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Compute posterior/predictive probability given data.

BM_Res.Rd

This function computes the posterior and predictive (if possible) probability of Bayesian Monitoring

Usage

BM_Res(
  nmax,
  n1,
  m,
  pt,
  theta0,
  eff_cut,
  fut_cut,
  a = 1,
  b = 1,
  pred_type = 2,
  hdi_num = 1000
)

Arguments

nmax

full sample size

n1

sample size for interim analysis, if n1 = nmax then this is a one-stage design

m

number of responders when doing the analysis

pt

posterior probability target during the computation of predictive probability

theta0

ORR target during the computation of predictive probability

eff_cut

efficacy boundary of ORR

fut_cut

futility boundary of ORR

a

1st parameter of prior beta distribution

b

2nd parameter of prior beta distribution

pred_type

type of predictive probability computation. It's STRONGLY recommended to set it as 2.

hdi_num

number of points to use when computing HDI

Value

An object of class gonogo_orr_bm_df, which is a data.frame with additional attributes and it contains the following:

  • arguments used to compute the results, namely nmax, n1, m, pt, theta0, eff_cut, fut_cut, a, b, pred_type and hdi_num.

  • obs_resp_num: number of observed responders.

  • obs_orr: observed ORR

  • ci_lower and ci_upper: 95% confidence interval for underlying ORR, based on Clopper-Pearson method

  • pmean: posterior mean of ORR

  • hdi_lower and hdi_upper: 95% credible interval based on HDI method

  • go_post_prob: posterior probability for efficacy criteria given current data, i.e. Pr(ORR > eff_cut| current data)

  • nogo_post_prob: posterior probability for futiliy criteria given current data, i.e. Pr(ORR <= eff_cut| current data)

  • pred_prob: predictive probability for "declaring efficacy at final analysis". This is only provided for interim analysis (n1 < nmax). Otherwise this is NA.

Examples

# sample size = 40, IA at n = 20, observed 10 responders
nmax <- 40
n1 <- 20
m <- 10
# ORR boundary to declare efficacy at FA is 0.35
theta0 <- 0.35
# Posterior probability target ("confidence") to declare efficacy is 0.6
pt <- 0.6
# efficacy boundary and futility boundary for computing posterior probability is 0.35 and 0.25
eff_cut <- 0.35    # `eff_cut` is usually the same as `theta0`
fut_cut <- 0.25
# Then the bayesian monitoring results at this IA is
BM_Res(nmax, n1, m, pt, theta0, eff_cut, fut_cut)
#>   nmax n1  m  pt theta0 eff_cut fut_cut a b pred_type hdi_num obs_resp_num
#> 1   40 20 10 0.6   0.35    0.35    0.25 1 1         2    1000           10
#>   obs_orr  ci_lower  ci_upper pmean hdi_lower hdi_upper go_post_prob
#> 1     0.5 0.2719578 0.7280422   0.5 0.2969266 0.7030734    0.9228185
#>   nogo_post_prob pred_prob
#> 1     0.00642271 0.9671298
# If at FA, we observed 20 responders, then the bayesian monitoring results at FA is
m <- 20
BM_Res(nmax, nmax, m, pt, theta0, eff_cut, fut_cut)
#>   nmax n1  m  pt theta0 eff_cut fut_cut a b pred_type hdi_num obs_resp_num
#> 1   40 40 20 0.6   0.35    0.35    0.25 1 1         2    1000           20
#>   obs_orr  ci_lower  ci_upper pmean hdi_lower hdi_upper go_post_prob
#> 1     0.5 0.3380178 0.6619822   0.5 0.3507131 0.6492869    0.9760651
#>   nogo_post_prob pred_prob
#> 1   0.0002742483        NA
# A `format` method is provided to provide more readable results
m_vec <- 0 : n1
res <- BM_Res(nmax, n1, m_vec, pt, theta0, eff_cut, fut_cut)
format(res)
#>    nmax n1      ORR          CI Post_mean         HDI Go_pprob Nogo_pprob
#> 1    40 20  0(0.00) 0.00 - 0.17      0.05 0.00 - 0.13     0.0%      99.8%
#> 2    40 20  1(0.05) 0.00 - 0.25      0.09 0.00 - 0.21     0.1%      98.1%
#> 3    40 20  2(0.10) 0.01 - 0.32      0.14 0.02 - 0.28     0.9%      92.5%
#> 4    40 20  3(0.15) 0.03 - 0.38      0.18 0.04 - 0.34     3.3%      80.8%
#> 5    40 20  4(0.20) 0.06 - 0.44      0.23 0.07 - 0.40     9.2%      63.3%
#> 6    40 20  5(0.25) 0.09 - 0.49      0.27 0.10 - 0.46    20.1%      43.3%
#> 7    40 20  6(0.30) 0.12 - 0.54      0.32 0.13 - 0.51    35.7%      25.6%
#> 8    40 20  7(0.35) 0.15 - 0.59      0.36 0.17 - 0.56    53.6%      13.0%
#> 9    40 20  8(0.40) 0.19 - 0.64      0.41 0.21 - 0.61    70.6%       5.6%
#> 10   40 20  9(0.45) 0.23 - 0.68      0.45 0.25 - 0.66    83.8%       2.1%
#> 11   40 20 10(0.50) 0.27 - 0.73      0.50 0.30 - 0.70    92.3%       0.6%
#> 12   40 20 11(0.55) 0.32 - 0.77      0.55 0.34 - 0.75    96.9%       0.2%
#> 13   40 20 12(0.60) 0.36 - 0.81      0.59 0.39 - 0.79    98.9%       0.0%
#> 14   40 20 13(0.65) 0.41 - 0.85      0.64 0.44 - 0.83    99.7%       0.0%
#> 15   40 20 14(0.70) 0.46 - 0.88      0.68 0.49 - 0.87    99.9%       0.0%
#> 16   40 20 15(0.75) 0.51 - 0.91      0.73 0.54 - 0.90   100.0%       0.0%
#> 17   40 20 16(0.80) 0.56 - 0.94      0.77 0.60 - 0.93   100.0%       0.0%
#> 18   40 20 17(0.85) 0.62 - 0.97      0.82 0.66 - 0.96   100.0%       0.0%
#> 19   40 20 18(0.90) 0.68 - 0.99      0.86 0.72 - 0.98   100.0%       0.0%
#> 20   40 20 19(0.95) 0.75 - 1.00      0.91 0.79 - 1.00   100.0%       0.0%
#> 21   40 20 20(1.00) 0.83 - 1.00      0.95 0.87 - 1.00   100.0%       0.0%
#>    Pred_prob
#> 1       0.0%
#> 2       0.0%
#> 3       0.0%
#> 4       0.3%
#> 5       1.9%
#> 6       7.8%
#> 7      22.2%
#> 8      45.3%
#> 9      70.1%
#> 10     88.1%
#> 11     96.7%
#> 12     99.4%
#> 13     99.9%
#> 14    100.0%
#> 15    100.0%
#> 16    100.0%
#> 17    100.0%
#> 18    100.0%
#> 19    100.0%
#> 20    100.0%
#> 21    100.0%