getgamma2bin: Find Optimal Go/NoGo Thresholds for Two Binary Endpoints
In BayesianQDM: Bayesian Quantitative Decision-Making Framework for Binary and Continuous Endpoints
getgamma2bin R Documentation
Find Optimal Go/NoGo Thresholds for Two Binary Endpoints
Description
Computes the optimal Go threshold \gamma_{\mathrm{go}} and NoGo
threshold \gamma_{\mathrm{nogo}} for two binary endpoints by
searching over a two-dimensional grid of candidate value pairs. The two
thresholds are calibrated independently under separate scenarios:
-
\gamma_{\mathrm{go}} is the smallest value in
gamma_go_grid such that the worst-case marginal Go
probability over all \gamma_{\mathrm{nogo}} in
gamma_nogo_grid is strictly less than target_go
under the Go-calibration scenario (pi_t1_go,
pi_t2_go, rho_t_go, pi_c1_go,
pi_c2_go, rho_c_go); typically the Null scenario.
-
\gamma_{\mathrm{nogo}} is the smallest value in
gamma_nogo_grid such that the worst-case marginal NoGo
probability over all \gamma_{\mathrm{go}} in
gamma_go_grid is strictly less than target_nogo
under the NoGo-calibration scenario (pi_t1_nogo,
pi_t2_nogo, rho_t_nogo, pi_c1_nogo,
pi_c2_nogo, rho_c_nogo); typically the Alternative
scenario.
Usage
getgamma2bin(
prob = "posterior",
design = "controlled",
GoRegions,
NoGoRegions,
pi_t1_go,
pi_t2_go,
rho_t_go,
pi_c1_go = NULL,
pi_c2_go = NULL,
rho_c_go = NULL,
pi_t1_nogo,
pi_t2_nogo,
rho_t_nogo,
pi_c1_nogo = NULL,
pi_c2_nogo = NULL,
rho_c_nogo = NULL,
target_go,
target_nogo,
n_t,
n_c,
a_t_00,
a_t_01,
a_t_10,
a_t_11,
a_c_00,
a_c_01,
a_c_10,
a_c_11,
theta_TV1 = NULL,
theta_MAV1 = NULL,
theta_TV2 = NULL,
theta_MAV2 = NULL,
theta_NULL1 = NULL,
theta_NULL2 = NULL,
m_t = NULL,
m_c = 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 = 1000L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
Arguments
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 of region indices (subset of
1:9 for prob = 'posterior' or 1:4 for
prob = 'predictive') that constitute the Go region.
NoGoRegions
An integer vector of region indices that constitute
the NoGo region. Must be disjoint from GoRegions.
pi_t1_go
A numeric scalar in (0, 1) giving the true
treatment response probability for Endpoint 1 under the
Go-calibration scenario (typically Null).
pi_t2_go
A numeric scalar in (0, 1) giving the true
treatment response probability for Endpoint 2 under the
Go-calibration scenario.
rho_t_go
A numeric scalar giving the within-group correlation in
the treatment group under the Go-calibration scenario.
pi_c1_go
A numeric scalar in (0, 1) giving the true
control response probability for Endpoint 1 under the
Go-calibration scenario. Required for
design = 'controlled' or 'external';
set to NULL for design = 'uncontrolled'.
pi_c2_go
A numeric scalar in (0, 1) giving the true
control response probability for Endpoint 2 under the
Go-calibration scenario. Required for
design = 'controlled' or 'external';
set to NULL for design = 'uncontrolled'.
rho_c_go
A numeric scalar giving the within-group correlation in
the control group under the Go-calibration scenario. Required for
design = 'controlled' or 'external';
set to NULL for design = 'uncontrolled'.
pi_t1_nogo
A numeric scalar in (0, 1) giving the true
treatment response probability for Endpoint 1 under the
NoGo-calibration scenario (typically Alternative).
pi_t2_nogo
A numeric scalar in (0, 1) giving the true
treatment response probability for Endpoint 2 under the
NoGo-calibration scenario.
rho_t_nogo
A numeric scalar giving the within-group correlation in
the treatment group under the NoGo-calibration scenario.
