Find Optimal Go/NoGo Thresholds for Two Continuous Endpoints
Source:R/getgamma2cont.R
getgamma2cont.RdComputes the optimal Go threshold \(\gamma_{\mathrm{go}}\) and NoGo threshold \(\gamma_{\mathrm{nogo}}\) for two continuous endpoints by searching independently over candidate threshold grids. The two thresholds are calibrated marginally under separate scenarios:
\(\gamma_{\mathrm{go}}\) is the smallest value in
gamma_go_gridsuch that the marginal Go probability is strictly less thantarget_gounder the Go-calibration scenario (mu_t_go,Sigma_t_go,mu_c_go,Sigma_c_go); typically the Null scenario.\(\gamma_{\mathrm{nogo}}\) is the smallest value in
gamma_nogo_gridsuch that the marginal NoGo probability is strictly less thantarget_nogounder the NoGo-calibration scenario (mu_t_nogo,Sigma_t_nogo,mu_c_nogo,Sigma_c_nogo); typically the Alternative scenario.
Usage
getgamma2cont(
nsim = 10000L,
prob = "posterior",
design = "controlled",
prior = "vague",
GoRegions,
NoGoRegions,
mu_t_go,
Sigma_t_go,
mu_c_go = NULL,
Sigma_c_go = NULL,
mu_t_nogo,
Sigma_t_nogo,
mu_c_nogo = NULL,
Sigma_c_nogo = NULL,
target_go,
target_nogo,
n_t,
n_c = NULL,
theta_TV1 = NULL,
theta_MAV1 = NULL,
theta_TV2 = NULL,
theta_MAV2 = NULL,
theta_NULL1 = NULL,
theta_NULL2 = NULL,
m_t = NULL,
m_c = NULL,
kappa0_t = NULL,
nu0_t = NULL,
mu0_t = NULL,
Lambda0_t = NULL,
kappa0_c = NULL,
nu0_c = NULL,
mu0_c = NULL,
Lambda0_c = NULL,
r = NULL,
ne_t = NULL,
ne_c = NULL,
alpha0e_t = NULL,
alpha0e_c = NULL,
bar_ye_t = NULL,
bar_ye_c = NULL,
se_t = NULL,
se_c = NULL,
nMC = NULL,
CalcMethod = "MC",
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed
)Arguments
- nsim
A positive integer giving the number of Monte Carlo datasets to simulate per calibration scenario. Default is
10000L.- prob
A character string specifying the probability type. Must be
'posterior'or'predictive'.- design
A character string specifying the trial design. Must be
'controlled','uncontrolled', or'external'.- prior
A character string specifying the prior distribution. Must be
'vague'or'N-Inv-Wishart'.- GoRegions
An integer vector of region indices (subset of
1:9) that constitute the Go region. The 9 regions are defined by the cross-classification of the two treatment effects \((\theta_1, \theta_2)\) relative to(TV1, MAV1)and(TV2, MAV2): region \(k = (z_1 - 1) \times 3 + z_2\) where \(z_i = 1\) if \(\theta_i > TV_i\), \(z_i = 2\) if \(MAV_i < \theta_i \le TV_i\), \(z_i = 3\) if \(\theta_i \le MAV_i\).- NoGoRegions
An integer vector of region indices (subset of
1:9) that constitute the NoGo region. Must be disjoint fromGoRegions.- mu_t_go
A length-2 numeric vector giving the true bivariate mean for the treatment group under the Go-calibration scenario (typically Null).
- Sigma_t_go
A 2x2 positive-definite numeric matrix giving the true within-group covariance in the treatment group under the Go-calibration scenario.
- mu_c_go
A length-2 numeric vector giving the true bivariate mean for the control group under the Go-calibration scenario. Required for
design = 'controlled'or'external'; set toNULLfordesign = 'uncontrolled'.- Sigma_c_go
A 2x2 positive-definite numeric matrix giving the true within-group covariance in the control group under the Go-calibration scenario. Required for
design = 'controlled'or'external'; set toNULLfordesign = 'uncontrolled'.- mu_t_nogo
A length-2 numeric vector giving the true bivariate mean for the treatment group under the NoGo-calibration scenario (typically Alternative).
- Sigma_t_nogo
A 2x2 positive-definite numeric matrix giving the true within-group covariance in the treatment group under the NoGo-calibration scenario.
