go/NoGo/Gray Decision Probabilities (Two Continuous Endpoints) 
#> ---------------------------------------------------------------- 
#>   Probability type : predictive 
#>   Design           : controlled 
#>   Prior            : N-Inv-Wishart 
#>   Method           : NULL 
#>   Simulations      : nsim = 100 
#>   MC draws         : nMC = 500 
#>   Seed             : 4 
#>   Threshold(s)     : NULL1 = 0.5, NULL2 = 0.3 
#>   Go  threshold    : gamma_go = 0.8 
#>   NoGo threshold   : gamma_nogo = 0.8 
#>   Go  regions      : {1} 
#>   NoGo regions     : {4} 
#>   Sample size      : n_t = 20, n_c = 20 
#>   True cov (treat.): Sigma_t = [4, 0.8; 0.8, 1] 
#>   True cov (cont.) : Sigma_c = [4, 0.8; 0.8, 1] 
#>   Prior (treatment): kappa0_t = 2, nu0_t = 5, mu0_t = (2, 1) 
#>                      Lambda0_t = [8, 0; 0, 2] 
#>   Prior (control)  : kappa0_c = 2, nu0_c = 5, mu0_c = (0, 0) 
#>                      Lambda0_c = [8, 0; 0, 2] 
#>   Future trial     : m_t = 60, m_c = 60 
#>   Miss handling    : error_if_Miss = TRUE, Gray_inc_Miss = FALSE 
#> ---------------------------------------------------------------- 
#>  mu_t1 mu_t2 mu_c1 mu_c2     Go   Gray   NoGo
#>    1.0   0.5     0     0 0.4700 0.5300 0.0000
#>    2.5   1.5     0     0 1.0000 0.0000 0.0000
#>    4.0   2.5     0     0 1.0000 0.0000 0.0000
#> ---------------------------------------------------------------- 

# Example 5: Uncontrolled design, predictive probability, vague prior
Sigma <- matrix(c(4.0, 0.8, 0.8, 1.0), 2, 2)
pbayesdecisionprob2cont(
  nsim = 100L, prob = 'predictive', design = 'uncontrolled',
  prior = 'vague',
  GoRegions = 1L, NoGoRegions = 4L,
  gamma_go = 0.8, gamma_nogo = 0.8,
  theta_TV1 = NULL, theta_MAV1 = NULL,
  theta_TV2 = NULL, theta_MAV2 = NULL,
  theta_NULL1 = 0.5, theta_NULL2 = 0.3,
  n_t = 20L, n_c = NULL, m_t = 60L, m_c = 60L,
  mu_t = rbind(c(1.0, 0.5), c(2.5, 1.5), c(4.0, 2.5)),
  Sigma_t = Sigma,
  mu_c = NULL,
  Sigma_c = NULL,
  kappa0_t = NULL, nu0_t = NULL, mu0_t = NULL, Lambda0_t = NULL,
  kappa0_c = NULL, nu0_c = NULL, mu0_c = c(0.0, 0.0), Lambda0_c = NULL,
  r = 1.0,
  ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
  bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
  nMC = 500L, CalcMethod = 'MC',
  error_if_Miss = TRUE, Gray_inc_Miss = FALSE, seed = 8L
)
#> Go/NoGo/Gray Decision Probabilities (Two Continuous Endpoints) 
#> ---------------------------------------------------------------- 
#>   Probability type : predictive 
#>   Design           : uncontrolled 
#>   Prior            : vague 
#>   Method           : NULL 
#>   Simulations      : nsim = 100 
#>   MC draws         : nMC = 500 
#>   Seed             : 8 
#>   Threshold(s)     : NULL1 = 0.5, NULL2 = 0.3 
#>   Go  threshold    : gamma_go = 0.8 
#>   NoGo threshold   : gamma_nogo = 0.8 
#>   Go  regions      : {1} 
#>   NoGo regions     : {4} 
#>   Sample size      : n_t = 20, n_c = NULL 
#>   True cov (treat.): Sigma_t = [4, 0.8; 0.8, 1] 
#>   Hyp. control     : mu0_c = (0, 0), r = 1 
#>   Future trial     : m_t = 60, m_c = 60 
