pbayesdecisionprob2bin: Go/NoGo/Gray Decision Probabilities for a Clinical Trial with...
In BayesianQDM: Bayesian Quantitative Decision-Making Framework for Binary and Continuous Endpoints
View source: R/pbayesdecisionprob2bin.R
pbayesdecisionprob2bin R Documentation
Go/NoGo/Gray Decision Probabilities for a Clinical Trial with Two Binary
Endpoints
Description
Evaluates operating characteristics (Go, NoGo, Gray probabilities) for
clinical trials with two binary endpoints under the Bayesian framework.
The function supports controlled, uncontrolled, and external designs,
and uses both posterior probability and posterior predictive probability
criteria.
Usage
pbayesdecisionprob2bin(
nsim = 10000L,
prob = "posterior",
design = "controlled",
GoRegions,
NoGoRegions,
gamma_go,
gamma_nogo,
pi_t1,
pi_t2,
rho_t,
pi_c1 = NULL,
pi_c2 = NULL,
rho_c = NULL,
n_t,
n_c = NULL,
a_t_00,
a_t_01,
a_t_10,
a_t_11,
a_c_00,
a_c_01,
a_c_10,
a_c_11,
m_t = NULL,
m_c = NULL,
theta_TV1 = NULL,
theta_MAV1 = NULL,
theta_TV2 = NULL,
theta_MAV2 = NULL,
theta_NULL1 = NULL,
theta_NULL2 = NULL,
z00 = NULL,
z01 = NULL,
z10 = NULL,
z11 = NULL,
xe_t_00 = NULL,
xe_t_01 = NULL,
xe_t_10 = NULL,
xe_t_11 = NULL,
xe_c_00 = NULL,
xe_c_01 = NULL,
xe_c_10 = NULL,
xe_c_11 = NULL,
alpha0e_t = NULL,
alpha0e_c = NULL,
nMC = 10000L,
CalcMethod = "Exact",
error_if_Miss = TRUE,
Gray_inc_Miss = FALSE
)
Arguments
nsim
A positive integer giving the number of PoC count vectors
sampled via rmultinom per arm per scenario when
CalcMethod = 'MC' (outer loop). The sampled vectors are
deduplicated into K_t and K_c unique vectors
(K_t, K_c \ll nsim); Dirichlet sampling is then
performed only for these unique vectors using nMC draws each.
Ignored when CalcMethod = 'Exact'. Default is 10000.
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'.
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.
pi_t1
A numeric vector of true treatment response probabilities
for Endpoint 1. Each element must be in (0, 1).
pi_t2
A numeric vector of true treatment response probabilities
for Endpoint 2. Must have the same length as pi_t1.
rho_t
A numeric vector of true within-treatment-arm correlations
between Endpoint 1 and Endpoint 2. Must have the same length as
pi_t1. If any element is outside the feasible range for
the corresponding (pi_t1, pi_t2) pair, that scenario returns
NA for all decision probabilities instead of stopping with
an error.
pi_c1
A numeric vector of true control response probabilities for
Endpoint 1. For design = 'uncontrolled', this parameter
is not used in probability calculations but must still be supplied;
it is retained in the output for reference. Must have the same
length as pi_t1.
pi_c2
A numeric vector of true control response probabilities for
Endpoint 2. For design = 'uncontrolled', see note for
pi_c1. Must have the same length as pi_t1.
rho_c
A numeric vector of true within-control-arm correlations.
For design = 'uncontrolled', not used in probability
calculations. Must have the same length as pi_t1. If any
element is outside the feasible range for the corresponding
(pi_c1, pi_c2) pair, that scenario returns NA for
all decision probabilities.