- mu_c_nogo
A length-2 numeric vector giving the true bivariate mean for the control group under the NoGo-calibration scenario. Required for
design = 'controlled'or'external'; set toNULLfordesign = 'uncontrolled'.- Sigma_c_nogo
A 2x2 positive-definite numeric matrix giving the true within-group covariance in the control group under the NoGo-calibration scenario. Required for
design = 'controlled'or'external'; set toNULLfordesign = '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 the constraint.- 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 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. Set to
NULLfordesign = 'uncontrolled'.- theta_TV1
A numeric scalar giving the TV threshold for Endpoint 1. Required when
prob = 'posterior'; otherwise set toNULL.- theta_MAV1
A numeric scalar giving the MAV threshold for Endpoint 1. Required when
prob = 'posterior'; otherwise set toNULL.- theta_TV2
A numeric scalar giving the TV threshold for Endpoint 2. Required when
prob = 'posterior'; otherwise set toNULL.- theta_MAV2
A numeric scalar giving the MAV threshold for Endpoint 2. Required when
prob = 'posterior'; otherwise set toNULL.- theta_NULL1
A numeric scalar giving the null hypothesis threshold for Endpoint 1. Required when
prob = 'predictive'; otherwise set toNULL.- theta_NULL2
A numeric scalar giving the null hypothesis threshold for Endpoint 2. Required when
prob = 'predictive'; otherwise set toNULL.- 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
Positive numeric scalar. NIW prior hyperparameter \(\kappa_{01}\) for the treatment group. Required when
prior = 'N-Inv-Wishart'; otherwiseNULL.- nu0_t
Positive numeric scalar. NIW prior degrees of freedom \(\nu_{01}\) for the treatment group. Required when
prior = 'N-Inv-Wishart'; otherwiseNULL.- mu0_t
Length-2 numeric vector. NIW prior mean \(\mu_{01}\) for the treatment group. Required when
prior = 'N-Inv-Wishart'; otherwiseNULL.- Lambda0_t
A 2x2 positive-definite numeric matrix. NIW prior scale matrix \(\Lambda_{01}\) for the treatment group. Required when
prior = 'N-Inv-Wishart'; otherwiseNULL.- kappa0_c
Positive numeric scalar; see
kappa0_t. For the control group.- nu0_c
Positive numeric scalar; see
nu0_t. For the control group.- mu0_c
Length-2 numeric vector; see
mu0_t. For the control group. May be required for the vague prior uncontrolled design; seepbayesdecisionprob2cont.- Lambda0_c
A 2x2 matrix; see
Lambda0_t. For the control group.- r
A positive numeric scalar giving the power prior weight for the control group when
design = 'uncontrolled'andprior = 'vague'. OtherwiseNULL.- ne_t
A positive integer giving the external treatment sample size. Required when
design = 'external'and external treatment data are used; otherwiseNULL.- ne_c
A positive integer giving the external control sample size. Required when
design = 'external'and external control data are used; otherwiseNULL.- alpha0e_t
A numeric scalar in
(0, 1]giving the power prior weight for external treatment data. Required when external treatment data are used; otherwiseNULL.- alpha0e_c
A numeric scalar in
(0, 1]giving the power prior weight for external control data. Required when external control data are used; otherwiseNULL.- bar_ye_t
A length-2 numeric vector. External treatment sample mean. Required when external treatment data are used; otherwise
NULL.- bar_ye_c
A length-2 numeric vector. External control sample mean. Required when external control data are used; otherwise
NULL.- se_t
A 2x2 numeric matrix. External treatment sum-of-squares matrix. Required when external treatment data are used; otherwise
NULL.- se_c
A 2x2 numeric matrix. External control sum-of-squares matrix. Required when external control data are used; otherwise
NULL.- nMC
A positive integer giving the number of Monte Carlo draws passed to
pbayespostpred2cont. Required whenCalcMethod = 'MC'. May be set toNULLwhenCalcMethod = 'MM'and \(\nu_k > 4\); ifCalcMethod = 'MM'but \(\nu_k \le 4\) causes a fallback to MC,nMCmust be a positive integer. Default isNULL.- CalcMethod
A character string specifying the computation method passed to
pbayespostpred2cont. Must be'MC'(default) or'MM'.- gamma_go_grid
A numeric vector of candidate Go threshold values in
(0, 1)to search over. Defaults toseq(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 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 getgamma2cont 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 \(\Pr(\mathrm{Go})\) at
gamma_gounder the Go-calibration scenario.NAifgamma_goisNA.- PrNoGo_opt
Marginal \(\Pr(\mathrm{NoGo})\) at
gamma_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).
Details
The function uses a two-stage simulate-then-sweep strategy:
Stage 1 (simulation and precomputation): nsim bivariate
datasets are generated independently for each calibration scenario.
For the Go-calibration scenario, datasets are drawn from
\(N_2(\mu_{t,\mathrm{go}}, \Sigma_{t,\mathrm{go}})\) (and
\(N_2(\mu_{c,\mathrm{go}}, \Sigma_{c,\mathrm{go}})\) for
controlled/external designs); for the NoGo-calibration scenario,
the corresponding _nogo parameters are used.
pbayespostpred2cont is called once per scenario in
vectorised mode to return an \(nsim \times 9\) matrix of region
probabilities. The probabilities are summed over GoRegions
(for the Go scenario) and NoGoRegions (for the NoGo scenario)
to obtain \(\hat{g}_{Go,i}\) and \(\hat{g}_{NoGo,i}\),
independent of the decision thresholds.
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: $$\Pr(\mathrm{Go}) = \frac{1}{n_{\mathrm{sim}}} \sum_{i=1}^{n_{\mathrm{sim}}} \mathbf{1}\!\left[\hat{g}_{Go,i} \ge \gamma_{\mathrm{go}},\; \hat{g}_{NoGo,i} < \gamma_{\mathrm{nogo}}\right]$$ $$\Pr(\mathrm{NoGo}) = \frac{1}{n_{\mathrm{sim}}} \sum_{i=1}^{n_{\mathrm{sim}}} \mathbf{1}\!\left[\hat{g}_{NoGo,i} \ge \gamma_{\mathrm{nogo}},\; \hat{g}_{Go,i} < \gamma_{\mathrm{go}}\right]$$
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.