#>   Miss handling    : error_if_Miss = TRUE, Gray_inc_Miss = FALSE 
#> ---------------------------------------------------------------- 
#>  mu_t1 mu_t2     Go   Gray   NoGo
#>    1.0   0.5 0.3300 0.6700 0.0000
#>    2.5   1.5 1.0000 0.0000 0.0000
#>    4.0   2.5 1.0000 0.0000 0.0000
#> ---------------------------------------------------------------- 

# Example 6: External design (control only), predictive probability, NIW prior
Sigma  <- matrix(c(4.0, 0.8, 0.8, 1.0), 2, 2)
L0     <- matrix(c(8.0, 0.0, 0.0, 2.0), 2, 2)
se_mat <- matrix(c(7.0, 1.2, 1.2, 1.8), 2, 2)
pbayesdecisionprob2cont(
  nsim = 100L, prob = 'predictive', design = 'external',
  prior = 'N-Inv-Wishart',
  GoRegions = 1L, NoGoRegions = 4L,
  gamma_go = 0.8, gamma_nogo = 0.8,
  theta_TV1 = NULL, theta_MAV1 = NULL,
  theta_TV2 = NULL, theta_MAV2 = NULL,
  theta_NULL1 = 0.5, theta_NULL2 = 0.3,
  n_t = 20L, n_c = 20L, m_t = 60L, m_c = 60L,
  mu_t = rbind(c(1.0, 0.5), c(2.5, 1.5), c(4.0, 2.5)),
  Sigma_t = Sigma,
  mu_c = rbind(c(0.0, 0.0), c(0.0, 0.0), c(0.0, 0.0)),
  Sigma_c = Sigma,
  kappa0_t = 2.0, nu0_t = 5.0, mu0_t = c(2.0, 1.0), Lambda0_t = L0,
  kappa0_c = 2.0, nu0_c = 5.0, mu0_c = c(0.0, 0.0), Lambda0_c = L0,
  r = NULL,
  ne_t = NULL, ne_c = 15L, alpha0e_t = NULL, alpha0e_c = 0.5,
  bar_ye_t = NULL, bar_ye_c = c(0.2, 0.1), se_t = NULL, se_c = se_mat,
  nMC = 500L, CalcMethod = 'MC',
  error_if_Miss = TRUE, Gray_inc_Miss = FALSE, seed = 9L
)
#> Go/NoGo/Gray Decision Probabilities (Two Continuous Endpoints) 
#> --------------------------------------------------------------------- 
#>   Probability type : predictive 
#>   Design           : external 
#>   Prior            : N-Inv-Wishart 
#>   Method           : NULL 
#>   Simulations      : nsim = 100 
#>   MC draws         : nMC = 500 
#>   Seed             : 9 
#>   Threshold(s)     : NULL1 = 0.5, NULL2 = 0.3 
#>   Go  threshold    : gamma_go = 0.8 
#>   NoGo threshold   : gamma_nogo = 0.8 
#>   Go  regions      : {1} 
#>   NoGo regions     : {4} 
#>   Sample size      : n_t = 20, n_c = 20 
#>   True cov (treat.): Sigma_t = [4, 0.8; 0.8, 1] 
#>   True cov (cont.) : Sigma_c = [4, 0.8; 0.8, 1] 
#>   Prior (treatment): kappa0_t = 2, nu0_t = 5, mu0_t = (2, 1) 
#>                      Lambda0_t = [8, 0; 0, 2] 
#>   Prior (control)  : kappa0_c = 2, nu0_c = 5, mu0_c = (0, 0) 
#>                      Lambda0_c = [8, 0; 0, 2] 
#>   Future trial     : m_t = 60, m_c = 60 
#>   External (treat.): ne_t = NULL, alpha0e_t = NULL 
#>   External (cont.) : ne_c = 15, alpha0e_c = 0.5 
#>                      bar_ye_c = (0.2, 0.1), se_c = (7, 1.2, 1.2, 1.8) 
#>   Miss handling    : error_if_Miss = TRUE, Gray_inc_Miss = FALSE 
#> --------------------------------------------------------------------- 
#>  mu_t1 mu_t2 mu_c1 mu_c2     Go   Gray   NoGo
#>    1.0   0.5     0     0 0.4100 0.5800 0.0100
#>    2.5   1.5     0     0 1.0000 0.0000 0.0000
#>    4.0   2.5     0     0 1.0000 0.0000 0.0000
#> ---------------------------------------------------------------------