Find Optimal Go/NoGo Thresholds for a Single Continuous Endpoint
Source:R/getgamma1cont.R
getgamma1cont.RdComputes the optimal Go threshold \(\gamma_{\mathrm{go}}\) and NoGo threshold \(\gamma_{\mathrm{nogo}}\) for a single continuous endpoint by searching over a grid of candidate values. The two thresholds are calibrated independently under separate scenarios:
\(\gamma_{\mathrm{go}}\) is the smallest value in
gamma_gridsuch that the marginal Go probability \(\Pr(g_{\mathrm{Go}} \ge \gamma_{\mathrm{go}})\) is strictly less thantarget_gounder the Go-calibration scenario (mu_t_go,mu_c_go,sigma_t_go,sigma_c_go); typically the Null scenario.\(\gamma_{\mathrm{nogo}}\) is the smallest value in
gamma_gridsuch that the marginal NoGo probability \(\Pr(g_{\mathrm{NoGo}} \ge \gamma_{\mathrm{nogo}})\) is strictly less thantarget_nogounder the NoGo-calibration scenario (mu_t_nogo,mu_c_nogo,sigma_t_nogo,sigma_c_nogo); typically the Alternative scenario.
Here \(g_{\mathrm{Go}} = P(\theta > \theta_{\mathrm{TV}} \mid \bar{y}_t, s_t, \bar{y}_c, s_c)\)
and \(g_{\mathrm{NoGo}} = P(\theta \le \theta_{\mathrm{MAV}} \mid \bar{y}_t, s_t, \bar{y}_c, s_c)\)
for prob = 'posterior', consistent with the decision rule in
pbayesdecisionprob1cont.
Usage
getgamma1cont(
nsim,
prob = "posterior",
design = "controlled",
prior = "vague",
CalcMethod = "NI",
theta_TV = NULL,
theta_MAV = NULL,
theta_NULL = NULL,
nMC = NULL,
mu_t_go,
mu_c_go = NULL,
sigma_t_go,
sigma_c_go = NULL,
mu_t_nogo,
mu_c_nogo = NULL,
sigma_t_nogo,
sigma_c_nogo = NULL,
target_go,
target_nogo,
n_t,
n_c = NULL,
m_t = NULL,
m_c = NULL,
kappa0_t = NULL,
kappa0_c = NULL,
nu0_t = NULL,
nu0_c = NULL,
mu0_t = NULL,
mu0_c = NULL,
sigma0_t = NULL,
sigma0_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,
gamma_grid = seq(0.01, 0.99, by = 0.01),
seed
)Arguments
- nsim
A positive integer giving the number of Monte Carlo simulation replicates used to approximate the operating characteristics.
- 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-Chisq'.- CalcMethod
A character string specifying the computation method for
pbayespostpred1cont. Must be'NI','MC', or'MM'.- theta_TV
A numeric scalar giving the Target Value (TV) threshold for the treatment effect. Required when
prob = 'posterior'; set toNULLotherwise.- theta_MAV
A numeric scalar giving the Minimum Acceptable Value (MAV) threshold. Must satisfy
theta_TV > theta_MAV. Required whenprob = 'posterior'; set toNULLotherwise.- theta_NULL
A numeric scalar giving the null hypothesis threshold for the predictive probability. Required when
prob = 'predictive'; set toNULLotherwise.- nMC
A positive integer giving the number of inner Monte Carlo draws passed to
pbayespostpred1cont. Required whenCalcMethod = 'MC'; set toNULLotherwise.- mu_t_go
A numeric scalar giving the true mean for the treatment group under the Go-calibration scenario (typically Null).
- mu_c_go
A numeric scalar giving the true mean for the control group under the Go-calibration scenario. Set to
NULLfordesign = 'uncontrolled'.- sigma_t_go
A positive numeric scalar giving the true standard deviation for the treatment group under the Go-calibration scenario.
- sigma_c_go
A positive numeric scalar giving the true standard deviation for the control group under the Go-calibration scenario. Set to
NULLfordesign = 'uncontrolled'.- mu_t_nogo
A numeric scalar giving the true mean for the treatment group under the NoGo-calibration scenario (typically Alternative).
- mu_c_nogo
A numeric scalar giving the true mean for the control group under the NoGo-calibration scenario. Set to
NULLfordesign = 'uncontrolled'.- sigma_t_nogo
A positive numeric scalar giving the true standard deviation for the treatment group under the NoGo-calibration scenario.