Examples
# Example 1: Controlled design, posterior probability, vague prior
# 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
# \donttest{
Sigma_null <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
Sigma_alt <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
getgamma2cont(
nsim = 1000L, prob = 'posterior', design = 'controlled',
prior = 'vague',
GoRegions = 1L, NoGoRegions = 9L,
mu_t_go = c(-5.0, 0.0), Sigma_t_go = Sigma_null,
mu_c_go = c(-10.0, -1.0), Sigma_c_go = Sigma_null,
mu_t_nogo = c(5.0, 1.0), Sigma_t_nogo = Sigma_alt,
mu_c_nogo = c(-10.0, -1.0), Sigma_c_nogo = Sigma_alt,
target_go = 0.05, target_nogo = 0.20,
n_t = 30L, n_c = 30L,
theta_TV1 = 10.0, theta_MAV1 = 5.0,
theta_TV2 = 2.0, theta_MAV2 = 1.0,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, nu0_t = NULL, mu0_t = NULL, Lambda0_t = NULL,
kappa0_c = NULL, nu0_c = NULL, mu0_c = NULL, Lambda0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
nMC = 500L, CalcMethod = 'MC',
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed = 1L
)
#> $gamma_go
#> [1] 0.54
#>
#> $gamma_nogo
#> [1] 0.2
#>
#> $PrGo_opt
#> [1] 0.048
#>
#> $PrNoGo_opt
#> [1] 0.199
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.869 0.790
#> 2 0.02 0.791 0.705
#> 3 0.03 0.720 0.630
#> 4 0.04 0.662 0.575
#> 5 0.05 0.611 0.538
#> 6 0.06 0.559 0.491
#> 7 0.07 0.534 0.452
#> 8 0.08 0.503 0.420
#> 9 0.09 0.476 0.390
#> 10 0.10 0.442 0.364
#> 11 0.11 0.406 0.340
#> 12 0.12 0.374 0.319
#> 13 0.13 0.355 0.298
#> 14 0.14 0.342 0.282
#> 15 0.15 0.321 0.265
#> 16 0.16 0.311 0.253
#> 17 0.17 0.296 0.238
#> 18 0.18 0.284 0.222
#> 19 0.19 0.274 0.208
#> 20 0.20 0.260 0.199
#> 21 0.21 0.243 0.186
#> 22 0.22 0.234 0.180
#> 23 0.23 0.222 0.173
#> 24 0.24 0.212 0.163
#> 25 0.25 0.204 0.156
#> 26 0.26 0.197 0.142
#> 27 0.27 0.185 0.133
#> 28 0.28 0.182 0.124
#> 29 0.29 0.175 0.112
#> 30 0.30 0.164 0.109
#> 31 0.31 0.154 0.104
#> 32 0.32 0.145 0.102
#> 33 0.33 0.142 0.099
#> 34 0.34 0.138 0.092
#> 35 0.35 0.126 0.083
#> 36 0.36 0.119 0.078
#> 37 0.37 0.114 0.075
#> 38 0.38 0.108 0.074
#> 39 0.39 0.103 0.071
#> 40 0.40 0.101 0.066
#> 41 0.41 0.096 0.059
#> 42 0.42 0.094 0.058
#> 43 0.43 0.090 0.053
#> 44 0.44 0.085 0.051
#> 45 0.45 0.081 0.048
#> 46 0.46 0.077 0.045
#> 47 0.47 0.073 0.043
#> 48 0.48 0.069 0.040
#> 49 0.49 0.064 0.040
#> 50 0.50 0.063 0.037
#> 51 0.51 0.059 0.036
#> 52 0.52 0.054 0.036
#> 53 0.53 0.051 0.036
#> 54 0.54 0.048 0.034
#> 55 0.55 0.044 0.030
#> 56 0.56 0.038 0.027
#> 57 0.57 0.036 0.022
#> 58 0.58 0.033 0.020
#> 59 0.59 0.033 0.019
#> 60 0.60 0.031 0.017
#> 61 0.61 0.028 0.016
#> 62 0.62 0.026 0.012
#> 63 0.63 0.025 0.012
#> 64 0.64 0.025 0.011
#> 65 0.65 0.025 0.010
#> 66 0.66 0.024 0.010
#> 67 0.67 0.021 0.010
#> 68 0.68 0.019 0.009
#> 69 0.69 0.017 0.006
#> 70 0.70 0.014 0.006
#> 71 0.71 0.013 0.004
#> 72 0.72 0.013 0.004
#> 73 0.73 0.011 0.004
#> 74 0.74 0.008 0.004
#> 75 0.75 0.008 0.004
#> 76 0.76 0.008 0.004
#> 77 0.77 0.006 0.004
#> 78 0.78 0.006 0.003
#> 79 0.79 0.005 0.002
#> 80 0.80 0.005 0.001
#> 81 0.81 0.005 0.001
#> 82 0.82 0.005 0.000
#> 83 0.83 0.003 0.000
#> 84 0.84 0.003 0.000
#> 85 0.85 0.002 0.000
#> 86 0.86 0.002 0.000
#> 87 0.87 0.001 0.000
#> 88 0.88 0.001 0.000
#> 89 0.89 0.001 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] "getgamma2cont"
