Find Optimal Go/NoGo Thresholds for a Single Binary Endpoint

Computes the optimal Go threshold \(\gamma_{\mathrm{go}}\) and NoGo threshold \(\gamma_{\mathrm{nogo}}\) for a single binary 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_grid such that the marginal Go probability \(\Pr(g_{\mathrm{Go}} \ge \gamma_{\mathrm{go}})\) is strictly less than target_go under the Go-calibration scenario (pi_t_go, pi_c_go); typically the Null scenario.
\(\gamma_{\mathrm{nogo}}\) is the smallest value in gamma_grid such that the marginal NoGo probability \(\Pr(g_{\mathrm{NoGo}} \ge \gamma_{\mathrm{nogo}})\) is strictly less than target_nogo under the NoGo-calibration scenario (pi_t_nogo, pi_c_nogo); typically the Alternative scenario.

Here \(g_{\mathrm{Go}} = P(\theta > \theta_{\mathrm{TV}} \mid y_t, y_c)\) and \(g_{\mathrm{NoGo}} = P(\theta \le \theta_{\mathrm{MAV}} \mid y_t, y_c)\) for prob = 'posterior', consistent with the decision rule in pbayesdecisionprob1bin.

Usage

getgamma1bin(
  prob = "posterior",
  design = "controlled",
  theta_TV = NULL,
  theta_MAV = NULL,
  theta_NULL = NULL,
  pi_t_go,
  pi_c_go = NULL,
  pi_t_nogo,
  pi_c_nogo = NULL,
  target_go,
  target_nogo,
  n_t,
  n_c,
  a_t,
  a_c,
  b_t,
  b_c,
  z = NULL,
  m_t = NULL,
  m_c = NULL,
  ne_t = NULL,
  ne_c = NULL,
  ye_t = NULL,
  ye_c = NULL,
  alpha0e_t = NULL,
  alpha0e_c = NULL,
  gamma_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'.
theta_TV: A numeric scalar in (-1, 1) giving the Target Value (TV) threshold for the treatment effect. Required when prob = 'posterior'; set to NULL otherwise.
theta_MAV: A numeric scalar in (-1, 1) giving the Minimum Acceptable Value (MAV) threshold. Must satisfy theta_TV > theta_MAV. Required when prob = 'posterior'; set to NULL otherwise.
theta_NULL: A numeric scalar in (-1, 1) giving the null hypothesis threshold used for the predictive probability. Required when prob = 'predictive'; set to NULL otherwise.
pi_t_go: A numeric scalar in (0, 1) giving the true treatment response rate under the Go-calibration scenario (typically Null).
pi_c_go: A numeric scalar in (0, 1) giving the true control response rate under the Go-calibration scenario. Set to NULL for design = 'uncontrolled'.
pi_t_nogo: A numeric scalar in (0, 1) giving the true treatment response rate under the NoGo-calibration scenario (typically Alternative).
pi_c_nogo: A numeric scalar in (0, 1) giving the true control response rate under the NoGo-calibration scenario. Set to NULL for design = '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 largest 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.
a_t: A positive numeric scalar giving the first shape parameter of the Beta prior for the treatment group.
a_c: A positive numeric scalar giving the first shape parameter of the Beta prior for the control group.
b_t: A positive numeric scalar giving the second shape parameter of the Beta prior for the treatment group.
b_c: A positive numeric scalar giving the second shape parameter of the Beta prior for the control group.
z: A non-negative integer giving the hypothetical number of responders in the control group. Required when design = 'uncontrolled'; set to NULL otherwise.
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.
ne_t: A positive integer giving the number of patients in the treatment group of the external data set. Required when design = 'external'; set to NULL otherwise.
ne_c: A positive integer giving the number of patients in the control group of the external data set. Required when design = 'external'; set to NULL otherwise.
ye_t: A non-negative integer giving the number of responders in the treatment group of the external data set. Required when design = 'external'; set to NULL otherwise.
ye_c: A non-negative integer giving the number of responders in the control group of the external data set. Required when design = 'external'; set to NULL otherwise.
alpha0e_t: A numeric scalar in (0, 1] giving the power prior weight for the treatment group. Required when design = 'external'; set to NULL otherwise.
alpha0e_c: A numeric scalar in (0, 1] giving the power prior weight for the control group. Required when design = 'external'; set to NULL otherwise.
gamma_grid: A numeric vector of candidate threshold values in (0, 1) to search over. Defaults to seq(0.01, 0.99, by = 0.01).

Value

A list of class getgamma1bin with the following elements:

gamma_go: Optimal Go threshold: the smallest value in gamma_grid for which \(\Pr(\mathrm{Go}) < \code{target\_go}\) under the Go-calibration scenario. NA if no such value exists.
gamma_nogo: Optimal NoGo threshold: the smallest value in gamma_grid for which \(\Pr(\mathrm{NoGo}) < \code{target\_nogo}\) under the NoGo-calibration scenario. NA if 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. NA if gamma_go is NA.
PrNoGo_opt: Marginal \(\Pr(g_{\mathrm{NoGo}} \ge \gamma_{\mathrm{nogo}})\) at the optimal \(\gamma_{\mathrm{nogo}}\) 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).

Details

The function uses a two-stage precompute-then-sweep strategy:

Precomputation: All possible outcome pairs \((y_t, y_c)\) are enumerated. For each pair, pbayespostpred1bin computes \(g_{\mathrm{Go}}\) (lower.tail = FALSE at theta_TV) and \(g_{\mathrm{NoGo}}\) (lower.tail = TRUE at theta_MAV). This step is independent of \(\gamma\).
Gamma sweep: Marginal probabilities are computed as weighted sums of binary indicators over the grid: \(\Pr(\mathrm{Go})\) uses w_go (weights under pi_t_go, pi_c_go) and the indicator \(g_{\mathrm{Go}} \ge \gamma\); \(\Pr(\mathrm{NoGo})\) uses w_nogo (weights under pi_t_nogo, pi_c_nogo) and the indicator \(g_{\mathrm{NoGo}} \ge \gamma\).