- sigma_c_nogo
A positive numeric scalar giving the true standard deviation for the control group under the NoGo-calibration scenario. Set to
NULLfordesign = 'uncontrolled'.- target_go
A numeric scalar in
(0, 1)giving the upper bound on the marginal Go probability under the Go-calibration scenario. The optimal \(\gamma_{\mathrm{go}}\) is the smallest grid value satisfying \(\Pr(\mathrm{Go}) < \code{target\_go}\).- target_nogo
A numeric scalar in
(0, 1)giving the upper bound on the marginal NoGo probability under the NoGo-calibration scenario. The optimal \(\gamma_{\mathrm{nogo}}\) is the smallest grid value satisfying \(\Pr(\mathrm{NoGo}) < \code{target\_nogo}\).- 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. Required for
design = 'controlled'or'external'; set toNULLfordesign = 'uncontrolled'.- m_t
A positive integer giving the future sample size for the treatment group. Required when
prob = 'predictive'; set toNULLotherwise.- m_c
A positive integer giving the future sample size for the control group. Required when
prob = 'predictive'; set toNULLotherwise.- kappa0_t
A positive numeric scalar giving the prior precision parameter for the treatment group under the N-Inv-Chi-squared prior. Required when
prior = 'N-Inv-Chisq'; set toNULLotherwise.- kappa0_c
A positive numeric scalar giving the prior precision parameter for the control group. Required when
prior = 'N-Inv-Chisq'anddesign != 'uncontrolled'; set toNULLotherwise.- nu0_t
A positive numeric scalar giving the prior degrees of freedom for the treatment group under the N-Inv-Chi-squared prior. Required when
prior = 'N-Inv-Chisq'; set toNULLotherwise.- nu0_c
A positive numeric scalar giving the prior degrees of freedom for the control group. Required when
prior = 'N-Inv-Chisq'anddesign != 'uncontrolled'; set toNULLotherwise.- mu0_t
A numeric scalar giving the prior mean for the treatment group under the N-Inv-Chi-squared prior. Required when
prior = 'N-Inv-Chisq'; set toNULLotherwise.- mu0_c
A numeric scalar giving the prior mean for the control group (or the fixed hypothetical control mean for uncontrolled design). Required when
prior = 'N-Inv-Chisq'; set toNULLotherwise.- sigma0_t
A positive numeric scalar giving the prior scale parameter for the treatment group under the N-Inv-Chi-squared prior. Required when
prior = 'N-Inv-Chisq'; set toNULLotherwise.- sigma0_c
A positive numeric scalar giving the prior scale parameter for the control group. Required when
prior = 'N-Inv-Chisq'anddesign != 'uncontrolled'; set toNULLotherwise.- r
A positive numeric scalar giving the variance ratio \(\sigma_c^2 / \sigma_t^2\) used for uncontrolled design. Required when
design = 'uncontrolled'; set toNULLotherwise.- ne_t
A positive integer giving the number of patients in the treatment group of the external data set. Required when
design = 'external'and external treatment data are available; otherwise set toNULL.- ne_c
A positive integer giving the number of patients in the control group of the external data set. Required when
design = 'external'and external control data are available; otherwise set toNULL.- alpha0e_t
A numeric scalar in
(0, 1]giving the power prior weight for external treatment group data. Required whendesign = 'external'andne_tis non-NULL; set toNULLotherwise.- alpha0e_c
A numeric scalar in
(0, 1]giving the power prior weight for external control group data. Required whendesign = 'external'andne_cis non-NULL; set toNULLotherwise.- bar_ye_t
A numeric scalar giving the sample mean of the external treatment group data. Required when
ne_tis non-NULL; set toNULLotherwise.- bar_ye_c
A numeric scalar giving the sample mean of the external control group data. Required when
ne_cis non-NULL; set toNULLotherwise.- se_t
A positive numeric scalar giving the sample standard deviation of the external treatment group data. Required when
ne_tis non-NULL; set toNULLotherwise.- se_c
A positive numeric scalar giving the sample standard deviation of the external control group data. Required when
ne_cis non-NULL; set toNULLotherwise.- gamma_grid
A numeric vector of candidate threshold values in
(0, 1)to search over. Defaults toseq(0.01, 0.99, by = 0.01).- seed
A numeric scalar for reproducible random number generation. The Go-calibration simulation uses
seedand the NoGo-calibration simulation usesseed + 1to ensure independence between the two scenarios.
Value
A list of class getgamma1cont with the following elements:
- gamma_go
Optimal Go threshold: the smallest value in
gamma_gridfor which \(\Pr(\mathrm{Go}) < \code{target\_go}\) under the Go-calibration scenario.NAif no such value exists.- gamma_nogo
Optimal NoGo threshold: the smallest value in
gamma_gridfor which \(\Pr(\mathrm{NoGo}) < \code{target\_nogo}\) under the NoGo-calibration scenario.NAif no such value exists.- PrGo_opt
Marginal \(\Pr(g_{\mathrm{Go}} \ge \gamma_{\mathrm{go}})\) at the optimal \(\gamma_{\mathrm{go}}\) under the Go-calibration scenario.
NAifgamma_goisNA.- PrNoGo_opt
Marginal \(\Pr(g_{\mathrm{NoGo}} \ge \gamma_{\mathrm{nogo}})\) at the optimal \(\gamma_{\mathrm{nogo}}\) under 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).
Details
The function uses a two-stage simulate-then-sweep strategy:
Simulation:
nsimdatasets are generated independently for each calibration scenario. For the Go-calibration scenario, standardised residuals are shifted bymu_t_goandmu_c_go; for the NoGo-calibration scenario, bymu_t_nogoandmu_c_nogo.pbayespostpred1contis called once per scenario to obtain \(g_{\mathrm{Go}}\) (lower.tail = FALSEattheta_TV) and \(g_{\mathrm{NoGo}}\) (lower.tail = TRUEattheta_MAV).Gamma sweep: Marginal probabilities are estimated as the proportion of simulated datasets satisfying the respective indicator: \(g_{\mathrm{Go}} \ge \gamma\) for
PrGo_grid, and \(g_{\mathrm{NoGo}} \ge \gamma\) forPrNoGo_grid. Both are monotone non-increasing in \(\gamma\).
The optimal \(\gamma_{\mathrm{go}}\) and \(\gamma_{\mathrm{nogo}}\) are each the smallest grid value crossing below the respective target probability.