# }
# Example 2: Uncontrolled design, posterior probability, vague prior
# \donttest{
Sigma_null <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
Sigma_alt <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
getgamma2cont(
nsim = 1000L, prob = 'posterior', design = 'uncontrolled',
prior = 'vague',
GoRegions = 1L, NoGoRegions = 9L,
mu_t_go = c(-5.0, 0.0), Sigma_t_go = Sigma_null,
mu_c_go = NULL, Sigma_c_go = NULL,
mu_t_nogo = c(5.0, 1.0), Sigma_t_nogo = Sigma_alt,
mu_c_nogo = NULL, Sigma_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 30L, n_c = NULL,
theta_TV1 = 10.0, theta_MAV1 = 5.0,
theta_TV2 = 2.0, theta_MAV2 = 1.0,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, nu0_t = NULL, mu0_t = NULL, Lambda0_t = NULL,
kappa0_c = NULL, nu0_c = NULL, mu0_c = c(-10.0, -1.0), Lambda0_c = NULL,
r = 1.0,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
nMC = NULL, CalcMethod = 'MM',
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed = 1L
)
#> $gamma_go
#> [1] 0.41
#>
#> $gamma_nogo
#> [1] 0.18
#>
#> $PrGo_opt
#> [1] 0.048
#>
#> $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 0.927 0.869
#> 2 0.02 0.855 0.784
#> 3 0.03 0.800 0.712
#> 4 0.04 0.746 0.647
#> 5 0.05 0.688 0.591
#> 6 0.06 0.636 0.541
#> 7 0.07 0.589 0.487
#> 8 0.08 0.554 0.448
#> 9 0.09 0.522 0.410
#> 10 0.10 0.470 0.385
#> 11 0.11 0.445 0.355
#> 12 0.12 0.416 0.327
#> 13 0.13 0.385 0.297
#> 14 0.14 0.352 0.271
#> 15 0.15 0.326 0.247
#> 16 0.16 0.304 0.227
#> 17 0.17 0.282 0.209
#> 18 0.18 0.258 0.188
#> 19 0.19 0.244 0.173
#> 20 0.20 0.228 0.166
#> 21 0.21 0.211 0.152
#> 22 0.22 0.194 0.138
#> 23 0.23 0.179 0.130
#> 24 0.24 0.167 0.125
#> 25 0.25 0.155 0.113
#> 26 0.26 0.145 0.101
#> 27 0.27 0.132 0.098
#> 28 0.28 0.118 0.085
#> 29 0.29 0.111 0.079
#> 30 0.30 0.103 0.076
#> 31 0.31 0.097 0.070
#> 32 0.32 0.090 0.066
#> 33 0.33 0.084 0.063
#> 34 0.34 0.078 0.061
#> 35 0.35 0.075 0.054
#> 36 0.36 0.069 0.050
#> 37 0.37 0.064 0.045
#> 38 0.38 0.059 0.042
#> 39 0.39 0.052 0.035
#> 40 0.40 0.050 0.032
#> 41 0.41 0.048 0.030
#> 42 0.42 0.043 0.029
#> 43 0.43 0.039 0.026
#> 44 0.44 0.034 0.024
#> 45 0.45 0.031 0.020
#> 46 0.46 0.028 0.019
#> 47 0.47 0.021 0.016
#> 48 0.48 0.021 0.015
#> 49 0.49 0.020 0.015
#> 50 0.50 0.019 0.012
#> 51 0.51 0.018 0.012
#> 52 0.52 0.018 0.012
#> 53 0.53 0.018 0.011
#> 54 0.54 0.016 0.008
#> 55 0.55 0.015 0.007
#> 56 0.56 0.012 0.006
#> 57 0.57 0.011 0.005
#> 58 0.58 0.010 0.005
#> 59 0.59 0.009 0.005
#> 60 0.60 0.007 0.005
#> 61 0.61 0.006 0.004
#> 62 0.62 0.005 0.004
#> 63 0.63 0.005 0.004
#> 64 0.64 0.005 0.004
#> 65 0.65 0.005 0.004
#> 66 0.66 0.004 0.003
#> 67 0.67 0.003 0.003
#> 68 0.68 0.002 0.002
#> 69 0.69 0.002 0.002
#> 70 0.70 0.001 0.001
#> 71 0.71 0.001 0.001
#> 72 0.72 0.001 0.001
#> 73 0.73 0.001 0.001
#> 74 0.74 0.001 0.001
#> 75 0.75 0.000 0.001
#> 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] "getgamma2cont"
# }
# Example 3: External design (control only), posterior probability, NIW prior
# \donttest{
Sigma <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
Lambda <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
se_c <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
getgamma2cont(
nsim = 1000L, prob = 'posterior', design = 'external',
prior = 'N-Inv-Wishart',
GoRegions = 1L, NoGoRegions = 9L,
mu_t_go = c(-5.0, 0.0), Sigma_t_go = Sigma,
mu_c_go = c(-10.0, -1.0), Sigma_c_go = Sigma,
mu_t_nogo = c(5.0, 1.0), Sigma_t_nogo = Sigma,