Both \(\Pr(\mathrm{Go})\) and \(\Pr(\mathrm{NoGo})\) are monotone non-increasing functions of \(\gamma\). The optimal \(\gamma_{\mathrm{go}}\) is the smallest grid value crossing below target_go. The optimal \(\gamma_{\mathrm{nogo}}\) is also the smallest grid value crossing below target_nogo: a smaller \(\gamma_{\mathrm{nogo}}\) makes NoGo harder to trigger (more permissive), so this is the least restrictive threshold that still controls the false NoGo rate.

Examples

# Example 1: Controlled design, posterior probability
# gamma_go  : smallest gamma s.t. Pr(Go)   < 0.05 under Null (pi_t = pi_c = 0.15)
# gamma_nogo: largest  gamma s.t. Pr(NoGo) < 0.20 under Alt  (pi_t = 0.35, pi_c = 0.15)
getgamma1bin(
  prob = 'posterior', design = 'controlled',
  theta_TV = 0.20, theta_MAV = 0.05, theta_NULL = NULL,
  pi_t_go = 0.15, pi_c_go = 0.15,
  pi_t_nogo = 0.35, pi_c_nogo = 0.15,
  target_go = 0.05, target_nogo = 0.20,
  n_t = 12L, n_c = 12L,
  a_t = 0.5, a_c = 0.5, b_t = 0.5, b_c = 0.5,
  z = NULL, m_t = NULL, m_c = NULL,
  ne_t = NULL, ne_c = NULL, ye_t = NULL, ye_c = NULL,
  alpha0e_t = NULL, alpha0e_c = NULL
)
#> $gamma_go
#> [1] 0.57
#> 
#> $gamma_nogo
#> [1] 0.44
#> 
#> $PrGo_opt
#> [1] 0.0487291
#> 
#> $PrNoGo_opt
#> [1] 0.1794458
#> 
#> $target_go
#> [1] 0.05
#> 
#> $target_nogo
#> [1] 0.2
#> 
#> $grid_results
#>    gamma_grid    PrGo_grid  PrNoGo_grid
#> 1        0.01 7.906176e-01 0.9134487961
#> 2        0.02 7.503791e-01 0.9067600866
#> 3        0.03 6.589998e-01 0.8345052466
#> 4        0.04 6.587169e-01 0.8134577555
#> 5        0.05 6.084383e-01 0.8134577555
#> 6        0.06 5.059629e-01 0.7520334991
#> 7        0.07 5.046463e-01 0.6867892755
#> 8        0.08 5.045674e-01 0.6765294767
#> 9        0.09 4.190939e-01 0.6751707735
#> 10       0.10 4.190939e-01 0.6751707735
#> 11       0.11 3.762482e-01 0.6751707735
#> 12       0.12 3.466726e-01 0.6038748091
#> 13       0.13 3.466726e-01 0.6038748091
#> 14       0.14 3.420098e-01 0.6038748091
#> 15       0.15 3.416219e-01 0.5442567305
#> 16       0.16 3.416219e-01 0.5222071858
#> 17       0.17 3.416219e-01 0.5177862622
#> 18       0.18 2.535583e-01 0.5023037761
#> 19       0.19 2.535583e-01 0.5023037761
#> 20       0.20 2.535583e-01 0.5023037761
#> 21       0.21 2.535583e-01 0.5023037761
#> 22       0.22 2.032798e-01 0.5023037761
#> 23       0.23 2.032798e-01 0.5023037761
#> 24       0.24 2.032798e-01 0.4434563172
#> 25       0.25 1.915366e-01 0.4434563172
#> 26       0.26 1.902200e-01 0.4434563172
#> 27       0.27 1.901411e-01 0.3742572468
#> 28       0.28 1.901411e-01 0.3391852014
#> 29       0.29 1.901411e-01 0.3292188163
#> 30       0.30 1.901411e-01 0.3292188163
#> 31       0.31 1.901411e-01 0.3292188163
#> 32       0.32 1.485555e-01 0.3292188163
#> 33       0.33 1.485555e-01 0.3292188163
#> 34       0.34 1.485555e-01 0.3292188163