Examples
# Example 1: Controlled design, vague prior, posterior probability
# gamma_go : smallest gamma s.t. Pr(Go) < 0.05 under Null (mu_t = mu_c = 1.0)
# gamma_nogo: smallest gamma s.t. Pr(NoGo) < 0.20 under Alt (mu_t = 2.5, mu_c = 1.0)
getgamma1cont(
nsim = 1000L, prob = 'posterior', design = 'controlled',
prior = 'vague', CalcMethod = 'MM',
theta_TV = 1.5, theta_MAV = 0.0, theta_NULL = NULL, nMC = NULL,
mu_t_go = 1.0, mu_c_go = 1.0, sigma_t_go = 2.0, sigma_c_go = 2.0,
mu_t_nogo = 2.5, mu_c_nogo = 1.0, sigma_t_nogo = 2.0, sigma_c_nogo = 2.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = 15L, m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_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,
gamma_grid = seq(0.01, 0.99, by = 0.01), seed = 1L
)
#> $gamma_go
#> [1] 0.34
#>
#> $gamma_nogo
#> [1] 0.13
#>
#> $PrGo_opt
#> [1] 0.049
#>
#> $PrNoGo_opt
#> [1] 0.191
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.664 0.692
#> 2 0.02 0.546 0.579
#> 3 0.03 0.468 0.492
#> 4 0.04 0.407 0.440
#> 5 0.05 0.364 0.395
#> 6 0.06 0.332 0.354
#> 7 0.07 0.296 0.321
#> 8 0.08 0.274 0.293
#> 9 0.09 0.247 0.263
#> 10 0.10 0.228 0.236
#> 11 0.11 0.213 0.218
#> 12 0.12 0.198 0.206
#> 13 0.13 0.179 0.191
#> 14 0.14 0.169 0.175
#> 15 0.15 0.160 0.164
#> 16 0.16 0.145 0.154
#> 17 0.17 0.134 0.143
#> 18 0.18 0.126 0.132
#> 19 0.19 0.116 0.126
#> 20 0.20 0.106 0.121
#> 21 0.21 0.099 0.113
#> 22 0.22 0.092 0.107
#> 23 0.23 0.084 0.094
#> 24 0.24 0.078 0.087
#> 25 0.25 0.076 0.084
#> 26 0.26 0.072 0.079
#> 27 0.27 0.067 0.076
#> 28 0.28 0.065 0.074
#> 29 0.29 0.063 0.066
#> 30 0.30 0.056 0.060
#> 31 0.31 0.056 0.057
#> 32 0.32 0.051 0.053
#> 33 0.33 0.051 0.049
#> 34 0.34 0.049 0.046
#> 35 0.35 0.047 0.046
#> 36 0.36 0.044 0.044
#> 37 0.37 0.040 0.040
#> 38 0.38 0.035 0.038
#> 39 0.39 0.032 0.034
#> 40 0.40 0.032 0.033
#> 41 0.41 0.032 0.032
#> 42 0.42 0.030 0.030
#> 43 0.43 0.028 0.028
#> 44 0.44 0.026 0.028
#> 45 0.45 0.026 0.027
#> 46 0.46 0.025 0.026
#> 47 0.47 0.023 0.024
#> 48 0.48 0.023 0.021
#> 49 0.49 0.023 0.019
#> 50 0.50 0.022 0.017
#> 51 0.51 0.021 0.016
#> 52 0.52 0.020 0.015
#> 53 0.53 0.018 0.015
#> 54 0.54 0.015 0.015
#> 55 0.55 0.012 0.014
#> 56 0.56 0.010 0.013
#> 57 0.57 0.010 0.012
#> 58 0.58 0.009 0.011
#> 59 0.59 0.009 0.011
#> 60 0.60 0.009 0.011
#> 61 0.61 0.008 0.011
#> 62 0.62 0.007 0.010
#> 63 0.63 0.007 0.009
#> 64 0.64 0.006 0.007
#> 65 0.65 0.005 0.006
#> 66 0.66 0.004 0.006
#> 67 0.67 0.004 0.006
#> 68 0.68 0.003 0.005
#> 69 0.69 0.003 0.004
#> 70 0.70 0.003 0.002
#> 71 0.71 0.003 0.002
#> 72 0.72 0.003 0.002
#> 73 0.73 0.003 0.002
#> 74 0.74 0.002 0.002
#> 75 0.75 0.002 0.002
#> 76 0.76 0.002 0.002
#> 77 0.77 0.002 0.001
#> 78 0.78 0.002 0.001
#> 79 0.79 0.002 0.001
#> 80 0.80 0.002 0.001
#> 81 0.81 0.002 0.001
#> 82 0.82 0.002 0.001
#> 83 0.83 0.001 0.001
#> 84 0.84 0.001 0.001
#> 85 0.85 0.001 0.001
#> 86 0.86 0.001 0.001
#> 87 0.87 0.000 0.001
#> 88 0.88 0.000 0.001
#> 89 0.89 0.000 0.001
#> 90 0.90 0.000 0.000
#> 91 0.91 0.000 0.000
#> 92 0.92 0.000 0.000
#> 93 0.93 0.000 0.000
#> 94 0.94 0.000 0.000
#> 95 0.95 0.000 0.000
#> 96 0.96 0.000 0.000
#> 97 0.97 0.000 0.000