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).
a_t_00
A positive numeric scalar giving the Dirichlet prior
parameter for the (0, 0) response pattern in the treatment
group.
a_t_01
A positive numeric scalar giving the Dirichlet prior
parameter for the (0, 1) response pattern in the treatment
group.
a_t_10
A positive numeric scalar giving the Dirichlet prior
parameter for the (1, 0) response pattern in the treatment
group.
a_t_11
A positive numeric scalar giving the Dirichlet prior
parameter for the (1, 1) response pattern in the treatment
group.
a_c_00
A positive numeric scalar giving the Dirichlet prior
parameter for the (0, 0) response pattern in the control
group. For design = 'uncontrolled', serves as a
hyperparameter of the hypothetical control distribution.
a_c_01
A positive numeric scalar giving the Dirichlet prior
parameter for the (0, 1) response pattern in the control
group. For design = 'uncontrolled', serves as a
hyperparameter of the hypothetical control distribution.
a_c_10
A positive numeric scalar giving the Dirichlet prior
parameter for the (1, 0) response pattern in the control
group. For design = 'uncontrolled', serves as a
hyperparameter of the hypothetical control distribution.
a_c_11
A positive numeric scalar giving the Dirichlet prior
parameter for the (1, 1) response pattern in the control
group. For design = 'uncontrolled', serves as a
hyperparameter of the hypothetical control distribution.
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.
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'.
z00
A non-negative integer giving the hypothetical control count
for pattern (0, 0). Required when
design = 'uncontrolled'; otherwise set to NULL.
z01
A non-negative integer giving the hypothetical control count
for pattern (0, 1). Required when
design = 'uncontrolled'; otherwise set to NULL.
z10
A non-negative integer giving the hypothetical control count
for pattern (1, 0). Required when
design = 'uncontrolled'; otherwise set to NULL.
z11
A non-negative integer giving the hypothetical control count
for pattern (1, 1). Required when
design = 'uncontrolled'; otherwise set to NULL.
xe_t_00
A non-negative integer giving the external treatment group
count for pattern (0, 0). Required when
design = 'external' and external treatment data are used;
otherwise NULL.
xe_t_01
A non-negative integer giving the external treatment group
count for pattern (0, 1). Required for external treatment
data; otherwise NULL.
xe_t_10
A non-negative integer giving the external treatment group
count for pattern (1, 0). Required for external treatment
data; otherwise NULL.
xe_t_11
A non-negative integer giving the external treatment group
count for pattern (1, 1). Required for external treatment
data; otherwise NULL.
xe_c_00
A non-negative integer giving the external control group
count for pattern (0, 0). Required when
design = 'external' and external control data are used;
otherwise NULL.
xe_c_01
A non-negative integer giving the external control group
count for pattern (0, 1). Required for external control
data; otherwise NULL.
xe_c_10
A non-negative integer giving the external control group
count for pattern (1, 0). Required for external control
data; otherwise NULL.
xe_c_11
A non-negative integer giving the external control group
count for pattern (1, 1). Required for external control
data; otherwise NULL.
alpha0e_t
A numeric scalar in (0, 1] giving the power prior
weight for the treatment group. Required when external treatment
data are used; otherwise NULL.
alpha0e_c
A numeric scalar in (0, 1] giving the power prior
weight for the control group. Required when external control
data are used; otherwise NULL.
nMC
A positive integer giving the number of Dirichlet draws used to
evaluate the decision probability for each count combination in
Stage 1. Used by both CalcMethod = 'Exact' and
CalcMethod = 'MC' (inner loop). Default is 10000.
CalcMethod
A character string specifying the computation method.
Must be 'Exact' (default) or 'MC'.
'Exact' uses full enumeration of all possible multinomial
count combinations (two-stage approach described in Details).
'MC' samples nsim (x_t, x_c) pairs via
rmultinom, deduplicates them into K unique pairs
(K \ll nsim), calls
pbayespostpred2bin for each unique pair to obtain
Go/NoGo probabilities, and weights the decisions by the observed
pair frequencies. This reuses the same validated probability logic
as the Exact method, avoiding any duplication of computation.