pi_c1_nogo
A numeric scalar in (0, 1) giving the true
control response probability for Endpoint 1 under the
NoGo-calibration scenario. Required for
design = 'controlled' or 'external';
set to NULL for design = 'uncontrolled'.
pi_c2_nogo
A numeric scalar in (0, 1) giving the true
control response probability for Endpoint 2 under the
NoGo-calibration scenario. Required for
design = 'controlled' or 'external';
set to NULL for design = 'uncontrolled'.
rho_c_nogo
A numeric scalar giving the within-group correlation in
the control group under the NoGo-calibration scenario. Required for
design = 'controlled' or 'external';
set to NULL for design = 'uncontrolled'.
target_go
A numeric scalar in (0, 1) giving the upper bound
on the worst-case marginal Go probability under the Go-calibration
scenario. The optimal \gamma_{\mathrm{go}} is the smallest
grid value satisfying the constraint.
target_nogo
A numeric scalar in (0, 1) giving the upper
bound on the worst-case marginal NoGo probability under the
NoGo-calibration scenario. The optimal \gamma_{\mathrm{nogo}}
is the smallest grid value satisfying the constraint.
n_t
A positive integer giving the number of patients in the
treatment group in the PoC trial.
n_c
A positive integer giving the number of patients in the
control group in the PoC trial.
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; see a_t_00.
a_t_10
A positive numeric scalar; see a_t_00.
a_t_11
A positive numeric scalar; see a_t_00.
a_c_00
A positive numeric scalar giving the Dirichlet prior
parameter for the (0,0) response pattern in the control group.
a_c_01
A positive numeric scalar; see a_c_00.
a_c_10
A positive numeric scalar; see a_c_00.
a_c_11
A positive numeric scalar; see a_c_00.
theta_TV1
A numeric scalar giving the TV threshold for
Endpoint 1. Required when prob = 'posterior';
otherwise set to NULL.
theta_MAV1
A numeric scalar giving the MAV threshold for
Endpoint 1. Required when prob = 'posterior';
otherwise set to NULL.
theta_TV2
A numeric scalar giving the TV threshold for
Endpoint 2. Required when prob = 'posterior';
otherwise set to NULL.
theta_MAV2
A numeric scalar giving the MAV threshold for
Endpoint 2. Required when prob = 'posterior';
otherwise set to NULL.
theta_NULL1
A numeric scalar giving the null hypothesis threshold
for Endpoint 1. Required when prob = 'predictive';
otherwise set to NULL.
theta_NULL2
A numeric scalar giving the null hypothesis threshold
for Endpoint 2. Required when prob = 'predictive';
otherwise set to NULL.
m_t
A positive integer giving the future sample size for the
treatment group. Required when prob = 'predictive';
set to NULL otherwise.
m_c
A positive integer giving the future sample size for the
control group. Required when prob = 'predictive';
set to NULL otherwise.
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; see z00.
z10
A non-negative integer; see z00.
z11
A non-negative integer; see z00.
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; see xe_t_00.
xe_t_10
A non-negative integer; see xe_t_00.
xe_t_11
A non-negative integer; see xe_t_00.
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; see xe_c_00.
xe_c_10
A non-negative integer; see xe_c_00.
xe_c_11
A non-negative integer; see xe_c_00.
alpha0e_t
A numeric scalar in (0, 1] giving the power prior
weight for external treatment group data. Required when external
treatment data are used; otherwise NULL.
alpha0e_c
A numeric scalar in (0, 1] giving the power prior
weight for external control group data. Required when external
control data are used; otherwise NULL.
nMC
A positive integer giving the number of Dirichlet draws used
to evaluate region probabilities for each count combination in
Stage 1. Default is 1000L.
gamma_go_grid
A numeric vector of candidate Go threshold values
in (0, 1) to search over. Defaults to
seq(0.01, 0.99, by = 0.01).
gamma_nogo_grid
A numeric vector of candidate NoGo threshold
values in (0, 1) to search over. Defaults to
seq(0.01, 0.99, by = 0.01).