#> 98 0.98 0.000 0.000
#> 99 0.99 0.000 0.000
#>
#> attr(,"class")
#> [1] "getgamma1cont"
# Example 2: Uncontrolled design, N-Inv-Chisq prior, posterior probability
getgamma1cont(
nsim = 1000L, prob = 'posterior', design = 'uncontrolled',
prior = 'N-Inv-Chisq', CalcMethod = 'NI',
theta_TV = 1.0, theta_MAV = 0.0, theta_NULL = NULL, nMC = NULL,
mu_t_go = 1.5, mu_c_go = NULL, sigma_t_go = 1.5, sigma_c_go = NULL,
mu_t_nogo = 3.0, mu_c_nogo = NULL, sigma_t_nogo = 1.5, sigma_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 20L, n_c = NULL, m_t = NULL, m_c = NULL,
kappa0_t = 2, kappa0_c = NULL, nu0_t = 5, nu0_c = NULL,
mu0_t = 3.0, mu0_c = 1.5, sigma0_t = 1.5, sigma0_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,
gamma_grid = seq(0.01, 0.99, by = 0.01), seed = 2L
)
#> $gamma_go
#> [1] 0.24
#>
#> $gamma_nogo
#> [1] 0.01
#>
#> $PrGo_opt
#> [1] 0.048
#>
#> $PrNoGo_opt
#> [1] 0.136
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.801 0.136
#> 2 0.02 0.653 0.056
#> 3 0.03 0.544 0.030
#> 4 0.04 0.459 0.014
#> 5 0.05 0.394 0.010
#> 6 0.06 0.337 0.007
#> 7 0.07 0.292 0.002
#> 8 0.08 0.253 0.001
#> 9 0.09 0.230 0.000
#> 10 0.10 0.199 0.000
#> 11 0.11 0.184 0.000
#> 12 0.12 0.165 0.000
#> 13 0.13 0.141 0.000
#> 14 0.14 0.127 0.000
#> 15 0.15 0.116 0.000
#> 16 0.16 0.107 0.000
#> 17 0.17 0.101 0.000
#> 18 0.18 0.095 0.000
#> 19 0.19 0.087 0.000
#> 20 0.20 0.070 0.000
#> 21 0.21 0.065 0.000
#> 22 0.22 0.061 0.000
#> 23 0.23 0.055 0.000
#> 24 0.24 0.048 0.000
#> 25 0.25 0.044 0.000
#> 26 0.26 0.040 0.000
#> 27 0.27 0.038 0.000
#> 28 0.28 0.034 0.000
#> 29 0.29 0.030 0.000
#> 30 0.30 0.027 0.000
#> 31 0.31 0.025 0.000
#> 32 0.32 0.022 0.000
#> 33 0.33 0.021 0.000
#> 34 0.34 0.020 0.000
#> 35 0.35 0.018 0.000
#> 36 0.36 0.017 0.000
#> 37 0.37 0.015 0.000
#> 38 0.38 0.015 0.000
#> 39 0.39 0.014 0.000
#> 40 0.40 0.009 0.000
#> 41 0.41 0.009 0.000
#> 42 0.42 0.006 0.000
#> 43 0.43 0.005 0.000
#> 44 0.44 0.004 0.000
#> 45 0.45 0.004 0.000
#> 46 0.46 0.003 0.000
#> 47 0.47 0.002 0.000
#> 48 0.48 0.001 0.000
#> 49 0.49 0.001 0.000
#> 50 0.50 0.001 0.000
#> 51 0.51 0.001 0.000
#> 52 0.52 0.001 0.000
#> 53 0.53 0.001 0.000
#> 54 0.54 0.001 0.000
#> 55 0.55 0.001 0.000
#> 56 0.56 0.001 0.000
#> 57 0.57 0.001 0.000
#> 58 0.58 0.001 0.000
#> 59 0.59 0.001 0.000
#> 60 0.60 0.001 0.000
#> 61 0.61 0.000 0.000
#> 62 0.62 0.000 0.000
#> 63 0.63 0.000 0.000
#> 64 0.64 0.000 0.000
#> 65 0.65 0.000 0.000
#> 66 0.66 0.000 0.000
#> 67 0.67 0.000 0.000
#> 68 0.68 0.000 0.000
#> 69 0.69 0.000 0.000
#> 70 0.70 0.000 0.000
#> 71 0.71 0.000 0.000
#> 72 0.72 0.000 0.000
#> 73 0.73 0.000 0.000
#> 74 0.74 0.000 0.000
#> 75 0.75 0.000 0.000
#> 76 0.76 0.000 0.000
#> 77 0.77 0.000 0.000
#> 78 0.78 0.000 0.000
#> 79 0.79 0.000 0.000
#> 80 0.80 0.000 0.000
#> 81 0.81 0.000 0.000
#> 82 0.82 0.000 0.000
#> 83 0.83 0.000 0.000
#> 84 0.84 0.000 0.000
#> 85 0.85 0.000 0.000
#> 86 0.86 0.000 0.000
#> 87 0.87 0.000 0.000
#> 88 0.88 0.000 0.000
#> 89 0.89 0.000 0.000
#> 90 0.90 0.000 0.000
#> 91 0.91 0.000 0.000
#> 92 0.92 0.000 0.000
#> 93 0.93 0.000 0.000
#> 94 0.94 0.000 0.000
#> 95 0.95 0.000 0.000
#> 96 0.96 0.000 0.000