The 'MC' method trades some Monte Carlo variance for
substantially reduced computation time when n_t and/or
n_c are large.
error_if_Miss
A logical scalar; if TRUE (default), the
function stops with an error if the Miss probability is positive,
prompting reconsideration of the thresholds.
Gray_inc_Miss
A logical scalar; if TRUE, the Miss
probability is added to Gray. If FALSE (default), Miss is
reported separately. Active only when
error_if_Miss = FALSE.
Details
Computation proceeds in two stages for efficiency. In Stage 1, posterior
or predictive probabilities are precomputed for every possible multinomial
count combination (x_t, x_c). In Stage 2, operating characteristics
for each scenario are obtained by weighting the Stage 1 decisions by their
multinomial probabilities under the true parameters, avoiding repeated Monte
Carlo sampling per scenario.
Two-stage computation.
Stage 1 (precomputation): All possible multinomial count combinations
x_t are enumerated using allmultinom.
For design = 'controlled' or 'external', all combinations
x_c are also enumerated and the Go/NoGo probability matrix
PrGo[i, j] has dimensions n_t \times n_c.
For design = 'uncontrolled', the control distribution is fixed as
\mathrm{Dir}(\alpha_{2,**} + z_{**}) and does not depend on any
observed control counts; the probability matrix therefore has dimensions
n_t \times 1, eliminating the \binom{n_2+3}{3}-row control
enumeration and the associated Gamma sampling.
This stage is independent of the true scenario parameters.
Stage 2 (scenario evaluation): For each scenario
(\pi_{t1}, \pi_{t2}, \rho_t, \pi_{c1}, \pi_{c2}, \rho_c),
getjointbin converts the marginal rates and correlation
into the four-cell probability vector p_k. The multinomial
probability mass function weights the Stage 1 decisions:
\Pr(\mathrm{Go} \mid \Theta) = \sum_{i,j}
\mathbf{1}(\mathrm{Go}_{ij}) \cdot
P(x_{t,i} \mid n_1, p_t) \cdot P(x_{c,j} \mid n_2, p_c),
where \mathbf{1}(\mathrm{Go}_{ij}) is the Go indicator from Stage 1.
Stage 2 requires no additional Monte Carlo and is fast even for large
scenario grids.
Decision categories.
-
Go: sum of Go region probabilities \ge \gamma_1
AND sum of NoGo region probabilities < \gamma_2.
-
NoGo: sum of Go region probabilities < \gamma_1
AND sum of NoGo region probabilities \ge \gamma_2.
-
Miss: both Go and NoGo criteria satisfied simultaneously.
-
Gray: neither Go nor NoGo criterion satisfied.
Value
A data frame with one row per scenario and columns:
- pi_t1
True treatment response probability for Endpoint 1.
- pi_t2
True treatment response probability for Endpoint 2.
- rho_t
True within-arm correlation in the treatment arm.
- pi_c1
True control response probability for Endpoint 1
(omitted when design = 'uncontrolled').
- pi_c2
True control response probability for Endpoint 2
(omitted when design = 'uncontrolled').
- rho_c
True within-arm correlation in the control arm
(omitted when design = 'uncontrolled').
- Go
Probability of making a Go decision.
- Gray
Probability of making a Gray (inconclusive) decision.
- NoGo
Probability of making a NoGo decision.
- Miss
Probability where Go and NoGo criteria are simultaneously
met. Included when error_if_Miss = FALSE and
Gray_inc_Miss = FALSE.
The returned object has S3 class pbayesdecisionprob2bin with
an associated print method.