mu_c_nogo = c(-10.0, -1.0), Sigma_c_nogo = Sigma,
target_go = 0.05, target_nogo = 0.20,
n_t = 30L, n_c = 30L,
theta_TV1 = 10.0, theta_MAV1 = 5.0,
theta_TV2 = 2.0, theta_MAV2 = 1.0,
theta_NULL1 = NULL, theta_NULL2 = NULL,
m_t = NULL, m_c = NULL,
kappa0_t = 0.1, nu0_t = 4.0, mu0_t = c(0.0, 1.0), Lambda0_t = Lambda,
kappa0_c = 0.1, nu0_c = 4.0, mu0_c = c(-10.0, -1.0), Lambda0_c = Lambda,
r = NULL,
ne_t = NULL, ne_c = 10L, alpha0e_t = NULL, alpha0e_c = 0.5,
bar_ye_t = NULL, bar_ye_c = c(-10.0, -1.0), se_t = NULL, se_c = se_c,
nMC = 500L, CalcMethod = 'MC',
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed = 1L
)
#> $gamma_go
#> [1] 0.53
#>
#> $gamma_nogo
#> [1] 0.2
#>
#> $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 0.803 0.770
#> 2 0.02 0.712 0.682
#> 3 0.03 0.648 0.617
#> 4 0.04 0.596 0.555
#> 5 0.05 0.550 0.498
#> 6 0.06 0.517 0.463
#> 7 0.07 0.491 0.435
#> 8 0.08 0.469 0.405
#> 9 0.09 0.435 0.383
#> 10 0.10 0.413 0.355
#> 11 0.11 0.397 0.335
#> 12 0.12 0.370 0.318
#> 13 0.13 0.350 0.293
#> 14 0.14 0.335 0.275
#> 15 0.15 0.320 0.254
#> 16 0.16 0.310 0.244
#> 17 0.17 0.298 0.228
#> 18 0.18 0.286 0.209
#> 19 0.19 0.271 0.201
#> 20 0.20 0.257 0.191
#> 21 0.21 0.242 0.175
#> 22 0.22 0.233 0.171
#> 23 0.23 0.218 0.160
#> 24 0.24 0.205 0.146
#> 25 0.25 0.198 0.140
#> 26 0.26 0.188 0.129
#> 27 0.27 0.181 0.123
#> 28 0.28 0.170 0.121
#> 29 0.29 0.162 0.112
#> 30 0.30 0.160 0.108
#> 31 0.31 0.154 0.103
#> 32 0.32 0.148 0.097
#> 33 0.33 0.144 0.090
#> 34 0.34 0.135 0.083
#> 35 0.35 0.127 0.081
#> 36 0.36 0.121 0.078
#> 37 0.37 0.115 0.073
#> 38 0.38 0.110 0.071
#> 39 0.39 0.106 0.067
#> 40 0.40 0.103 0.063
#> 41 0.41 0.093 0.059
#> 42 0.42 0.088 0.057
#> 43 0.43 0.085 0.055
#> 44 0.44 0.082 0.051
#> 45 0.45 0.077 0.046
#> 46 0.46 0.071 0.043
#> 47 0.47 0.066 0.038
#> 48 0.48 0.060 0.037
#> 49 0.49 0.058 0.036
#> 50 0.50 0.057 0.036
#> 51 0.51 0.054 0.036
#> 52 0.52 0.052 0.035
#> 53 0.53 0.049 0.034
#> 54 0.54 0.047 0.034
#> 55 0.55 0.041 0.033
#> 56 0.56 0.037 0.033
#> 57 0.57 0.031 0.029
#> 58 0.58 0.029 0.025
#> 59 0.59 0.028 0.021
#> 60 0.60 0.028 0.016
#> 61 0.61 0.027 0.015
#> 62 0.62 0.027 0.013
#> 63 0.63 0.027 0.013
#> 64 0.64 0.026 0.012
#> 65 0.65 0.024 0.012
#> 66 0.66 0.022 0.009
#> 67 0.67 0.020 0.008
#> 68 0.68 0.018 0.007
#> 69 0.69 0.014 0.007
#> 70 0.70 0.013 0.007
#> 71 0.71 0.012 0.007
#> 72 0.72 0.011 0.007
#> 73 0.73 0.011 0.006
#> 74 0.74 0.010 0.006
#> 75 0.75 0.008 0.006
#> 76 0.76 0.008 0.005
#> 77 0.77 0.006 0.005
#> 78 0.78 0.005 0.004
#> 79 0.79 0.005 0.004
#> 80 0.80 0.005 0.003
#> 81 0.81 0.005 0.003
#> 82 0.82 0.005 0.002
#> 83 0.83 0.005 0.002
#> 84 0.84 0.005 0.000
#> 85 0.85 0.004 0.000
#> 86 0.86 0.003 0.000
#> 87 0.87 0.002 0.000
#> 88 0.88 0.002 0.000
#> 89 0.89 0.002 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] "getgamma2cont"
# }
# Example 4: Controlled design, predictive probability, vague prior
# \donttest{
Sigma_null <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
Sigma_alt <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
getgamma2cont(
nsim = 1000L, prob = 'predictive', design = 'controlled',
prior = 'vague',
GoRegions = 1L, NoGoRegions = 4L,
mu_t_go = c(-5.0, 0.0), Sigma_t_go = Sigma_null,
mu_c_go = c(-10.0, -1.0), Sigma_c_go = Sigma_null,
mu_t_nogo = c(5.0, 1.0), Sigma_t_nogo = Sigma_alt,
mu_c_nogo = c(-10.0, -1.0), Sigma_c_nogo = Sigma_alt,