#> 97 0.97 0.000 0.000
#> 98 0.98 0.000 0.000
#> 99 0.99 0.000 0.000
#>
#> attr(,"class")
#> [1] "getgamma1cont"
# Example 3: External design, vague prior, posterior probability
getgamma1cont(
nsim = 1000L, prob = 'posterior', design = 'external',
prior = 'vague', CalcMethod = 'MM',
theta_TV = 1.0, theta_MAV = 0.0, theta_NULL = NULL, nMC = NULL,
mu_t_go = 1.0, mu_c_go = 1.0, sigma_t_go = 1.5, sigma_c_go = 1.5,
mu_t_nogo = 2.5, mu_c_nogo = 1.0, sigma_t_nogo = 1.5, sigma_c_nogo = 1.5,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = 15L, m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL, ne_t = NULL, ne_c = 20L, alpha0e_t = NULL, alpha0e_c = 0.5,
bar_ye_t = NULL, bar_ye_c = 0.0, se_t = NULL, se_c = 1.5,
gamma_grid = seq(0.01, 0.99, by = 0.01), seed = 4L
)
#> $gamma_go
#> [1] 0.6
#>
#> $gamma_nogo
#> [1] 0.01
#>
#> $PrGo_opt
#> [1] 0.049
#>
#> $PrNoGo_opt
#> [1] 0.098
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.915 0.098
#> 2 0.02 0.853 0.050
#> 3 0.03 0.792 0.028
#> 4 0.04 0.741 0.018
#> 5 0.05 0.706 0.016
#> 6 0.06 0.664 0.010
#> 7 0.07 0.632 0.008
#> 8 0.08 0.600 0.004
#> 9 0.09 0.575 0.003
#> 10 0.10 0.543 0.003
#> 11 0.11 0.508 0.003
#> 12 0.12 0.489 0.001
#> 13 0.13 0.466 0.001
#> 14 0.14 0.442 0.000
#> 15 0.15 0.429 0.000
#> 16 0.16 0.415 0.000
#> 17 0.17 0.391 0.000
#> 18 0.18 0.372 0.000
#> 19 0.19 0.354 0.000
#> 20 0.20 0.339 0.000
#> 21 0.21 0.325 0.000
#> 22 0.22 0.307 0.000
#> 23 0.23 0.289 0.000
#> 24 0.24 0.279 0.000
#> 25 0.25 0.267 0.000
#> 26 0.26 0.249 0.000
#> 27 0.27 0.241 0.000
#> 28 0.28 0.227 0.000
#> 29 0.29 0.215 0.000
#> 30 0.30 0.206 0.000
#> 31 0.31 0.203 0.000
#> 32 0.32 0.198 0.000
#> 33 0.33 0.184 0.000
#> 34 0.34 0.175 0.000
#> 35 0.35 0.165 0.000
#> 36 0.36 0.161 0.000
#> 37 0.37 0.156 0.000
#> 38 0.38 0.151 0.000
#> 39 0.39 0.144 0.000
#> 40 0.40 0.135 0.000
#> 41 0.41 0.131 0.000
#> 42 0.42 0.128 0.000
#> 43 0.43 0.122 0.000
#> 44 0.44 0.117 0.000
#> 45 0.45 0.111 0.000
#> 46 0.46 0.105 0.000
#> 47 0.47 0.101 0.000
#> 48 0.48 0.098 0.000
#> 49 0.49 0.088 0.000
#> 50 0.50 0.081 0.000
#> 51 0.51 0.076 0.000
#> 52 0.52 0.071 0.000
#> 53 0.53 0.068 0.000
#> 54 0.54 0.065 0.000
#> 55 0.55 0.061 0.000
#> 56 0.56 0.058 0.000
#> 57 0.57 0.057 0.000
#> 58 0.58 0.055 0.000
#> 59 0.59 0.052 0.000
#> 60 0.60 0.049 0.000
#> 61 0.61 0.046 0.000
#> 62 0.62 0.043 0.000
#> 63 0.63 0.039 0.000
#> 64 0.64 0.039 0.000
#> 65 0.65 0.037 0.000
#> 66 0.66 0.034 0.000
#> 67 0.67 0.032 0.000
#> 68 0.68 0.031 0.000
#> 69 0.69 0.029 0.000
#> 70 0.70 0.029 0.000
#> 71 0.71 0.026 0.000
#> 72 0.72 0.026 0.000
#> 73 0.73 0.026 0.000
#> 74 0.74 0.026 0.000
#> 75 0.75 0.022 0.000
#> 76 0.76 0.021 0.000
#> 77 0.77 0.018 0.000
#> 78 0.78 0.017 0.000
#> 79 0.79 0.017 0.000
#> 80 0.80 0.015 0.000
#> 81 0.81 0.013 0.000
#> 82 0.82 0.013 0.000
#> 83 0.83 0.010 0.000
#> 84 0.84 0.010 0.000
#> 85 0.85 0.010 0.000
#> 86 0.86 0.008 0.000
#> 87 0.87 0.008 0.000
#> 88 0.88 0.008 0.000
#> 89 0.89 0.006 0.000
#> 90 0.90 0.006 0.000
#> 91 0.91 0.006 0.000
#> 92 0.92 0.005 0.000
#> 93 0.93 0.004 0.000
#> 94 0.94 0.003 0.000
#> 95 0.95 0.002 0.000
#> 96 0.96 0.001 0.000
#> 97 0.97 0.001 0.000