Examples
# Example 1: Posterior probability, controlled design (rho > 0)
# Explores the impact of positive within-arm endpoint correlation.
pbayesdecisionprob2bin(
prob = 'posterior',
design = 'controlled',
GoRegions = 1L,
NoGoRegions = 9L,
gamma_go = 0.52,
gamma_nogo = 0.52,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.6, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.6, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = NULL, m_c = NULL,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 2: Posterior probability, uncontrolled design
# Hypothetical control specified via pseudo-counts.
pbayesdecisionprob2bin(
prob = 'posterior',
design = 'uncontrolled',
GoRegions = 1L,
NoGoRegions = 9L,
gamma_go = 0.27,
gamma_nogo = 0.36,
pi_t1 = c(0.15, 0.30, 0.40),
pi_t2 = c(0.20, 0.35, 0.45),
rho_t = rep(0.2, 3),
pi_c1 = NULL,
pi_c2 = NULL,
rho_c = NULL,
n_t = 10, n_c = NULL,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = NULL, m_c = NULL,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
z00 = 2L, z01 = 1L, z10 = 2L, z11 = 1L,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 3: Posterior probability, external control design
# External control data incorporated via power prior (alpha0e_c = 0.5).
pbayesdecisionprob2bin(
prob = 'posterior',
design = 'external',
GoRegions = 1L,
NoGoRegions = 9L,
gamma_go = 0.27,
gamma_nogo = 0.36,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.0, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.0, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = NULL, m_c = NULL,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = 4L, xe_c_01 = 2L, xe_c_10 = 3L, xe_c_11 = 1L,
alpha0e_t = NULL, alpha0e_c = 0.5,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 4: Predictive probability, controlled design
# Future trial has m_t = m_c = 30 patients per arm.
pbayesdecisionprob2bin(
prob = 'predictive',
design = 'controlled',
GoRegions = 1L,
NoGoRegions = 4L,
gamma_go = 0.60,
gamma_nogo = 0.80,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.3, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.3, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = 30L, m_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 5: Predictive probability, uncontrolled design
# Hypothetical control specified via pseudo-counts; future trial m_t = m_c = 30.
pbayesdecisionprob2bin(
prob = 'predictive',
design = 'uncontrolled',
GoRegions = 1L,
NoGoRegions = 4L,
gamma_go = 0.60,
gamma_nogo = 0.80,
pi_t1 = c(0.15, 0.30, 0.40),
pi_t2 = c(0.20, 0.35, 0.45),
rho_t = rep(0.7, 3),
pi_c1 = rep(0.15, 3),
pi_c2 = rep(0.20, 3),
rho_c = rep(0.7, 3),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = 30L, m_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
z00 = 2L, z01 = 1L, z10 = 2L, z11 = 1L,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 6: Predictive probability, external treatment design
# External treatment data incorporated via power prior (alpha0e_t = 0.5).
pbayesdecisionprob2bin(
prob = 'predictive',
design = 'external',
GoRegions = 1L,
NoGoRegions = 4L,
gamma_go = 0.60,
gamma_nogo = 0.80,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.5, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.5, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = 30L, m_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = 3L, xe_t_01 = 2L, xe_t_10 = 3L, xe_t_11 = 2L,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = 0.5, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
BayesianQDM documentation built on April 22, 2026, 1:09 a.m.
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View source: R/pbayesdecisionprob2bin.R
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Go/NoGo/Gray Decision Probabilities for a Clinical Trial with Two Binary Endpoints
Description
Evaluates operating characteristics (Go, NoGo, Gray probabilities) for clinical trials with two binary endpoints under the Bayesian framework. The function supports controlled, uncontrolled, and external designs, and uses both posterior probability and posterior predictive probability criteria.