target_go = 0.05, target_nogo = 0.20,
n_t = 30L, n_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 5.0, theta_NULL2 = 1.0,
m_t = 100L, m_c = 100L,
kappa0_t = NULL, nu0_t = NULL, mu0_t = NULL, Lambda0_t = NULL,
kappa0_c = NULL, nu0_c = NULL, mu0_c = NULL, Lambda0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
nMC = 500L, CalcMethod = 'MC',
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed = 1L
)
#> $gamma_go
#> [1] 0.92
#>
#> $gamma_nogo
#> [1] 0.15
#>
#> $PrGo_opt
#> [1] 0.042
#>
#> $PrNoGo_opt
#> [1] 0.198
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.781 0.482
#> 2 0.02 0.716 0.424
#> 3 0.03 0.663 0.389
#> 4 0.04 0.637 0.348
#> 5 0.05 0.607 0.323
#> 6 0.06 0.577 0.297
#> 7 0.07 0.562 0.280
#> 8 0.08 0.552 0.262
#> 9 0.09 0.527 0.255
#> 10 0.10 0.512 0.245
#> 11 0.11 0.495 0.235
#> 12 0.12 0.483 0.223
#> 13 0.13 0.473 0.217
#> 14 0.14 0.457 0.203
#> 15 0.15 0.445 0.198
#> 16 0.16 0.437 0.188
#> 17 0.17 0.423 0.182
#> 18 0.18 0.417 0.171
#> 19 0.19 0.410 0.164
#> 20 0.20 0.398 0.156
#> 21 0.21 0.384 0.149
#> 22 0.22 0.376 0.146
#> 23 0.23 0.366 0.141
#> 24 0.24 0.354 0.132
#> 25 0.25 0.350 0.131
#> 26 0.26 0.344 0.128
#> 27 0.27 0.336 0.124
#> 28 0.28 0.331 0.120
#> 29 0.29 0.320 0.115
#> 30 0.30 0.316 0.113
#> 31 0.31 0.310 0.110
#> 32 0.32 0.305 0.108
#> 33 0.33 0.300 0.104
#> 34 0.34 0.296 0.099
#> 35 0.35 0.294 0.097
#> 36 0.36 0.290 0.096
#> 37 0.37 0.284 0.093
#> 38 0.38 0.280 0.088
#> 39 0.39 0.274 0.082
#> 40 0.40 0.267 0.080
#> 41 0.41 0.263 0.077
#> 42 0.42 0.258 0.076
#> 43 0.43 0.256 0.076
#> 44 0.44 0.255 0.071
#> 45 0.45 0.247 0.069
#> 46 0.46 0.246 0.068
#> 47 0.47 0.236 0.065
#> 48 0.48 0.229 0.062
#> 49 0.49 0.224 0.059
#> 50 0.50 0.222 0.059
#> 51 0.51 0.215 0.057
#> 52 0.52 0.207 0.056
#> 53 0.53 0.203 0.052
#> 54 0.54 0.199 0.051
#> 55 0.55 0.191 0.051
#> 56 0.56 0.187 0.051
#> 57 0.57 0.184 0.050
#> 58 0.58 0.180 0.048
#> 59 0.59 0.176 0.046
#> 60 0.60 0.173 0.046
#> 61 0.61 0.170 0.046
#> 62 0.62 0.167 0.044
#> 63 0.63 0.162 0.042
#> 64 0.64 0.159 0.041
#> 65 0.65 0.155 0.039
#> 66 0.66 0.153 0.039
#> 67 0.67 0.150 0.037
#> 68 0.68 0.145 0.036
#> 69 0.69 0.136 0.036
#> 70 0.70 0.133 0.034
#> 71 0.71 0.126 0.034
#> 72 0.72 0.126 0.032
#> 73 0.73 0.122 0.030
#> 74 0.74 0.120 0.029
#> 75 0.75 0.112 0.029
#> 76 0.76 0.112 0.026
#> 77 0.77 0.108 0.023
#> 78 0.78 0.102 0.021
#> 79 0.79 0.097 0.021
#> 80 0.80 0.092 0.018
#> 81 0.81 0.087 0.017
#> 82 0.82 0.080 0.014
#> 83 0.83 0.079 0.012
#> 84 0.84 0.074 0.010
#> 85 0.85 0.072 0.010
#> 86 0.86 0.070 0.009
#> 87 0.87 0.069 0.008
#> 88 0.88 0.062 0.008
#> 89 0.89 0.059 0.008
#> 90 0.90 0.056 0.007
#> 91 0.91 0.050 0.007
#> 92 0.92 0.042 0.006
#> 93 0.93 0.035 0.005
#> 94 0.94 0.027 0.004
#> 95 0.95 0.021 0.004
#> 96 0.96 0.018 0.003
#> 97 0.97 0.017 0.002
#> 98 0.98 0.013 0.000
#> 99 0.99 0.008 0.000
#>
#> attr(,"class")
#> [1] "getgamma2cont"
# }
# Example 5: Uncontrolled design, predictive probability, vague prior
# \donttest{
Sigma_null <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
Sigma_alt <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
getgamma2cont(
nsim = 1000L, prob = 'predictive', design = 'uncontrolled',
prior = 'vague',
GoRegions = 1L, NoGoRegions = 4L,
mu_t_go = c(-5.0, 0.0), Sigma_t_go = Sigma_null,
mu_c_go = NULL, Sigma_c_go = NULL,
mu_t_nogo = c(5.0, 1.0), Sigma_t_nogo = Sigma_alt,