#> 35       0.35 1.485555e-01 0.3292188163
#> 36       0.36 1.485555e-01 0.3292188163
#> 37       0.37 9.675338e-02 0.3292188163
#> 38       0.38 9.675338e-02 0.3292188163
#> 39       0.39 9.675338e-02 0.3292188163
#> 40       0.40 7.678984e-02 0.3292188163
#> 41       0.41 7.320278e-02 0.3292188163
#> 42       0.42 7.319121e-02 0.3292188163
#> 43       0.43 7.319121e-02 0.2912045226
#> 44       0.44 7.319121e-02 0.1794457698
#> 45       0.45 7.319121e-02 0.1767412048
#> 46       0.46 7.319121e-02 0.1767412048
#> 47       0.47 7.319121e-02 0.1767412048
#> 48       0.48 7.319121e-02 0.1767412048
#> 49       0.49 7.319121e-02 0.1767412048
#> 50       0.50 7.319121e-02 0.1767412048
#> 51       0.51 7.319121e-02 0.1767412048
#> 52       0.52 7.319121e-02 0.1767412048
#> 53       0.53 7.319121e-02 0.1767412048
#> 54       0.54 7.319121e-02 0.1767412048
#> 55       0.55 7.319121e-02 0.1767412048
#> 56       0.56 7.319121e-02 0.1767412048
#> 57       0.57 4.872910e-02 0.1767412048
#> 58       0.58 2.179890e-02 0.1767412048
#> 59       0.59 2.179890e-02 0.1767412048
#> 60       0.60 2.179890e-02 0.1767412048
#> 61       0.61 2.179890e-02 0.1561018516
#> 62       0.62 2.179890e-02 0.1225037969
#> 63       0.63 2.179890e-02 0.1225037969
#> 64       0.64 2.179890e-02 0.0906816626
#> 65       0.65 2.179890e-02 0.0906816626
#> 66       0.66 2.179890e-02 0.0906816626
#> 67       0.67 2.179890e-02 0.0906816626
#> 68       0.68 2.179890e-02 0.0906816626
#> 69       0.69 2.179890e-02 0.0796109163
#> 70       0.70 2.179890e-02 0.0796109163
#> 71       0.71 2.179890e-02 0.0796109163
#> 72       0.72 2.179890e-02 0.0796109163
#> 73       0.73 2.179438e-02 0.0796109163
#> 74       0.74 2.053051e-02 0.0796109163
#> 75       0.75 2.053051e-02 0.0787245462
#> 76       0.76 1.472294e-02 0.0741571294
#> 77       0.77 1.472294e-02 0.0608166318
#> 78       0.78 5.010040e-03 0.0608166318
#> 79       0.79 5.010040e-03 0.0608166318
#> 80       0.80 5.010040e-03 0.0420977281
#> 81       0.81 5.010040e-03 0.0420977281
#> 82       0.82 5.010040e-03 0.0420977281
#> 83       0.83 5.010040e-03 0.0420977281
#> 84       0.84 5.010040e-03 0.0305435195
#> 85       0.85 5.010040e-03 0.0305435195
#> 86       0.86 4.822752e-03 0.0304210811
#> 87       0.87 4.822752e-03 0.0294730533
#> 88       0.88 3.627075e-03 0.0257060467
#> 89       0.89 3.627075e-03 0.0257060467
#> 90       0.90 3.627075e-03 0.0182735358
#> 91       0.91 8.846099e-04 0.0182735358
#> 92       0.92 8.846099e-04 0.0182735358
#> 93       0.93 8.846099e-04 0.0119528674
#> 94       0.94 8.643370e-04 0.0093077551
#> 95       0.95 6.834781e-04 0.0072091491
#> 96       0.96 6.834781e-04 0.0072091491
#> 97       0.97 1.188530e-04 0.0046994718
#> 98       0.98 9.733899e-05 0.0024704004
#> 99       0.99 1.193351e-05 0.0007835865
#> 
#> attr(,"class")
#> [1] "getgamma1bin"