Details
The function uses the same two-stage precompute-then-sweep strategy as
pbayesdecisionprob2bin.
Stage 1 (precomputation): pbayespostpred2bin is
called for every possible multinomial outcome combination (x_t, x_c)
enumerated by allmultinom. The resulting region probability
vector is summed over GoRegions and NoGoRegions to obtain
\hat{g}_{Go,ij} and \hat{g}_{NoGo,ij}. These are independent
of the calibration scenario; only the multinomial weights differ.
Stage 2 (gamma sweep): For each pair
(\gamma_{\mathrm{go}}, \gamma_{\mathrm{nogo}}) in the
two-dimensional grid, operating characteristics are computed separately
under each calibration scenario using the respective multinomial weights:
\Pr(\mathrm{Go}) = \sum_{i,j} w_{ij}^{(\mathrm{go})}
\mathbf{1}\!\left[\hat{g}_{Go,ij} \ge \gamma_{\mathrm{go}},\;
\hat{g}_{NoGo,ij} < \gamma_{\mathrm{nogo}}\right]
\Pr(\mathrm{NoGo}) = \sum_{i,j} w_{ij}^{(\mathrm{nogo})}
\mathbf{1}\!\left[\hat{g}_{NoGo,ij} \ge \gamma_{\mathrm{nogo}},\;
\hat{g}_{Go,ij} < \gamma_{\mathrm{go}}\right]
Stage 3 (optimal threshold selection): For each candidate
\gamma_{\mathrm{go}}, the worst-case \Pr(\mathrm{Go}) over all
\gamma_{\mathrm{nogo}} in gamma_nogo_grid is computed; the
optimal \gamma_{\mathrm{go}} is the smallest grid value for
which this worst-case probability is less than target_go.
Analogously, the optimal \gamma_{\mathrm{nogo}} is the
smallest grid value for which the worst-case \Pr(\mathrm{NoGo})
is less than target_nogo.
Value
A list of class getgamma2bin with the following elements:
- gamma_go
Optimal Go threshold: the smallest value in
gamma_go_grid for which the marginal
\Pr(\mathrm{Go}) < \code{target\_go} under the
Go-calibration scenario. NA if no such value exists.
- gamma_nogo
Optimal NoGo threshold: the smallest value in
gamma_nogo_grid for which the marginal
\Pr(\mathrm{NoGo}) < \code{target\_nogo} under the
NoGo-calibration scenario. NA if no such value exists.
- PrGo_opt
Marginal \Pr(\mathrm{Go}) at
gamma_go under the Go-calibration scenario.
NA if gamma_go is NA.
- PrNoGo_opt
Marginal \Pr(\mathrm{NoGo}) at
gamma_nogo under the NoGo-calibration scenario.
NA if gamma_nogo is NA.
- target_go
The value of target_go supplied by the user.
- target_nogo
The value of target_nogo supplied by the user.
- grid_results
A data frame with columns gamma_grid,
PrGo_grid (marginal Go probability under the Go-calibration
scenario), and PrNoGo_grid (marginal NoGo probability under
the NoGo-calibration scenario).