mu_c_nogo = NULL, Sigma_c_nogo = NULL,
target_go = 0.05, target_nogo = 0.20,
n_t = 30L, n_c = NULL,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 5.0, theta_NULL2 = 1.0,
m_t = 100L, m_c = 100L,
kappa0_t = NULL, nu0_t = NULL, mu0_t = NULL, Lambda0_t = NULL,
kappa0_c = NULL, nu0_c = NULL, mu0_c = c(-10.0, -1.0), Lambda0_c = NULL,
r = 1.0,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
nMC = 500L, CalcMethod = 'MC',
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed = 1L
)
#> $gamma_go
#> [1] 0.8
#>
#> $gamma_nogo
#> [1] 0.11
#>
#> $PrGo_opt
#> [1] 0.049
#>
#> $PrNoGo_opt
#> [1] 0.194
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.899 0.570
#> 2 0.02 0.847 0.465
#> 3 0.03 0.796 0.408
#> 4 0.04 0.762 0.360
#> 5 0.05 0.719 0.318
#> 6 0.06 0.682 0.275
#> 7 0.07 0.663 0.257
#> 8 0.08 0.623 0.227
#> 9 0.09 0.603 0.214
#> 10 0.10 0.588 0.205
#> 11 0.11 0.567 0.194
#> 12 0.12 0.554 0.181
#> 13 0.13 0.536 0.171
#> 14 0.14 0.519 0.163
#> 15 0.15 0.504 0.149
#> 16 0.16 0.495 0.143
#> 17 0.17 0.477 0.135
#> 18 0.18 0.463 0.130
#> 19 0.19 0.444 0.128
#> 20 0.20 0.431 0.123
#> 21 0.21 0.414 0.116
#> 22 0.22 0.408 0.110
#> 23 0.23 0.401 0.107
#> 24 0.24 0.385 0.099
#> 25 0.25 0.371 0.094
#> 26 0.26 0.356 0.092
#> 27 0.27 0.343 0.090
#> 28 0.28 0.335 0.089
#> 29 0.29 0.318 0.085
#> 30 0.30 0.314 0.083
#> 31 0.31 0.307 0.081
#> 32 0.32 0.298 0.076
#> 33 0.33 0.290 0.072
#> 34 0.34 0.281 0.069
#> 35 0.35 0.271 0.065
#> 36 0.36 0.264 0.062
#> 37 0.37 0.257 0.061
#> 38 0.38 0.249 0.060
#> 39 0.39 0.243 0.055
#> 40 0.40 0.236 0.054
#> 41 0.41 0.228 0.054
#> 42 0.42 0.226 0.053
#> 43 0.43 0.221 0.052
#> 44 0.44 0.217 0.048
#> 45 0.45 0.208 0.046
#> 46 0.46 0.202 0.042
#> 47 0.47 0.196 0.034
#> 48 0.48 0.184 0.034
#> 49 0.49 0.180 0.032
#> 50 0.50 0.171 0.031
#> 51 0.51 0.167 0.030
#> 52 0.52 0.160 0.027
#> 53 0.53 0.158 0.027
#> 54 0.54 0.155 0.026
#> 55 0.55 0.148 0.024
#> 56 0.56 0.143 0.024
#> 57 0.57 0.138 0.024
#> 58 0.58 0.135 0.023
#> 59 0.59 0.127 0.022
#> 60 0.60 0.127 0.021
#> 61 0.61 0.123 0.020
#> 62 0.62 0.111 0.018
#> 63 0.63 0.106 0.017
#> 64 0.64 0.102 0.015
#> 65 0.65 0.101 0.014
#> 66 0.66 0.097 0.013
#> 67 0.67 0.093 0.012
#> 68 0.68 0.086 0.011
#> 69 0.69 0.078 0.011
#> 70 0.70 0.076 0.010
#> 71 0.71 0.076 0.010
#> 72 0.72 0.075 0.010
#> 73 0.73 0.072 0.009
#> 74 0.74 0.067 0.009
#> 75 0.75 0.067 0.008
#> 76 0.76 0.060 0.008
#> 77 0.77 0.059 0.007
#> 78 0.78 0.057 0.007
#> 79 0.79 0.052 0.006
#> 80 0.80 0.049 0.006
#> 81 0.81 0.046 0.005
#> 82 0.82 0.038 0.004
#> 83 0.83 0.032 0.004
#> 84 0.84 0.032 0.004
#> 85 0.85 0.029 0.004
#> 86 0.86 0.026 0.004
#> 87 0.87 0.023 0.004
#> 88 0.88 0.019 0.004
#> 89 0.89 0.017 0.004
#> 90 0.90 0.017 0.003
#> 91 0.91 0.013 0.001
#> 92 0.92 0.010 0.001
#> 93 0.93 0.009 0.001
#> 94 0.94 0.006 0.000
#> 95 0.95 0.004 0.000
#> 96 0.96 0.003 0.000
#> 97 0.97 0.002 0.000
#> 98 0.98 0.002 0.000
#> 99 0.99 0.001 0.000
#>
#> attr(,"class")
#> [1] "getgamma2cont"
# }
# Example 6: External design (control only), predictive probability, NIW prior
# \donttest{
Sigma <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
Lambda <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
se_c <- matrix(c(6400.0, 15.0, 15.0, 36.0), 2, 2)
getgamma2cont(
nsim = 1000L, prob = 'predictive', design = 'external',
prior = 'N-Inv-Wishart',