# Example 2: Uncontrolled design, posterior probability
getgamma1bin(
  prob = 'posterior', design = 'uncontrolled',
  theta_TV = 0.20, theta_MAV = 0.05, theta_NULL = NULL,
  pi_t_go = 0.15, pi_c_go = NULL,
  pi_t_nogo = 0.35, pi_c_nogo = NULL,
  target_go = 0.05, target_nogo = 0.20,
  n_t = 12L, n_c = 12L,
  a_t = 0.5, a_c = 0.5, b_t = 0.5, b_c = 0.5,
  z = 3L, m_t = NULL, m_c = NULL,
  ne_t = NULL, ne_c = NULL, ye_t = NULL, ye_c = NULL,
  alpha0e_t = NULL, alpha0e_c = NULL
)
#> $gamma_go
#> [1] 0.25
#> 
#> $gamma_nogo
#> [1] 0.62
#> 
#> $PrGo_opt
#> [1] 0.02392191
#> 
#> $PrNoGo_opt
#> [1] 0.1512876
#> 
#> $target_go
#> [1] 0.05
#> 
#> $target_nogo
#> [1] 0.2
#> 
#> $grid_results
#>    gamma_grid    PrGo_grid PrNoGo_grid
#> 1        0.01 5.565404e-01 0.999152092
#> 2        0.02 5.565404e-01 0.994390248
#> 3        0.03 5.565404e-01 0.994390248
#> 4        0.04 5.565404e-01 0.974492543
#> 5        0.05 2.641819e-01 0.974492543
#> 6        0.06 2.641819e-01 0.974492543
#> 7        0.07 2.641819e-01 0.974492543
#> 8        0.08 2.641819e-01 0.915367935
#> 9        0.09 2.641819e-01 0.915367935
#> 10       0.10 2.641819e-01 0.915367935
#> 11       0.11 2.641819e-01 0.915367935
#> 12       0.12 9.220633e-02 0.915367935
#> 13       0.13 9.220633e-02 0.915367935
#> 14       0.14 9.220633e-02 0.915367935
#> 15       0.15 9.220633e-02 0.915367935
#> 16       0.16 9.220633e-02 0.787264617
#> 17       0.17 9.220633e-02 0.787264617
#> 18       0.18 9.220633e-02 0.787264617
#> 19       0.19 9.220633e-02 0.787264617
#> 20       0.20 9.220633e-02 0.787264617
#> 21       0.21 9.220633e-02 0.787264617
#> 22       0.22 9.220633e-02 0.787264617
#> 23       0.23 9.220633e-02 0.787264617
#> 24       0.24 9.220633e-02 0.787264617
#> 25       0.25 2.392191e-02 0.787264617
#> 26       0.26 2.392191e-02 0.787264617
#> 27       0.27 2.392191e-02 0.787264617
#> 28       0.28 2.392191e-02 0.583345050
#> 29       0.29 2.392191e-02 0.583345050
#> 30       0.30 2.392191e-02 0.583345050
#> 31       0.31 2.392191e-02 0.583345050
#> 32       0.32 2.392191e-02 0.583345050
#> 33       0.33 2.392191e-02 0.583345050
#> 34       0.34 2.392191e-02 0.583345050
#> 35       0.35 2.392191e-02 0.583345050
#> 36       0.36 2.392191e-02 0.583345050
#> 37       0.37 2.392191e-02 0.583345050
#> 38       0.38 2.392191e-02 0.583345050
#> 39       0.39 2.392191e-02 0.583345050
#> 40       0.40 2.392191e-02 0.583345050
#> 41       0.41 4.641601e-03 0.583345050
#> 42       0.42 4.641601e-03 0.583345050
#> 43       0.43 4.641601e-03 0.583345050
#> 44       0.44 4.641601e-03 0.346652696
#> 45       0.45 4.641601e-03 0.346652696
#> 46       0.46 4.641601e-03 0.346652696
#> 47       0.47 4.641601e-03 0.346652696
#> 48       0.48 4.641601e-03 0.346652696
#> 49       0.49 4.641601e-03 0.346652696
#> 50       0.50 4.641601e-03 0.346652696
#> 51       0.51 4.641601e-03 0.346652696
#> 52       0.52 4.641601e-03 0.346652696
#> 53       0.53 4.641601e-03 0.346652696
#> 54       0.54 4.641601e-03 0.346652696
#> 55       0.55 4.641601e-03 0.346652696
#> 56       0.56 4.641601e-03 0.346652696
#> 57       0.57 4.641601e-03 0.346652696
#> 58       0.58 6.721260e-04 0.346652696
#> 59       0.59 6.721260e-04 0.346652696
#> 60       0.60 6.721260e-04 0.346652696
#> 61       0.61 6.721260e-04 0.346652696
#> 62       0.62 6.721260e-04 0.151287578
#> 63       0.63 6.721260e-04 0.151287578
#> 64       0.64 6.721260e-04 0.151287578
#> 65       0.65 6.721260e-04 0.151287578
#> 66       0.66 6.721260e-04 0.151287578
#> 67       0.67 6.721260e-04 0.151287578
#> 68       0.68 6.721260e-04 0.151287578
#> 69       0.69 6.721260e-04 0.151287578
#> 70       0.70 6.721260e-04 0.151287578
#> 71       0.71 6.721260e-04 0.151287578
#> 72       0.72 6.721260e-04 0.151287578
#> 73       0.73 6.721260e-04 0.151287578
#> 74       0.74 7.170124e-05 0.151287578
#> 75       0.75 7.170124e-05 0.151287578
#> 76       0.76 7.170124e-05 0.151287578
#> 77       0.77 7.170124e-05 0.151287578
#> 78       0.78 7.170124e-05 0.151287578
#> 79       0.79 7.170124e-05 0.151287578
#> 80       0.80 7.170124e-05 0.042441298
#> 81       0.81 7.170124e-05 0.042441298
#> 82       0.82 7.170124e-05 0.042441298
#> 83       0.83 7.170124e-05 0.042441298
#> 84       0.84 7.170124e-05 0.042441298
#> 85       0.85 7.170124e-05 0.042441298
#> 86       0.86 5.477914e-06 0.042441298
#> 87       0.87 5.477914e-06 0.042441298
#> 88       0.88 5.477914e-06 0.042441298
#> 89       0.89 5.477914e-06 0.042441298
#> 90       0.90 5.477914e-06 0.042441298
#> 91       0.91 5.477914e-06 0.042441298
#> 92       0.92 5.477914e-06 0.042441298
#> 93       0.93 5.477914e-06 0.005688009
#> 94       0.94 2.839282e-07 0.005688009
#> 95       0.95 2.839282e-07 0.005688009
#> 96       0.96 2.839282e-07 0.005688009
#> 97       0.97 2.839282e-07 0.005688009
#> 98       0.98 8.952497e-09 0.005688009
#> 99       0.99 8.952497e-09 0.000000000
#> 
#> attr(,"class")
#> [1] "getgamma1bin"