#> 98 0.98 0.001 0.000
#> 99 0.99 0.001 0.000
#>
#> attr(,"class")
#> [1] "getgamma1cont"
# Example 4: Controlled design, vague prior, predictive probability
getgamma1cont(
nsim = 1000L, prob = 'predictive', design = 'controlled',
prior = 'vague', CalcMethod = 'MM',
theta_TV = NULL, theta_MAV = NULL, theta_NULL = 1.0, nMC = NULL,
mu_t_go = 1.0, mu_c_go = 1.0, sigma_t_go = 2.0, sigma_c_go = 2.0,
mu_t_nogo = 2.5, mu_c_nogo = 1.0, sigma_t_nogo = 2.0, sigma_c_nogo = 2.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = 15L, m_t = 50L, m_c = 50L,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_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,
gamma_grid = seq(0.01, 0.99, by = 0.01), seed = 3L
)
#> $gamma_go
#> [1] 0.64
#>
#> $gamma_nogo
#> [1] 0.63
#>
#> $PrGo_opt
#> [1] 0.048
#>
#> $PrNoGo_opt
#> [1] 0.197
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.535 0.786
#> 2 0.02 0.451 0.730
#> 3 0.03 0.417 0.695
#> 4 0.04 0.391 0.669
#> 5 0.05 0.364 0.637
#> 6 0.06 0.335 0.617
#> 7 0.07 0.317 0.590
#> 8 0.08 0.300 0.568
#> 9 0.09 0.288 0.551
#> 10 0.10 0.279 0.532
#> 11 0.11 0.270 0.523
#> 12 0.12 0.261 0.514
#> 13 0.13 0.251 0.500
#> 14 0.14 0.240 0.492
#> 15 0.15 0.230 0.487
#> 16 0.16 0.221 0.474
#> 17 0.17 0.216 0.463
#> 18 0.18 0.208 0.458
#> 19 0.19 0.198 0.450
#> 20 0.20 0.193 0.441
#> 21 0.21 0.183 0.434
#> 22 0.22 0.177 0.430
#> 23 0.23 0.175 0.425
#> 24 0.24 0.173 0.410
#> 25 0.25 0.167 0.405
#> 26 0.26 0.162 0.396
#> 27 0.27 0.157 0.389
#> 28 0.28 0.151 0.382
#> 29 0.29 0.148 0.374
#> 30 0.30 0.142 0.362
#> 31 0.31 0.138 0.358
#> 32 0.32 0.135 0.347
#> 33 0.33 0.130 0.342
#> 34 0.34 0.127 0.333
#> 35 0.35 0.126 0.329
#> 36 0.36 0.119 0.327
#> 37 0.37 0.116 0.322
#> 38 0.38 0.110 0.314
#> 39 0.39 0.109 0.309
#> 40 0.40 0.107 0.306
#> 41 0.41 0.105 0.302
#> 42 0.42 0.103 0.295
#> 43 0.43 0.096 0.289
#> 44 0.44 0.091 0.286
#> 45 0.45 0.089 0.281
#> 46 0.46 0.087 0.276
#> 47 0.47 0.086 0.272
#> 48 0.48 0.085 0.265
#> 49 0.49 0.081 0.255
#> 50 0.50 0.077 0.250
#> 51 0.51 0.076 0.244
#> 52 0.52 0.072 0.241
#> 53 0.53 0.069 0.235
#> 54 0.54 0.067 0.229
#> 55 0.55 0.062 0.227
#> 56 0.56 0.060 0.220
#> 57 0.57 0.059 0.216
#> 58 0.58 0.057 0.209
#> 59 0.59 0.055 0.207
#> 60 0.60 0.054 0.205
#> 61 0.61 0.054 0.203
#> 62 0.62 0.053 0.201
#> 63 0.63 0.051 0.197
#> 64 0.64 0.048 0.193
#> 65 0.65 0.048 0.191
#> 66 0.66 0.043 0.182
#> 67 0.67 0.040 0.179
#> 68 0.68 0.039 0.172
#> 69 0.69 0.039 0.167
#> 70 0.70 0.038 0.160
#> 71 0.71 0.038 0.158
#> 72 0.72 0.037 0.152
#> 73 0.73 0.034 0.148
#> 74 0.74 0.033 0.145
#> 75 0.75 0.032 0.144
#> 76 0.76 0.029 0.140
#> 77 0.77 0.029 0.132
#> 78 0.78 0.026 0.126
#> 79 0.79 0.025 0.119
#> 80 0.80 0.025 0.116
#> 81 0.81 0.022 0.111
#> 82 0.82 0.019 0.106
#> 83 0.83 0.017 0.103
#> 84 0.84 0.017 0.096
#> 85 0.85 0.017 0.094
#> 86 0.86 0.015 0.091
#> 87 0.87 0.015 0.086
#> 88 0.88 0.012 0.083
#> 89 0.89 0.011 0.076
#> 90 0.90 0.009 0.072
#> 91 0.91 0.008 0.067
#> 92 0.92 0.005 0.058
#> 93 0.93 0.003 0.052
#> 94 0.94 0.003 0.047
#> 95 0.95 0.002 0.043
#> 96 0.96 0.002 0.034
#> 97 0.97 0.001 0.028
#> 98 0.98 0.001 0.021
#> 99 0.99 0.000 0.016
#>
#> attr(,"class")