GoRegions = 1L, NoGoRegions = 4L,
mu_t_go = c(-5.0, 0.0), Sigma_t_go = Sigma,
mu_c_go = c(-10.0, -1.0), Sigma_c_go = Sigma,
mu_t_nogo = c(5.0, 1.0), Sigma_t_nogo = Sigma,
mu_c_nogo = c(-10.0, -1.0), Sigma_c_nogo = Sigma,
target_go = 0.05, target_nogo = 0.20,
n_t = 30L, n_c = 30L,
theta_TV1 = NULL, theta_MAV1 = NULL,
theta_TV2 = NULL, theta_MAV2 = NULL,
theta_NULL1 = 5.0, theta_NULL2 = 1.0,
m_t = 100L, m_c = 100L,
kappa0_t = 0.1, nu0_t = 4.0, mu0_t = c(0.0, 1.0), Lambda0_t = Lambda,
kappa0_c = 0.1, nu0_c = 4.0, mu0_c = c(-10.0, -1.0), Lambda0_c = Lambda,
r = NULL,
ne_t = NULL, ne_c = 10L, alpha0e_t = NULL, alpha0e_c = 0.5,
bar_ye_t = NULL, bar_ye_c = c(-10.0, -1.0), se_t = NULL, se_c = se_c,
nMC = 500L, CalcMethod = 'MC',
gamma_go_grid = seq(0.01, 0.99, by = 0.01),
gamma_nogo_grid = seq(0.01, 0.99, by = 0.01),
seed = 1L
)
#> $gamma_go
#> [1] 0.92
#>
#> $gamma_nogo
#> [1] 0.14
#>
#> $PrGo_opt
#> [1] 0.045
#>
#> $PrNoGo_opt
#> [1] 0.192
#>
#> $target_go
#> [1] 0.05
#>
#> $target_nogo
#> [1] 0.2
#>
#> $grid_results
#> gamma_grid PrGo_grid PrNoGo_grid
#> 1 0.01 0.764 0.486
#> 2 0.02 0.698 0.417
#> 3 0.03 0.658 0.358
#> 4 0.04 0.633 0.329
#> 5 0.05 0.603 0.310
#> 6 0.06 0.577 0.281
#> 7 0.07 0.561 0.271
#> 8 0.08 0.538 0.257
#> 9 0.09 0.523 0.244
#> 10 0.10 0.511 0.233
#> 11 0.11 0.499 0.219
#> 12 0.12 0.492 0.211
#> 13 0.13 0.471 0.204
#> 14 0.14 0.462 0.192
#> 15 0.15 0.447 0.181
#> 16 0.16 0.442 0.177
#> 17 0.17 0.431 0.172
#> 18 0.18 0.422 0.161
#> 19 0.19 0.412 0.158
#> 20 0.20 0.404 0.152
#> 21 0.21 0.398 0.144
#> 22 0.22 0.389 0.141
#> 23 0.23 0.384 0.138
#> 24 0.24 0.379 0.129
#> 25 0.25 0.370 0.126
#> 26 0.26 0.362 0.123
#> 27 0.27 0.356 0.119
#> 28 0.28 0.345 0.114
#> 29 0.29 0.334 0.111
#> 30 0.30 0.326 0.109
#> 31 0.31 0.321 0.106
#> 32 0.32 0.313 0.100
#> 33 0.33 0.306 0.095
#> 34 0.34 0.301 0.090
#> 35 0.35 0.296 0.087
#> 36 0.36 0.291 0.084
#> 37 0.37 0.286 0.082
#> 38 0.38 0.281 0.079
#> 39 0.39 0.275 0.079
#> 40 0.40 0.267 0.075
#> 41 0.41 0.263 0.074
#> 42 0.42 0.258 0.072
#> 43 0.43 0.254 0.072
#> 44 0.44 0.245 0.071
#> 45 0.45 0.240 0.069
#> 46 0.46 0.236 0.066
#> 47 0.47 0.233 0.062
#> 48 0.48 0.229 0.060
#> 49 0.49 0.224 0.060
#> 50 0.50 0.221 0.057
#> 51 0.51 0.216 0.053
#> 52 0.52 0.213 0.053
#> 53 0.53 0.208 0.052
#> 54 0.54 0.201 0.051
#> 55 0.55 0.196 0.048
#> 56 0.56 0.193 0.048
#> 57 0.57 0.189 0.046
#> 58 0.58 0.186 0.043
#> 59 0.59 0.181 0.042
#> 60 0.60 0.175 0.042
#> 61 0.61 0.170 0.041
#> 62 0.62 0.169 0.039
#> 63 0.63 0.168 0.039
#> 64 0.64 0.159 0.038
#> 65 0.65 0.156 0.036
#> 66 0.66 0.151 0.036
#> 67 0.67 0.149 0.035
#> 68 0.68 0.145 0.035
#> 69 0.69 0.141 0.034
#> 70 0.70 0.138 0.034
#> 71 0.71 0.132 0.034
#> 72 0.72 0.126 0.032
#> 73 0.73 0.123 0.030
#> 74 0.74 0.120 0.029
#> 75 0.75 0.118 0.027
#> 76 0.76 0.113 0.025
#> 77 0.77 0.109 0.023
#> 78 0.78 0.102 0.023
#> 79 0.79 0.101 0.017
#> 80 0.80 0.096 0.017
#> 81 0.81 0.092 0.014
#> 82 0.82 0.086 0.014
#> 83 0.83 0.082 0.013
#> 84 0.84 0.079 0.009
#> 85 0.85 0.078 0.008
#> 86 0.86 0.075 0.007
#> 87 0.87 0.073 0.007
#> 88 0.88 0.066 0.006
#> 89 0.89 0.063 0.006
#> 90 0.90 0.059 0.006
#> 91 0.91 0.053 0.006
#> 92 0.92 0.045 0.005
#> 93 0.93 0.041 0.005
#> 94 0.94 0.036 0.005
#> 95 0.95 0.030 0.004
#> 96 0.96 0.019 0.003
#> 97 0.97 0.017 0.002
#> 98 0.98 0.016 0.001
#> 99 0.99 0.011 0.001
#>
#> attr(,"class")
#> [1] "getgamma2cont"
# }