# Example 3: External design, posterior probability
getgamma1bin(
  prob = 'posterior', design = 'external',
  theta_TV = 0.20, theta_MAV = 0.05, theta_NULL = NULL,
  pi_t_go = 0.15, pi_c_go = 0.15,
  pi_t_nogo = 0.35, pi_c_nogo = 0.15,
  target_go = 0.05, target_nogo = 0.20,
  n_t = 12L, n_c = 12L,
  a_t = 0.5, a_c = 0.5, b_t = 0.5, b_c = 0.5,
  z = NULL, m_t = NULL, m_c = NULL,
  ne_t = 15L, ne_c = 15L, ye_t = 6L, ye_c = 4L,
  alpha0e_t = 0.5, alpha0e_c = 0.5
)
#> $gamma_go
#> [1] 0.49
#> 
#> $gamma_nogo
#> [1] 0.37
#> 
#> $PrGo_opt
#> [1] 0.02816061
#> 
#> $PrNoGo_opt
#> [1] 0.1933826
#> 
#> $target_go
#> [1] 0.05
#> 
#> $target_nogo
#> [1] 0.2
#> 
#> $grid_results
#>    gamma_grid    PrGo_grid  PrNoGo_grid
#> 1        0.01 9.538469e-01 9.800168e-01
#> 2        0.02 9.275337e-01 9.424561e-01
#> 3        0.03 8.334211e-01 9.357660e-01
#> 4        0.04 8.134576e-01 8.681731e-01
#> 5        0.05 7.670250e-01 8.508875e-01
#> 6        0.06 6.789496e-01 8.471253e-01
#> 7        0.07 6.286711e-01 8.134578e-01
#> 8        0.08 5.966951e-01 7.520335e-01
#> 9        0.09 5.953785e-01 7.145815e-01
#> 10       0.10 5.952996e-01 7.029599e-01
#> 11       0.11 5.045674e-01 7.029599e-01
#> 12       0.12 5.045674e-01 6.751708e-01
#> 13       0.13 4.190939e-01 6.751708e-01
#> 14       0.14 3.895183e-01 6.038748e-01
#> 15       0.15 3.848555e-01 5.442572e-01
#> 16       0.16 3.844838e-01 5.222266e-01
#> 17       0.17 3.844677e-01 5.177863e-01
#> 18       0.18 3.416219e-01 5.177863e-01
#> 19       0.19 3.416219e-01 5.177863e-01
#> 20       0.20 3.416219e-01 5.177863e-01
#> 21       0.21 2.535583e-01 5.023038e-01
#> 22       0.22 2.535583e-01 5.023038e-01
#> 23       0.23 2.032798e-01 4.434563e-01
#> 24       0.24 1.915366e-01 3.742573e-01
#> 25       0.25 1.902200e-01 3.391881e-01
#> 26       0.26 1.901411e-01 3.293007e-01
#> 27       0.27 1.901411e-01 3.292188e-01
#> 28       0.28 1.901411e-01 3.292188e-01
#> 29       0.29 1.901411e-01 3.292188e-01
#> 30       0.30 1.901411e-01 3.292188e-01
#> 31       0.31 1.901411e-01 3.292188e-01
#> 32       0.32 1.485555e-01 3.292188e-01
#> 33       0.33 1.485555e-01 3.292188e-01
#> 34       0.34 9.675338e-02 3.239910e-01
#> 35       0.35 9.675338e-02 3.239910e-01
#> 36       0.36 7.347410e-02 2.340879e-01
#> 37       0.37 7.319121e-02 1.933826e-01
#> 38       0.38 7.319121e-02 1.767412e-01
#> 39       0.39 7.319121e-02 1.767412e-01
#> 40       0.40 7.319121e-02 1.767412e-01
#> 41       0.41 7.319121e-02 1.767412e-01
#> 42       0.42 7.319121e-02 1.767412e-01
#> 43       0.43 7.319121e-02 1.767412e-01
#> 44       0.44 7.319121e-02 1.767412e-01
#> 45       0.45 7.319121e-02 1.767412e-01
#> 46       0.46 7.319121e-02 1.767412e-01
#> 47       0.47 7.319121e-02 1.767412e-01
#> 48       0.48 7.319121e-02 1.767412e-01
#> 49       0.49 2.816061e-02 1.767412e-01
#> 50       0.50 2.179890e-02 1.767412e-01
#> 51       0.51 2.179890e-02 7.961092e-02
#> 52       0.52 2.179890e-02 7.880184e-02
#> 53       0.53 2.179890e-02 7.880184e-02
#> 54       0.54 2.179890e-02 7.880184e-02
#> 55       0.55 2.179890e-02 7.880184e-02
#> 56       0.56 2.179890e-02 7.880184e-02
#> 57       0.57 2.179890e-02 7.880184e-02
#> 58       0.58 2.179890e-02 7.880184e-02
#> 59       0.59 2.179890e-02 7.880184e-02
#> 60       0.60 2.179890e-02 7.880184e-02
#> 61       0.61 2.179890e-02 7.880184e-02
#> 62       0.62 2.179890e-02 7.880184e-02
#> 63       0.63 2.053051e-02 7.791146e-02
#> 64       0.64 5.010040e-03 6.000756e-02
#> 65       0.65 5.010040e-03 4.128866e-02
#> 66       0.66 5.010040e-03 3.054352e-02
#> 67       0.67 5.010040e-03 3.054352e-02
#> 68       0.68 5.010040e-03 2.883019e-02
#> 69       0.69 5.010040e-03 2.883019e-02
#> 70       0.70 5.010040e-03 2.883019e-02
#> 71       0.71 5.010040e-03 2.883019e-02
#> 72       0.72 5.010040e-03 2.883019e-02
#> 73       0.73 5.010040e-03 2.883019e-02
#> 74       0.74 5.010040e-03 2.882171e-02
#> 75       0.75 4.822751e-03 2.775941e-02
#> 76       0.76 3.627075e-03 2.399271e-02
#> 77       0.77 8.846099e-04 1.656021e-02
#> 78       0.78 8.846099e-04 1.023954e-02
#> 79       0.79 8.846099e-04 1.023954e-02
#> 80       0.80 8.846099e-04 8.576600e-03
#> 81       0.81 8.846099e-04 8.576600e-03
#> 82       0.82 8.846099e-04 8.576600e-03
#> 83       0.83 8.846099e-04 8.576600e-03
#> 84       0.84 8.836978e-04 8.420298e-03
#> 85       0.85 8.643368e-04 7.644801e-03
#> 86       0.86 6.834781e-04 5.546211e-03
#> 87       0.87 1.188530e-04 3.036534e-03
#> 88       0.88 1.188530e-04 3.036534e-03
#> 89       0.89 1.188530e-04 2.058335e-03
#> 90       0.90 1.188530e-04 2.058335e-03
#> 91       0.91 1.188051e-04 1.924264e-03
#> 92       0.92 9.733899e-05 1.492201e-03
#> 93       0.93 1.193351e-05 7.835865e-04
#> 94       0.94 1.193351e-05 3.951841e-04
#> 95       0.95 1.193351e-05 3.809598e-04
#> 96       0.96 1.028707e-05 1.697145e-04
#> 97       0.97 8.673521e-07 6.004796e-05
#> 98       0.98 7.819228e-07 2.969059e-05
#> 99       0.99 4.312104e-08 6.491000e-06
#> 
#> attr(,"class")
#> [1] "getgamma1bin"