#> [1] "getgamma1cont"
# Example 5: Uncontrolled design, vague prior, predictive probability
getgamma1cont(
nsim = 1000L, prob = 'predictive', design = 'uncontrolled',
prior = 'vague', CalcMethod = 'MM',
theta_TV = NULL, theta_MAV = NULL, theta_NULL = 1.0, nMC = NULL,
mu_t_go = 1.0, mu_c_go = NULL, sigma_t_go = 2.0, sigma_c_go = NULL,
mu_t_nogo = 2.5, mu_c_nogo = NULL, sigma_t_nogo = 2.0, sigma_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = NULL, m_t = 50L, m_c = 50L,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = 0.0, sigma0_t = NULL, sigma0_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,
gamma_grid = seq(0.01, 0.99, by = 0.01), seed = 5L
)
#> $gamma_go
#> [1] 0.98
#>
#> $gamma_nogo
#> [1] 0.02
#>
#> $PrGo_opt
#> [1] 0.044
#>
#> $PrNoGo_opt
#> [1] 0.136
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.971 0.205
#> 2 0.02 0.954 0.136
#> 3 0.03 0.942 0.113
#> 4 0.04 0.927 0.092
#> 5 0.05 0.910 0.067
#> 6 0.06 0.898 0.058
#> 7 0.07 0.878 0.049
#> 8 0.08 0.862 0.039
#> 9 0.09 0.847 0.035
#> 10 0.10 0.833 0.032
#> 11 0.11 0.823 0.029
#> 12 0.12 0.812 0.025
#> 13 0.13 0.805 0.020
#> 14 0.14 0.798 0.019
#> 15 0.15 0.793 0.017
#> 16 0.16 0.780 0.017
#> 17 0.17 0.773 0.016
#> 18 0.18 0.764 0.013
#> 19 0.19 0.751 0.013
#> 20 0.20 0.742 0.011
#> 21 0.21 0.733 0.009
#> 22 0.22 0.728 0.008
#> 23 0.23 0.717 0.005
#> 24 0.24 0.709 0.004
#> 25 0.25 0.702 0.004
#> 26 0.26 0.686 0.004
#> 27 0.27 0.672 0.004
#> 28 0.28 0.664 0.004
#> 29 0.29 0.655 0.004
#> 30 0.30 0.653 0.004
#> 31 0.31 0.646 0.004
#> 32 0.32 0.636 0.004
#> 33 0.33 0.629 0.004
#> 34 0.34 0.619 0.004
#> 35 0.35 0.611 0.004
#> 36 0.36 0.604 0.004
#> 37 0.37 0.594 0.003
#> 38 0.38 0.587 0.003
#> 39 0.39 0.578 0.003
#> 40 0.40 0.573 0.003
#> 41 0.41 0.568 0.003
#> 42 0.42 0.562 0.003
#> 43 0.43 0.559 0.003
#> 44 0.44 0.550 0.002
#> 45 0.45 0.540 0.002
#> 46 0.46 0.532 0.002
#> 47 0.47 0.524 0.002
#> 48 0.48 0.518 0.002
#> 49 0.49 0.511 0.002
#> 50 0.50 0.502 0.002
#> 51 0.51 0.493 0.002
#> 52 0.52 0.484 0.002
#> 53 0.53 0.473 0.002
#> 54 0.54 0.468 0.002
#> 55 0.55 0.462 0.002
#> 56 0.56 0.453 0.002
#> 57 0.57 0.451 0.002
#> 58 0.58 0.437 0.002
#> 59 0.59 0.425 0.002
#> 60 0.60 0.415 0.002
#> 61 0.61 0.412 0.002
#> 62 0.62 0.404 0.002
#> 63 0.63 0.395 0.001
#> 64 0.64 0.386 0.001
#> 65 0.65 0.379 0.001
#> 66 0.66 0.370 0.001
#> 67 0.67 0.363 0.001
#> 68 0.68 0.357 0.001
#> 69 0.69 0.350 0.001
#> 70 0.70 0.333 0.001
#> 71 0.71 0.330 0.001
#> 72 0.72 0.321 0.001
#> 73 0.73 0.314 0.001
#> 74 0.74 0.303 0.001
#> 75 0.75 0.291 0.001
#> 76 0.76 0.279 0.001
#> 77 0.77 0.273 0.001
#> 78 0.78 0.261 0.001
#> 79 0.79 0.255 0.001
#> 80 0.80 0.249 0.001
#> 81 0.81 0.240 0.001
#> 82 0.82 0.226 0.001
#> 83 0.83 0.217 0.001
#> 84 0.84 0.209 0.001
#> 85 0.85 0.201 0.001
#> 86 0.86 0.189 0.001
#> 87 0.87 0.169 0.001
#> 88 0.88 0.163 0.000
#> 89 0.89 0.151 0.000
#> 90 0.90 0.140 0.000
#> 91 0.91 0.130 0.000
#> 92 0.92 0.118 0.000
#> 93 0.93 0.109 0.000
#> 94 0.94 0.099 0.000
#> 95 0.95 0.087 0.000
#> 96 0.96 0.076 0.000
#> 97 0.97 0.065 0.000
#> 98 0.98 0.044 0.000
#> 99 0.99 0.024 0.000
#>
#> attr(,"class")
#> [1] "getgamma1cont"