Usage
pbayesdecisionprob2bin(
nsim = 10000L,
prob = "posterior",
design = "controlled",
GoRegions,
NoGoRegions,
gamma_go,
gamma_nogo,
pi_t1,
pi_t2,
rho_t,
pi_c1 = NULL,
pi_c2 = NULL,
rho_c = NULL,
n_t,
n_c = NULL,
a_t_00,
a_t_01,
a_t_10,
a_t_11,
a_c_00,
a_c_01,
a_c_10,
a_c_11,
m_t = NULL,
m_c = NULL,
theta_TV1 = NULL,
theta_MAV1 = NULL,
theta_TV2 = NULL,
theta_MAV2 = NULL,
theta_NULL1 = NULL,
theta_NULL2 = NULL,
z00 = NULL,
z01 = NULL,
z10 = NULL,
z11 = NULL,
xe_t_00 = NULL,
xe_t_01 = NULL,
xe_t_10 = NULL,
xe_t_11 = NULL,
xe_c_00 = NULL,
xe_c_01 = NULL,
xe_c_10 = NULL,
xe_c_11 = NULL,
alpha0e_t = NULL,
alpha0e_c = NULL,
nMC = 10000L,
CalcMethod = "Exact",
error_if_Miss = TRUE,
Gray_inc_Miss = FALSE
)
Arguments
nsim |
A positive integer giving the number of PoC count vectors
sampled via |
prob |
A character string specifying the probability type.
Must be |
design |
A character string specifying the trial design.
Must be |
GoRegions |
An integer vector specifying which of the nine posterior
regions (R1–R9) or four predictive regions (R1–R4) constitute a
Go decision. For |
NoGoRegions |
An integer vector specifying which regions constitute a
NoGo decision. A common choice is |
gamma_go |
A numeric scalar in |
gamma_nogo |
A numeric scalar in |
pi_t1 |
A numeric vector of true treatment response probabilities
for Endpoint 1. Each element must be in |
pi_t2 |
A numeric vector of true treatment response probabilities
for Endpoint 2. Must have the same length as |
rho_t |
A numeric vector of true within-treatment-arm correlations
between Endpoint 1 and Endpoint 2. Must have the same length as
|
pi_c1 |
A numeric vector of true control response probabilities for
Endpoint 1. For |
pi_c2 |
A numeric vector of true control response probabilities for
Endpoint 2. For |
rho_c |
A numeric vector of true within-control-arm correlations.
For |
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 |
a_t_00 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_t_01 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_t_10 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_t_11 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_c_00 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_c_01 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_c_10 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
a_c_11 |
A positive numeric scalar giving the Dirichlet prior
parameter for the |
m_t |
A positive integer giving the number of patients in the
treatment group for the future trial. Required when
|
m_c |
A positive integer giving the number of patients in the
control group for the future trial. Required when
|
theta_TV1 |
A numeric scalar giving the target value (TV) threshold
for Endpoint 1. Required when |
theta_MAV1 |
A numeric scalar giving the minimum acceptable value
(MAV) threshold for Endpoint 1. Required when
|
theta_TV2 |
A numeric scalar giving the target value (TV) threshold
for Endpoint 2. Required when |
theta_MAV2 |
A numeric scalar giving the minimum acceptable value
(MAV) threshold for Endpoint 2. Required when
|
theta_NULL1 |
A numeric scalar giving the null hypothesis threshold
for Endpoint 1. Required when |
theta_NULL2 |
A numeric scalar giving the null hypothesis threshold
for Endpoint 2. Required when |
z00 |
A non-negative integer giving the hypothetical control count
for pattern |
z01 |
A non-negative integer giving the hypothetical control count
for pattern |
z10 |
A non-negative integer giving the hypothetical control count
for pattern |
z11 |
A non-negative integer giving the hypothetical control count
for pattern |
xe_t_00 |
A non-negative integer giving the external treatment group
count for pattern |
xe_t_01 |
A non-negative integer giving the external treatment group
count for pattern |
xe_t_10 |
A non-negative integer giving the external treatment group
count for pattern |
xe_t_11 |
A non-negative integer giving the external treatment group
count for pattern |
xe_c_00 |
A non-negative integer giving the external control group
count for pattern |
xe_c_01 |
A non-negative integer giving the external control group
count for pattern |
xe_c_10 |
A non-negative integer giving the external control group
count for pattern |
xe_c_11 |
A non-negative integer giving the external control group
count for pattern |
alpha0e_t |
A numeric scalar in |
alpha0e_c |
A numeric scalar in |
nMC |
A positive integer giving the number of Dirichlet draws used to
evaluate the decision probability for each count combination in
Stage 1. Used by both |
CalcMethod |
A character string specifying the computation method.