# Example 4: Controlled design, predictive probability
getgamma1bin(
  prob = 'predictive', design = 'controlled',
  theta_TV = NULL, theta_MAV = NULL, theta_NULL = 0.10,
  pi_t_go = 0.15, pi_c_go = 0.15,
  pi_t_nogo = 0.35, pi_c_nogo = 0.15,
  target_go = 0.05, target_nogo = 0.20,
  n_t = 12L, n_c = 12L,
  a_t = 0.5, a_c = 0.5, b_t = 0.5, b_c = 0.5,
  z = NULL, m_t = 30L, m_c = 30L,
  ne_t = NULL, ne_c = NULL, ye_t = NULL, ye_c = NULL,
  alpha0e_t = NULL, alpha0e_c = NULL
)
#> $gamma_go
#> [1] 0.74
#> 
#> $gamma_nogo
#> [1] 0.62
#> 
#> $PrGo_opt
#> [1] 0.04626101
#> 
#> $PrNoGo_opt
#> [1] 0.1819691
#> 
#> $target_go
#> [1] 0.05
#> 
#> $target_nogo
#> [1] 0.2
#> 
#> $grid_results
#>    gamma_grid    PrGo_grid PrNoGo_grid
#> 1        0.01 9.610022e-01 0.986010307
#> 2        0.02 9.134218e-01 0.980011621
#> 3        0.03 8.915849e-01 0.960265514
#> 4        0.04 8.487392e-01 0.960265514
#> 5        0.05 8.431024e-01 0.942454676
#> 6        0.06 7.906176e-01 0.906760087
#> 7        0.07 7.905753e-01 0.906760087
#> 8        0.08 7.703426e-01 0.906760087
#> 9        0.09 7.503791e-01 0.868172783
#> 10       0.10 7.503791e-01 0.850872371
#> 11       0.11 6.589998e-01 0.847125292
#> 12       0.12 6.587169e-01 0.813457755
#> 13       0.13 6.587169e-01 0.813457755
#> 14       0.14 6.587169e-01 0.813457755
#> 15       0.15 6.084383e-01 0.813457755
#> 16       0.16 6.084383e-01 0.752033499
#> 17       0.17 6.084383e-01 0.752033499
#> 18       0.18 5.966951e-01 0.714578353
#> 19       0.19 5.059629e-01 0.702959851
#> 20       0.20 5.045674e-01 0.702959851
#> 21       0.21 5.045674e-01 0.702959851
#> 22       0.22 5.045674e-01 0.702959851
#> 23       0.23 5.045674e-01 0.702959851
#> 24       0.24 5.045674e-01 0.675170773
#> 25       0.25 4.190939e-01 0.675170773
#> 26       0.26 4.190939e-01 0.675170773
#> 27       0.27 4.190939e-01 0.603874809
#> 28       0.28 3.895183e-01 0.603874809
#> 29       0.29 3.895183e-01 0.544256731
#> 30       0.30 3.848555e-01 0.517786262
#> 31       0.31 3.844677e-01 0.517786262
#> 32       0.32 3.416219e-01 0.517786262
#> 33       0.33 3.416219e-01 0.517786262
#> 34       0.34 3.416219e-01 0.517786262
#> 35       0.35 3.416219e-01 0.517786262
#> 36       0.36 3.416219e-01 0.517786262
#> 37       0.37 3.416219e-01 0.517786262
#> 38       0.38 3.416219e-01 0.517786262
#> 39       0.39 2.535583e-01 0.517786262
#> 40       0.40 2.535583e-01 0.517786262
#> 41       0.41 2.535583e-01 0.517786262
#> 42       0.42 2.032798e-01 0.517786262
#> 43       0.43 1.915366e-01 0.329218816
#> 44       0.44 1.901411e-01 0.329218816
#> 45       0.45 1.901411e-01 0.329218816
#> 46       0.46 1.901411e-01 0.329218816
#> 47       0.47 1.901411e-01 0.329218816
#> 48       0.48 1.901411e-01 0.329218816
#> 49       0.49 1.901411e-01 0.329218816
#> 50       0.50 1.901411e-01 0.329218816
#> 51       0.51 1.901411e-01 0.329218816
#> 52       0.52 1.901411e-01 0.329218816
#> 53       0.53 1.901411e-01 0.329218816
#> 54       0.54 1.901411e-01 0.329218816
#> 55       0.55 1.901411e-01 0.329218816
#> 56       0.56 1.901411e-01 0.329218816
#> 57       0.57 1.901411e-01 0.312577774
#> 58       0.58 7.319121e-02 0.271872153
#> 59       0.59 7.319121e-02 0.214755498
#> 60       0.60 7.319121e-02 0.214755498
#> 61       0.61 7.319121e-02 0.214755498
#> 62       0.62 7.319121e-02 0.181969057
#> 63       0.63 7.319121e-02 0.181969057
#> 64       0.64 7.319121e-02 0.181969057
#> 65       0.65 7.319121e-02 0.181969057
#> 66       0.66 7.319121e-02 0.181969057
#> 67       0.67 7.319121e-02 0.181969057
#> 68       0.68 7.319121e-02 0.181969057
#> 69       0.69 7.319121e-02 0.176741205
#> 70       0.70 7.319121e-02 0.172265570
#> 71       0.71 7.246626e-02 0.156101852
#> 72       0.72 6.682949e-02 0.156101852
#> 73       0.73 6.682949e-02 0.122503797
#> 74       0.74 4.626101e-02 0.122503797
#> 75       0.75 4.626101e-02 0.122503797
#> 76       0.76 4.626101e-02 0.090681663
#> 77       0.77 2.179890e-02 0.090681663
#> 78       0.78 2.179890e-02 0.090681663
#> 79       0.79 2.179890e-02 0.090681663
#> 80       0.80 2.179890e-02 0.090681663
#> 81       0.81 2.179890e-02 0.085227876
#> 82       0.82 2.169102e-02 0.074157129
#> 83       0.83 2.053051e-02 0.060816632
#> 84       0.84 2.053051e-02 0.060816632
#> 85       0.85 1.472294e-02 0.060816632
#> 86       0.86 1.472294e-02 0.042097728
#> 87       0.87 1.472294e-02 0.042097728
#> 88       0.88 1.472294e-02 0.042097728
#> 89       0.89 5.010040e-03 0.041027262
#> 90       0.90 4.998296e-03 0.026515119
#> 91       0.91 4.822752e-03 0.026515119
#> 92       0.92 3.627075e-03 0.019082608
#> 93       0.93 3.627075e-03 0.018273536
#> 94       0.94 3.627075e-03 0.018117916
#> 95       0.95 8.643370e-04 0.011021085
#> 96       0.96 6.834781e-04 0.008922479
#> 97       0.97 6.834781e-04 0.007209149
#> 98       0.98 1.172872e-04 0.004133338
#> 99       0.99 9.733899e-05 0.001682208
#> 
#> attr(,"class")
#> [1] "getgamma1bin"