Examples
# Example 1: Controlled design, posterior probability
# gamma_go : smallest gamma_go s.t. max_{gamma_nogo} Pr(Go) < 0.05 under Null
# gamma_nogo: smallest gamma_nogo s.t. max_{gamma_go} Pr(NoGo) < 0.20 under Alt
getgamma2bin(
prob = 'posterior', design = 'controlled',
GoRegions = 1L, NoGoRegions = 9L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = 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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 2: Uncontrolled design, posterior probability
getgamma2bin(
prob = 'posterior', design = 'uncontrolled',
GoRegions = 1L, NoGoRegions = 9L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = NULL, pi_c2_go = NULL, rho_c_go = NULL,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = NULL, pi_c2_nogo = NULL, rho_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = NULL,
z00 = 3L, z01 = 2L, z10 = 3L, z11 = 2L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 3: External design, posterior probability
getgamma2bin(
prob = 'posterior', design = 'external',
GoRegions = 1L, NoGoRegions = 9L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = 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 = 3L, xe_c_01 = 2L, xe_c_10 = 3L, xe_c_11 = 2L,
alpha0e_t = NULL, alpha0e_c = 0.5,
nMC = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 4: Controlled design, predictive probability
getgamma2bin(
prob = 'predictive', design = 'controlled',
GoRegions = 1L, NoGoRegions = 4L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
m_t = 5L, m_c = 5L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 5: Uncontrolled design, predictive probability
getgamma2bin(
prob = 'predictive', design = 'uncontrolled',
GoRegions = 1L, NoGoRegions = 4L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = NULL, pi_c2_go = NULL, rho_c_go = NULL,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = NULL, pi_c2_nogo = NULL, rho_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
m_t = 5L, m_c = 5L,
z00 = 3L, z01 = 2L, z10 = 3L, z11 = 2L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 6: External design, predictive probability
getgamma2bin(
prob = 'predictive', design = 'external',
GoRegions = 1L, NoGoRegions = 4L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
m_t = 5L, m_c = 5L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
BayesianQDM documentation built on April 22, 2026, 1:09 a.m.
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| getgamma2bin | R Documentation |
Find Optimal Go/NoGo Thresholds for Two Binary Endpoints
Description
Computes the optimal Go threshold \gamma_{\mathrm{go}} and NoGo
threshold \gamma_{\mathrm{nogo}} for two binary endpoints by
searching over a two-dimensional grid of candidate value pairs. The two
thresholds are calibrated independently under separate scenarios:
-
\gamma_{\mathrm{go}}is the smallest value ingamma_go_gridsuch that the worst-case marginal Go probability over all\gamma_{\mathrm{nogo}}ingamma_nogo_gridis strictly less thantarget_gounder the Go-calibration scenario (pi_t1_go,pi_t2_go,rho_t_go,pi_c1_go,pi_c2_go,rho_c_go); typically the Null scenario. -
\gamma_{\mathrm{nogo}}is the smallest value ingamma_nogo_gridsuch that the worst-case marginal NoGo probability over all\gamma_{\mathrm{go}}ingamma_go_gridis strictly less thantarget_nogounder the NoGo-calibration scenario (pi_t1_nogo,pi_t2_nogo,rho_t_nogo,pi_c1_nogo,pi_c2_nogo,rho_c_nogo); typically the Alternative scenario.
Usage
getgamma2bin(
prob = "posterior",
design = "controlled",
GoRegions,
NoGoRegions,
pi_t1_go,
pi_t2_go,
rho_t_go,
pi_c1_go = NULL,
pi_c2_go = NULL,
rho_c_go = NULL,
pi_t1_nogo,
pi_t2_nogo,
rho_t_nogo,
pi_c1_nogo = NULL,
pi_c2_nogo = NULL,
rho_c_nogo = NULL,
target_go,
target_nogo,
n_t,
n_c,
a_t_00,
a_t_01,
a_t_10,
a_t_11,
a_c_00,
a_c_01,
a_c_10,
a_c_11,
theta_TV1 = NULL,
theta_MAV1 = NULL,
theta_TV2 = NULL,
theta_MAV2 = NULL,
theta_NULL1 = NULL,
theta_NULL2 = NULL,
m_t = NULL,
m_c = 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 = 1000L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
Arguments
prob |
A character string specifying the probability type.
Must be |
design |
A character string specifying the trial design.