Must be |
error_if_Miss |
A logical scalar; if |
Gray_inc_Miss |
A logical scalar; if |
Details
Computation proceeds in two stages for efficiency. In Stage 1, posterior
or predictive probabilities are precomputed for every possible multinomial
count combination (x_t, x_c). In Stage 2, operating characteristics
for each scenario are obtained by weighting the Stage 1 decisions by their
multinomial probabilities under the true parameters, avoiding repeated Monte
Carlo sampling per scenario.
Two-stage computation.
Stage 1 (precomputation): All possible multinomial count combinations
x_t are enumerated using allmultinom.
For design = 'controlled' or 'external', all combinations
x_c are also enumerated and the Go/NoGo probability matrix
PrGo[i, j] has dimensions n_t \times n_c.
For design = 'uncontrolled', the control distribution is fixed as
\mathrm{Dir}(\alpha_{2,**} + z_{**}) and does not depend on any
observed control counts; the probability matrix therefore has dimensions
n_t \times 1, eliminating the \binom{n_2+3}{3}-row control
enumeration and the associated Gamma sampling.
This stage is independent of the true scenario parameters.
Stage 2 (scenario evaluation): For each scenario
(\pi_{t1}, \pi_{t2}, \rho_t, \pi_{c1}, \pi_{c2}, \rho_c),
getjointbin converts the marginal rates and correlation
into the four-cell probability vector p_k. The multinomial
probability mass function weights the Stage 1 decisions:
\Pr(\mathrm{Go} \mid \Theta) = \sum_{i,j}
\mathbf{1}(\mathrm{Go}_{ij}) \cdot
P(x_{t,i} \mid n_1, p_t) \cdot P(x_{c,j} \mid n_2, p_c),
where \mathbf{1}(\mathrm{Go}_{ij}) is the Go indicator from Stage 1.
Stage 2 requires no additional Monte Carlo and is fast even for large
scenario grids.
Decision categories.
-
Go: sum of Go region probabilities
\ge \gamma_1AND sum of NoGo region probabilities< \gamma_2. -
NoGo: sum of Go region probabilities
< \gamma_1AND sum of NoGo region probabilities\ge \gamma_2. -
Miss: both Go and NoGo criteria satisfied simultaneously.
-
Gray: neither Go nor NoGo criterion satisfied.
Value
A data frame with one row per scenario and columns:
- pi_t1
True treatment response probability for Endpoint 1.
- pi_t2
True treatment response probability for Endpoint 2.
- rho_t
True within-arm correlation in the treatment arm.
- pi_c1
True control response probability for Endpoint 1 (omitted when
design = 'uncontrolled').- pi_c2
True control response probability for Endpoint 2 (omitted when
design = 'uncontrolled').- rho_c
True within-arm correlation in the control arm (omitted when
design = 'uncontrolled').- Go
Probability of making a Go decision.
- Gray
Probability of making a Gray (inconclusive) decision.
- NoGo
Probability of making a NoGo decision.
- Miss
Probability where Go and NoGo criteria are simultaneously met. Included when
error_if_Miss = FALSEandGray_inc_Miss = FALSE.
The returned object has S3 class pbayesdecisionprob2bin with
an associated print method.