# Example 5: Uncontrolled design, predictive probability
getgamma1bin(
  prob = 'predictive', design = 'uncontrolled',
  theta_TV = NULL, theta_MAV = NULL, theta_NULL = 0.10,
  pi_t_go = 0.15, pi_c_go = NULL,
  pi_t_nogo = 0.35, pi_c_nogo = NULL,
  target_go = 0.05, target_nogo = 0.20,
  n_t = 12L, n_c = 12L,
  a_t = 0.5, a_c = 0.5, b_t = 0.5, b_c = 0.5,
  z = 3L, m_t = 30L, m_c = 30L,
  ne_t = NULL, ne_c = NULL, ye_t = NULL, ye_c = NULL,
  alpha0e_t = NULL, alpha0e_c = NULL
)
#> $gamma_go
#> [1] 0.43
#> 
#> $gamma_nogo
#> [1] 0.73
#> 
#> $PrGo_opt
#> [1] 0.02392191
#> 
#> $PrNoGo_opt
#> [1] 0.1512876
#> 
#> $target_go
#> [1] 0.05
#> 
#> $target_nogo
#> [1] 0.2
#> 
#> $grid_results
#>    gamma_grid    PrGo_grid PrNoGo_grid
#> 1        0.01 8.577582e-01 0.999921312
#> 2        0.02 8.577582e-01 0.999921312
#> 3        0.03 8.577582e-01 0.999152092
#> 4        0.04 8.577582e-01 0.999152092
#> 5        0.05 8.577582e-01 0.999152092
#> 6        0.06 5.565404e-01 0.994390248
#> 7        0.07 5.565404e-01 0.994390248
#> 8        0.08 5.565404e-01 0.994390248
#> 9        0.09 5.565404e-01 0.994390248
#> 10       0.10 5.565404e-01 0.994390248
#> 11       0.11 5.565404e-01 0.974492543
#> 12       0.12 5.565404e-01 0.974492543
#> 13       0.13 5.565404e-01 0.974492543
#> 14       0.14 5.565404e-01 0.974492543
#> 15       0.15 2.641819e-01 0.974492543
#> 16       0.16 2.641819e-01 0.974492543
#> 17       0.17 2.641819e-01 0.974492543
#> 18       0.18 2.641819e-01 0.974492543
#> 19       0.19 2.641819e-01 0.915367935
#> 20       0.20 2.641819e-01 0.915367935
#> 21       0.21 2.641819e-01 0.915367935
#> 22       0.22 2.641819e-01 0.915367935
#> 23       0.23 2.641819e-01 0.915367935
#> 24       0.24 2.641819e-01 0.915367935
#> 25       0.25 2.641819e-01 0.915367935
#> 26       0.26 2.641819e-01 0.915367935
#> 27       0.27 2.641819e-01 0.915367935
#> 28       0.28 9.220633e-02 0.915367935
#> 29       0.29 9.220633e-02 0.915367935
#> 30       0.30 9.220633e-02 0.787264617
#> 31       0.31 9.220633e-02 0.787264617
#> 32       0.32 9.220633e-02 0.787264617
#> 33       0.33 9.220633e-02 0.787264617
#> 34       0.34 9.220633e-02 0.787264617
#> 35       0.35 9.220633e-02 0.787264617
#> 36       0.36 9.220633e-02 0.787264617
#> 37       0.37 9.220633e-02 0.787264617
#> 38       0.38 9.220633e-02 0.787264617
#> 39       0.39 9.220633e-02 0.787264617
#> 40       0.40 9.220633e-02 0.787264617
#> 41       0.41 9.220633e-02 0.787264617
#> 42       0.42 9.220633e-02 0.787264617
#> 43       0.43 2.392191e-02 0.583345050
#> 44       0.44 2.392191e-02 0.583345050
#> 45       0.45 2.392191e-02 0.583345050
#> 46       0.46 2.392191e-02 0.583345050
#> 47       0.47 2.392191e-02 0.583345050
#> 48       0.48 2.392191e-02 0.583345050
#> 49       0.49 2.392191e-02 0.583345050
#> 50       0.50 2.392191e-02 0.583345050
#> 51       0.51 2.392191e-02 0.583345050
#> 52       0.52 2.392191e-02 0.583345050
#> 53       0.53 2.392191e-02 0.583345050
#> 54       0.54 2.392191e-02 0.583345050
#> 55       0.55 2.392191e-02 0.583345050
#> 56       0.56 2.392191e-02 0.583345050
#> 57       0.57 2.392191e-02 0.583345050
#> 58       0.58 4.641601e-03 0.346652696
#> 59       0.59 4.641601e-03 0.346652696
#> 60       0.60 4.641601e-03 0.346652696
#> 61       0.61 4.641601e-03 0.346652696
#> 62       0.62 4.641601e-03 0.346652696
#> 63       0.63 4.641601e-03 0.346652696
#> 64       0.64 4.641601e-03 0.346652696
#> 65       0.65 4.641601e-03 0.346652696
#> 66       0.66 4.641601e-03 0.346652696
#> 67       0.67 4.641601e-03 0.346652696
#> 68       0.68 4.641601e-03 0.346652696
#> 69       0.69 4.641601e-03 0.346652696
#> 70       0.70 4.641601e-03 0.346652696
#> 71       0.71 6.721260e-04 0.346652696
#> 72       0.72 6.721260e-04 0.346652696
#> 73       0.73 6.721260e-04 0.151287578
#> 74       0.74 6.721260e-04 0.151287578
#> 75       0.75 6.721260e-04 0.151287578
#> 76       0.76 6.721260e-04 0.151287578
#> 77       0.77 6.721260e-04 0.151287578
#> 78       0.78 6.721260e-04 0.151287578
#> 79       0.79 6.721260e-04 0.151287578
#> 80       0.80 6.721260e-04 0.151287578
#> 81       0.81 6.721260e-04 0.151287578
#> 82       0.82 7.170124e-05 0.151287578
#> 83       0.83 7.170124e-05 0.151287578
#> 84       0.84 7.170124e-05 0.151287578
#> 85       0.85 7.170124e-05 0.151287578
#> 86       0.86 7.170124e-05 0.042441298
#> 87       0.87 7.170124e-05 0.042441298
#> 88       0.88 7.170124e-05 0.042441298
#> 89       0.89 7.170124e-05 0.042441298
#> 90       0.90 5.477914e-06 0.042441298
#> 91       0.91 5.477914e-06 0.042441298
#> 92       0.92 5.477914e-06 0.042441298
#> 93       0.93 5.477914e-06 0.042441298
#> 94       0.94 5.477914e-06 0.042441298
#> 95       0.95 2.839282e-07 0.005688009
#> 96       0.96 2.839282e-07 0.005688009
#> 97       0.97 2.839282e-07 0.005688009
#> 98       0.98 8.952497e-09 0.005688009
#> 99       0.99 8.952497e-09 0.005688009
#> 
#> attr(,"class")
#> [1] "getgamma1bin"