# Example 6: External design, vague prior, predictive probability
getgamma1cont(
nsim = 1000L, prob = 'predictive', design = 'external',
prior = 'vague', CalcMethod = 'MM',
theta_TV = NULL, theta_MAV = NULL, theta_NULL = 1.0, nMC = NULL,
mu_t_go = 1.0, mu_c_go = 1.0, sigma_t_go = 1.5, sigma_c_go = 1.5,
mu_t_nogo = 2.5, mu_c_nogo = 1.0, sigma_t_nogo = 1.5, sigma_c_nogo = 1.5,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = 15L, m_t = 50L, m_c = 50L,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL, ne_t = NULL, ne_c = 20L, alpha0e_t = NULL, alpha0e_c = 0.5,
bar_ye_t = NULL, bar_ye_c = 0.0, se_t = NULL, se_c = 1.5,
gamma_grid = seq(0.01, 0.99, by = 0.01), seed = 6L
)
#> $gamma_go
#> [1] 0.73
#>
#> $gamma_nogo
#> [1] 0.06
#>
#> $PrGo_opt
#> [1] 0.049
#>
#> $PrNoGo_opt
#> [1] 0.188
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.667 0.395
#> 2 0.02 0.593 0.310
#> 3 0.03 0.530 0.261
#> 4 0.04 0.496 0.236
#> 5 0.05 0.462 0.212
#> 6 0.06 0.445 0.188
#> 7 0.07 0.417 0.161
#> 8 0.08 0.391 0.152
#> 9 0.09 0.374 0.139
#> 10 0.10 0.355 0.132
#> 11 0.11 0.341 0.128
#> 12 0.12 0.322 0.122
#> 13 0.13 0.307 0.112
#> 14 0.14 0.299 0.104
#> 15 0.15 0.288 0.101
#> 16 0.16 0.280 0.100
#> 17 0.17 0.268 0.096
#> 18 0.18 0.260 0.092
#> 19 0.19 0.253 0.087
#> 20 0.20 0.239 0.082
#> 21 0.21 0.231 0.081
#> 22 0.22 0.226 0.074
#> 23 0.23 0.217 0.072
#> 24 0.24 0.211 0.066
#> 25 0.25 0.204 0.062
#> 26 0.26 0.197 0.059
#> 27 0.27 0.192 0.057
#> 28 0.28 0.187 0.057
#> 29 0.29 0.179 0.055
#> 30 0.30 0.175 0.052
#> 31 0.31 0.170 0.051
#> 32 0.32 0.166 0.050
#> 33 0.33 0.162 0.047
#> 34 0.34 0.158 0.046
#> 35 0.35 0.154 0.041
#> 36 0.36 0.150 0.039
#> 37 0.37 0.147 0.039
#> 38 0.38 0.145 0.038
#> 39 0.39 0.136 0.037
#> 40 0.40 0.131 0.037
#> 41 0.41 0.129 0.034
#> 42 0.42 0.128 0.033
#> 43 0.43 0.125 0.032
#> 44 0.44 0.123 0.030
#> 45 0.45 0.121 0.030
#> 46 0.46 0.118 0.030
#> 47 0.47 0.111 0.028
#> 48 0.48 0.107 0.025
#> 49 0.49 0.103 0.023
#> 50 0.50 0.102 0.023
#> 51 0.51 0.099 0.020
#> 52 0.52 0.099 0.017
#> 53 0.53 0.095 0.017
#> 54 0.54 0.093 0.017
#> 55 0.55 0.092 0.016
#> 56 0.56 0.090 0.015
#> 57 0.57 0.088 0.015
#> 58 0.58 0.086 0.015
#> 59 0.59 0.085 0.013
#> 60 0.60 0.080 0.013
#> 61 0.61 0.079 0.013
#> 62 0.62 0.075 0.013
#> 63 0.63 0.071 0.013
#> 64 0.64 0.067 0.012
#> 65 0.65 0.063 0.012
#> 66 0.66 0.063 0.011
#> 67 0.67 0.060 0.010
#> 68 0.68 0.059 0.010
#> 69 0.69 0.059 0.010
#> 70 0.70 0.057 0.010
#> 71 0.71 0.055 0.010
#> 72 0.72 0.051 0.010
#> 73 0.73 0.049 0.010
#> 74 0.74 0.048 0.009
#> 75 0.75 0.044 0.008
#> 76 0.76 0.040 0.007
#> 77 0.77 0.036 0.007
#> 78 0.78 0.032 0.007
#> 79 0.79 0.028 0.007
#> 80 0.80 0.027 0.007
#> 81 0.81 0.025 0.007
#> 82 0.82 0.024 0.007
#> 83 0.83 0.023 0.007
#> 84 0.84 0.022 0.005
#> 85 0.85 0.020 0.004
#> 86 0.86 0.017 0.003
#> 87 0.87 0.012 0.003
#> 88 0.88 0.012 0.002
#> 89 0.89 0.010 0.002
#> 90 0.90 0.008 0.002
#> 91 0.91 0.007 0.002
#> 92 0.92 0.007 0.002
#> 93 0.93 0.007 0.002
#> 94 0.94 0.005 0.002
#> 95 0.95 0.005 0.002
#> 96 0.96 0.003 0.001
#> 97 0.97 0.003 0.001
#> 98 0.98 0.002 0.001
#> 99 0.99 0.002 0.001
#>
#> attr(,"class")
#> [1] "getgamma1cont"