Examples
# Example 1: Posterior probability, controlled design (rho > 0)
# Explores the impact of positive within-arm endpoint correlation.
pbayesdecisionprob2bin(
prob = 'posterior',
design = 'controlled',
GoRegions = 1L,
NoGoRegions = 9L,
gamma_go = 0.52,
gamma_nogo = 0.52,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.6, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.6, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = NULL, m_c = NULL,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 2: Posterior probability, uncontrolled design
# Hypothetical control specified via pseudo-counts.
pbayesdecisionprob2bin(
prob = 'posterior',
design = 'uncontrolled',
GoRegions = 1L,
NoGoRegions = 9L,
gamma_go = 0.27,
gamma_nogo = 0.36,
pi_t1 = c(0.15, 0.30, 0.40),
pi_t2 = c(0.20, 0.35, 0.45),
rho_t = rep(0.2, 3),
pi_c1 = NULL,
pi_c2 = NULL,
rho_c = NULL,
n_t = 10, n_c = NULL,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = NULL, m_c = NULL,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
z00 = 2L, z01 = 1L, z10 = 2L, z11 = 1L,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 3: Posterior probability, external control design
# External control data incorporated via power prior (alpha0e_c = 0.5).
pbayesdecisionprob2bin(
prob = 'posterior',
design = 'external',
GoRegions = 1L,
NoGoRegions = 9L,
gamma_go = 0.27,
gamma_nogo = 0.36,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.0, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.0, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = NULL, m_c = NULL,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = 4L, xe_c_01 = 2L, xe_c_10 = 3L, xe_c_11 = 1L,
alpha0e_t = NULL, alpha0e_c = 0.5,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 4: Predictive probability, controlled design
# Future trial has m_t = m_c = 30 patients per arm.
pbayesdecisionprob2bin(
prob = 'predictive',
design = 'controlled',
GoRegions = 1L,
NoGoRegions = 4L,
gamma_go = 0.60,
gamma_nogo = 0.80,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.3, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.3, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = 30L, m_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 5: Predictive probability, uncontrolled design
# Hypothetical control specified via pseudo-counts; future trial m_t = m_c = 30.
pbayesdecisionprob2bin(
prob = 'predictive',
design = 'uncontrolled',
GoRegions = 1L,
NoGoRegions = 4L,
gamma_go = 0.60,
gamma_nogo = 0.80,
pi_t1 = c(0.15, 0.30, 0.40),
pi_t2 = c(0.20, 0.35, 0.45),
rho_t = rep(0.7, 3),
pi_c1 = rep(0.15, 3),
pi_c2 = rep(0.20, 3),
rho_c = rep(0.7, 3),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = 30L, m_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
z00 = 2L, z01 = 1L, z10 = 2L, z11 = 1L,
xe_t_00 = NULL, xe_t_01 = NULL, xe_t_10 = NULL, xe_t_11 = NULL,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = NULL, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
# Example 6: Predictive probability, external treatment design
# External treatment data incorporated via power prior (alpha0e_t = 0.5).
pbayesdecisionprob2bin(
prob = 'predictive',
design = 'external',
GoRegions = 1L,
NoGoRegions = 4L,
gamma_go = 0.60,
gamma_nogo = 0.80,
pi_t1 = c(0.15, 0.25, 0.30, 0.40),
pi_t2 = c(0.20, 0.30, 0.35, 0.45),
rho_t = rep(0.5, 4),
pi_c1 = rep(0.15, 4),
pi_c2 = rep(0.20, 4),
rho_c = rep(0.5, 4),
n_t = 10, n_c = 10,
a_t_00 = 0.25, a_t_01 = 0.25, a_t_10 = 0.25, a_t_11 = 0.25,
a_c_00 = 0.25, a_c_01 = 0.25, a_c_10 = 0.25, a_c_11 = 0.25,
m_t = 30L, m_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
z00 = NULL, z01 = NULL, z10 = NULL, z11 = NULL,
xe_t_00 = 3L, xe_t_01 = 2L, xe_t_10 = 3L, xe_t_11 = 2L,
xe_c_00 = NULL, xe_c_01 = NULL, xe_c_10 = NULL, xe_c_11 = NULL,
alpha0e_t = 0.5, alpha0e_c = NULL,
nMC = 100,
error_if_Miss = FALSE, Gray_inc_Miss = FALSE
)
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