# Example 6: External design, predictive probability
getgamma1bin(
  prob = 'predictive', design = 'external',
  theta_TV = NULL, theta_MAV = NULL, theta_NULL = 0.10,
  pi_t_go = 0.15, pi_c_go = 0.15,
  pi_t_nogo = 0.35, pi_c_nogo = 0.15,
  target_go = 0.05, target_nogo = 0.20,
  n_t = 12L, n_c = 12L,
  a_t = 0.5, a_c = 0.5, b_t = 0.5, b_c = 0.5,
  z = NULL, m_t = 30L, m_c = 30L,
  ne_t = 15L, ne_c = 15L, ye_t = 6L, ye_c = 4L,
  alpha0e_t = 0.5, alpha0e_c = 0.5
)
#> $gamma_go
#> [1] 0.68
#> 
#> $gamma_nogo
#> [1] 0.55
#> 
#> $PrGo_opt
#> [1] 0.04626101
#> 
#> $PrNoGo_opt
#> [1] 0.1819691
#> 
#> $target_go
#> [1] 0.05
#> 
#> $target_nogo
#> [1] 0.2
#> 
#> $grid_results
#>    gamma_grid    PrGo_grid  PrNoGo_grid
#> 1        0.01 9.999881e-01 9.998784e-01
#> 2        0.02 9.998811e-01 9.991774e-01
#> 3        0.03 9.991357e-01 9.989231e-01
#> 4        0.04 9.963729e-01 9.946584e-01
#> 5        0.05 9.951772e-01 9.944204e-01
#> 6        0.06 9.852771e-01 9.860104e-01
#> 7        0.07 9.852771e-01 9.786247e-01
#> 8        0.08 9.794695e-01 9.784872e-01
#> 9        0.09 9.782057e-01 9.784872e-01
#> 10       0.10 9.537390e-01 9.602655e-01
#> 11       0.11 9.331705e-01 9.424561e-01
#> 12       0.12 9.331705e-01 9.357660e-01
#> 13       0.13 9.275337e-01 9.357660e-01
#> 14       0.14 9.268101e-01 9.357660e-01
#> 15       0.15 8.852232e-01 9.067601e-01
#> 16       0.16 8.852232e-01 8.681731e-01
#> 17       0.17 8.334211e-01 8.508875e-01
#> 18       0.18 8.134576e-01 8.471253e-01
#> 19       0.19 8.101418e-01 8.471253e-01
#> 20       0.20 8.098708e-01 8.471253e-01
#> 21       0.21 7.670132e-01 8.471253e-01
#> 22       0.22 7.670132e-01 8.134578e-01
#> 23       0.23 7.670132e-01 7.520335e-01
#> 24       0.24 6.789496e-01 7.145815e-01
#> 25       0.25 6.789496e-01 7.044134e-01
#> 26       0.26 6.286711e-01 7.029599e-01
#> 27       0.27 6.169278e-01 7.029599e-01
#> 28       0.28 6.155347e-01 7.029599e-01
#> 29       0.29 6.155323e-01 7.029599e-01
#> 30       0.30 6.155323e-01 7.029599e-01
#> 31       0.31 5.952996e-01 7.029599e-01
#> 32       0.32 5.952996e-01 6.751708e-01
#> 33       0.33 5.045674e-01 5.442572e-01
#> 34       0.34 5.045674e-01 5.177863e-01
#> 35       0.35 4.190939e-01 5.177863e-01
#> 36       0.36 3.895183e-01 5.177863e-01
#> 37       0.37 3.844677e-01 5.177863e-01
#> 38       0.38 3.844677e-01 5.177863e-01
#> 39       0.39 3.844677e-01 5.177863e-01
#> 40       0.40 3.844677e-01 5.177863e-01
#> 41       0.41 3.844677e-01 5.177863e-01
#> 42       0.42 3.844677e-01 5.177863e-01
#> 43       0.43 3.844677e-01 4.434563e-01
#> 44       0.44 3.416219e-01 3.292188e-01
#> 45       0.45 3.416219e-01 3.292188e-01
#> 46       0.46 2.032798e-01 3.292188e-01
#> 47       0.47 1.901411e-01 3.292188e-01
#> 48       0.48 1.901411e-01 3.292188e-01
#> 49       0.49 1.901411e-01 3.292188e-01
#> 50       0.50 1.901411e-01 3.292188e-01
#> 51       0.51 1.901411e-01 3.292188e-01
#> 52       0.52 1.901411e-01 3.292188e-01
#> 53       0.53 1.901411e-01 3.292188e-01
#> 54       0.54 1.901411e-01 2.718721e-01
#> 55       0.55 1.901411e-01 1.819691e-01
#> 56       0.56 1.901411e-01 1.819691e-01
#> 57       0.57 1.665789e-01 1.767412e-01
#> 58       0.58 7.319121e-02 1.767412e-01
#> 59       0.59 7.319121e-02 1.767412e-01
#> 60       0.60 7.319121e-02 1.767412e-01
#> 61       0.61 7.319121e-02 1.767412e-01
#> 62       0.62 7.319121e-02 1.767412e-01
#> 63       0.63 7.319121e-02 1.767412e-01
#> 64       0.64 7.319121e-02 1.561018e-01
#> 65       0.65 7.319121e-02 1.225038e-01
#> 66       0.66 7.319121e-02 9.068166e-02
#> 67       0.67 7.246626e-02 9.068166e-02
#> 68       0.68 4.626101e-02 7.961092e-02
#> 69       0.69 2.179890e-02 7.961092e-02
#> 70       0.70 2.179890e-02 7.880184e-02
#> 71       0.71 2.179890e-02 7.880184e-02
#> 72       0.72 2.179890e-02 7.872101e-02
#> 73       0.73 2.179890e-02 7.334795e-02
#> 74       0.74 2.179890e-02 6.000756e-02
#> 75       0.75 2.179428e-02 4.128866e-02
#> 76       0.76 2.169102e-02 4.128866e-02
#> 77       0.77 2.053051e-02 3.054352e-02
#> 78       0.78 1.472294e-02 3.054352e-02
#> 79       0.79 5.010040e-03 3.054352e-02
#> 80       0.80 5.010040e-03 2.869896e-02
#> 81       0.81 5.010040e-03 2.775941e-02
#> 82       0.82 5.010040e-03 2.399271e-02
#> 83       0.83 4.998291e-03 1.656021e-02
#> 84       0.84 4.822751e-03 1.023954e-02
#> 85       0.85 3.627075e-03 1.023954e-02
#> 86       0.86 8.846099e-04 8.562430e-03
#> 87       0.87 8.846099e-04 7.644801e-03
#> 88       0.88 8.846099e-04 5.546211e-03
#> 89       0.89 8.643368e-04 5.546211e-03
#> 90       0.90 6.834781e-04 3.036534e-03
#> 91       0.91 1.188530e-04 2.041566e-03
#> 92       0.92 1.188530e-04 1.492201e-03
#> 93       0.93 1.188051e-04 7.835865e-04
#> 94       0.94 9.733899e-05 7.835865e-04
#> 95       0.95 1.193351e-05 3.156058e-04
#> 96       0.96 1.185160e-05 1.697145e-04
#> 97       0.97 8.673521e-07 5.175818e-05
#> 98       0.98 7.819228e-07 7.112181e-06
#> 99       0.99 4.042553e-08 6.418529e-07
#> 
#> attr(,"class")
#> [1] "getgamma1bin"