Must be |
GoRegions |
An integer vector of region indices (subset of
|
NoGoRegions |
An integer vector of region indices that constitute
the NoGo region. Must be disjoint from |
pi_t1_go |
A numeric scalar in |
pi_t2_go |
A numeric scalar in |
rho_t_go |
A numeric scalar giving the within-group correlation in the treatment group under the Go-calibration scenario. |
pi_c1_go |
A numeric scalar in |
pi_c2_go |
A numeric scalar in |
rho_c_go |
A numeric scalar giving the within-group correlation in
the control group under the Go-calibration scenario. Required for
|
pi_t1_nogo |
A numeric scalar in |
pi_t2_nogo |
A numeric scalar in |
rho_t_nogo |
A numeric scalar giving the within-group correlation in the treatment group under the NoGo-calibration scenario. |
pi_c1_nogo |
A numeric scalar in |
pi_c2_nogo |
A numeric scalar in |
rho_c_nogo |
A numeric scalar giving the within-group correlation in
the control group under the NoGo-calibration scenario. Required for
|
target_go |
A numeric scalar in |
target_nogo |
A numeric scalar in |
n_t |
A positive integer giving the number of patients in the treatment group in the PoC trial. |
n_c |
A positive integer giving the number of patients in the control group in the PoC trial. |
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; see |
a_t_10 |
A positive numeric scalar; see |
a_t_11 |
A positive numeric scalar; see |
a_c_00 |
A positive numeric scalar giving the Dirichlet prior parameter for the (0,0) response pattern in the control group. |
a_c_01 |
A positive numeric scalar; see |
a_c_10 |
A positive numeric scalar; see |
a_c_11 |
A positive numeric scalar; see |
theta_TV1 |
A numeric scalar giving the TV threshold for
Endpoint 1. Required when |
theta_MAV1 |
A numeric scalar giving the MAV threshold for
Endpoint 1. Required when |
theta_TV2 |
A numeric scalar giving the TV threshold for
Endpoint 2. Required when |
theta_MAV2 |
A numeric scalar giving the 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 |
m_t |
A positive integer giving the future sample size for the
treatment group. Required when |
m_c |
A positive integer giving the future sample size for the
control group. Required when |
z00 |
A non-negative integer giving the hypothetical control count
for pattern (0,0). Required when
|
z01 |
A non-negative integer; see |
z10 |
A non-negative integer; see |
z11 |
A non-negative integer; see |
xe_t_00 |
A non-negative integer giving the external treatment group
count for pattern (0,0). Required when
|
xe_t_01 |
A non-negative integer; see |
xe_t_10 |
A non-negative integer; see |
xe_t_11 |
A non-negative integer; see |
xe_c_00 |
A non-negative integer giving the external control group
count for pattern (0,0). Required when
|
xe_c_01 |
A non-negative integer; see |
xe_c_10 |
A non-negative integer; see |
xe_c_11 |
A non-negative integer; see |
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 region probabilities for each count combination in
Stage 1. Default is |
gamma_go_grid |
A numeric vector of candidate Go threshold values
in |
gamma_nogo_grid |
A numeric vector of candidate NoGo threshold
values in |
Details
The function uses the same two-stage precompute-then-sweep strategy as
pbayesdecisionprob2bin.
Stage 1 (precomputation): pbayespostpred2bin is
called for every possible multinomial outcome combination (x_t, x_c)
enumerated by allmultinom. The resulting region probability
vector is summed over GoRegions and NoGoRegions to obtain
\hat{g}_{Go,ij} and \hat{g}_{NoGo,ij}. These are independent
of the calibration scenario; only the multinomial weights differ.
Stage 2 (gamma sweep): For each pair
(\gamma_{\mathrm{go}}, \gamma_{\mathrm{nogo}}) in the
two-dimensional grid, operating characteristics are computed separately
under each calibration scenario using the respective multinomial weights:
\Pr(\mathrm{Go}) = \sum_{i,j} w_{ij}^{(\mathrm{go})}
\mathbf{1}\!\left[\hat{g}_{Go,ij} \ge \gamma_{\mathrm{go}},\;
\hat{g}_{NoGo,ij} < \gamma_{\mathrm{nogo}}\right]
\Pr(\mathrm{NoGo}) = \sum_{i,j} w_{ij}^{(\mathrm{nogo})}
\mathbf{1}\!\left[\hat{g}_{NoGo,ij} \ge \gamma_{\mathrm{nogo}},\;
\hat{g}_{Go,ij} < \gamma_{\mathrm{go}}\right]
Stage 3 (optimal threshold selection): For each candidate
\gamma_{\mathrm{go}}, the worst-case \Pr(\mathrm{Go}) over all
\gamma_{\mathrm{nogo}} in gamma_nogo_grid is computed; the
optimal \gamma_{\mathrm{go}} is the smallest grid value for
which this worst-case probability is less than target_go.
Analogously, the optimal \gamma_{\mathrm{nogo}} is the
smallest grid value for which the worst-case \Pr(\mathrm{NoGo})
is less than target_nogo.
Value
A list of class getgamma2bin with the following elements:
- gamma_go
Optimal Go threshold: the smallest value in
gamma_go_gridfor which the marginal\Pr(\mathrm{Go}) < \code{target\_go}under the Go-calibration scenario.NAif no such value exists.- gamma_nogo
Optimal NoGo threshold: the smallest value in
gamma_nogo_gridfor which the marginal\Pr(\mathrm{NoGo}) < \code{target\_nogo}under the NoGo-calibration scenario.NAif no such value exists.- PrGo_opt
Marginal
\Pr(\mathrm{Go})atgamma_gounder the Go-calibration scenario.NAifgamma_goisNA.- PrNoGo_opt
Marginal
\Pr(\mathrm{NoGo})atgamma_nogounder the NoGo-calibration scenario.NAifgamma_nogoisNA.- target_go
The value of
target_gosupplied by the user.- target_nogo
The value of
target_nogosupplied by the user.- grid_results
A data frame with columns
gamma_grid,PrGo_grid(marginal Go probability under the Go-calibration scenario), andPrNoGo_grid(marginal NoGo probability under the NoGo-calibration scenario).
Examples
# Example 1: Controlled design, posterior probability
# gamma_go : smallest gamma_go s.t. max_{gamma_nogo} Pr(Go) < 0.05 under Null
# gamma_nogo: smallest gamma_nogo s.t. max_{gamma_go} Pr(NoGo) < 0.20 under Alt
getgamma2bin(
prob = 'posterior', design = 'controlled',
GoRegions = 1L, NoGoRegions = 9L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = 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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 2: Uncontrolled design, posterior probability
getgamma2bin(
prob = 'posterior', design = 'uncontrolled',
GoRegions = 1L, NoGoRegions = 9L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = NULL, pi_c2_go = NULL, rho_c_go = NULL,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = NULL, pi_c2_nogo = NULL, rho_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = NULL,
z00 = 3L, z01 = 2L, z10 = 3L, z11 = 2L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 3: External design, posterior probability
getgamma2bin(
prob = 'posterior', design = 'external',
GoRegions = 1L, NoGoRegions = 9L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = 0.15, theta_MAV1 = 0.10,
theta_TV2 = 0.15, theta_MAV2 = 0.10,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = 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 = 3L, xe_c_01 = 2L, xe_c_10 = 3L, xe_c_11 = 2L,
alpha0e_t = NULL, alpha0e_c = 0.5,
nMC = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 4: Controlled design, predictive probability
getgamma2bin(
prob = 'predictive', design = 'controlled',
GoRegions = 1L, NoGoRegions = 4L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
m_t = 5L, m_c = 5L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 5: Uncontrolled design, predictive probability
getgamma2bin(
prob = 'predictive', design = 'uncontrolled',
GoRegions = 1L, NoGoRegions = 4L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = NULL, pi_c2_go = NULL, rho_c_go = NULL,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = NULL, pi_c2_nogo = NULL, rho_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
m_t = 5L, m_c = 5L,
z00 = 3L, z01 = 2L, z10 = 3L, z11 = 2L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
# Example 6: External design, predictive probability
getgamma2bin(
prob = 'predictive', design = 'external',
GoRegions = 1L, NoGoRegions = 4L,
pi_t1_go = 0.15, pi_t2_go = 0.20, rho_t_go = 0.0,
pi_c1_go = 0.15, pi_c2_go = 0.20, rho_c_go = 0.0,
pi_t1_nogo = 0.35, pi_t2_nogo = 0.40, rho_t_nogo = 0.0,
pi_c1_nogo = 0.15, pi_c2_nogo = 0.20, rho_c_nogo = 0.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 7L, n_c = 7L,
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,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 0.10, theta_NULL2 = 0.10,
m_t = 5L, m_c = 5L,
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 = 100L,
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01)
)
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