intro
(x = clinfun::ph2simon(pu = .2, pa = .4, ep1 = .05, ep2 = .1))
#>
#> Simon 2-stage Phase II design
#>
#> Unacceptable response rate: 0.2
#> Desirable response rate: 0.4
#> Error rates: alpha = 0.05 ; beta = 0.1
#>
#> r1 n1 r n EN(p0) PET(p0) qLo qHi
#> Minimax 5 24 13 45 31.23 0.6559 0.108 1.000
#> Admissible 4 20 14 49 30.74 0.6296 0.058 0.108
#> Optimal 4 19 15 54 30.43 0.6733 0.000 0.058ph2simon4(x) # default type = 'minimax'
#>
#> Simon's 2-Stage Design
#>
#> Unacceptable Response Rate: 20.0%
#> Desirable Response Rate: 40.0%
#> Controlled Error Rates: α ≤ 5%, β ≤ 10%
#> Maximum Sample Size Allowed: 100
#>
#> r1 n1 r n EN(pu) EN(pa) PET(pu) PET(pa) α β
#> minimax 5 24 13 45 31.2 44.2 65.6% 4.0% 4.8% 10.0%ph2simon4(x, type = 'opt')
#>
#> Simon's 2-Stage Design
#>
#> Unacceptable Response Rate: 20.0%
#> Desirable Response Rate: 40.0%
#> Controlled Error Rates: α ≤ 5%, β ≤ 10%
#> Maximum Sample Size Allowed: 100
#>
#> r1 n1 r n EN(pu) EN(pa) PET(pu) PET(pa) α β
#> optimal 4 19 15 54 30.4 51.6 67.3% 7.0% 4.8% 9.6%an alternative print
print_ph2simon(x)
#>
#> Simon's 2-Stage Design
#>
#> Unacceptable Response Rate: 20.0%
#> Desirable Response Rate: 40.0%
#> Controlled Error Rates: α ≤ 5%, β ≤ 10%
#> Maximum Sample Size Allowed: 100
#>
#> r1 n1 r n EN(pu) EN(pa) PET(pu) PET(pa) α β
#> minimax 5 24 13 45 31.2 44.2 65.6% 4.0% 4.8% 10.0%
#> optimal 4 19 15 54 30.4 51.6 67.3% 7.0% 4.8% 9.6%
#> n1 3 15 19 71 34.7 65.9 64.8% 9.1% 4.5% 9.8%
#> maximax 7 27 28 100 38.4 93.0 84.4% 9.5% 1.2% 9.9%set.seed(1532); r = r_simon(R = 1e2L, prob = .2, object = x)
set.seed(1532); r1 = r_simon.ph2simon4(R = 1e2L, prob = .2, r1 = 5L, n1 = 24L, r = 13L, n = 45L)
stopifnot(identical(r, r1))table(attr(r, 'dx')) # look at beta, <10%
#>
#> (0,5] (5,13] (13,45]
#> 59 32 8
set.seed(24315); r2 = r_simon(R = 1e2L, prob = .4, object = x)
table(attr(r2, 'dx')) # look at alpha, <5%
#>
#> (0,5] (5,13] (13,45]
#> 2 7 91summary(x)
#> $design
#> r1 n1 r n
#> minimax 5 24 13 45
#>
#> $EN
#> EN(pu) EN(pa)
#> minimax 31.22626 44.16061
#>
#> $p
#> PET(pu) PET(pa) α β
#> minimax 0.6558924 0.03997094 0.04828531 0.09987135
summary(x, type = c('minimax', 'optimal', 'n1', 'maximax'))
#> $design
#> r1 n1 r n
#> minimax 5 24 13 45
#> optimal 4 19 15 54
#> n1 3 15 19 71
#> maximax 7 27 28 100
#>
#> $EN
#> EN(pu) EN(pa)
#> minimax 31.22626 44.16061
#> optimal 30.43491 51.56352
#> n1 34.70292 65.93189
#> maximax 38.35586 93.04398
#>
#> $p
#> PET(pu) PET(pa) α β
#> minimax 0.6558924 0.03997094 0.04828531 0.09987135
#> optimal 0.6732881 0.06961371 0.04817245 0.09553198
#> n1 0.6481621 0.09050190 0.04475938 0.09847759
#> maximax 0.8444403 0.09528790 0.01231841 0.09905236simon_pr(prob = c(.2, .3, .4), object = x)
#> Probabilities
#> Response Rate & E(N) Early Termination Fail Success
#> 20%; 31.2 65.6% 29.6% 4.8%
#> 30%; 40.2 22.9% 30.3% 46.8%
#> 40%; 44.2 4.0% 6.0% 90.0%
simon_pr.ph2simon4(prob = c(.2, .3, .4), r1 = 5L, n1 = 24L, r = 13L, n = 45L) # internal use
#> Probabilities
#> Response Rate & E(N) Early Termination Fail Success
#> 20%; 31.2 65.6% 29.6% 4.8%
#> 30%; 40.2 22.9% 30.3% 46.8%
#> 40%; 44.2 4.0% 6.0% 90.0%
language for a report
Sprintf.ph2simon(x, type = 'minimax')
#> [1] "Simon's minimax two-stage design for testing the null hypothesis p⁺≤20% versus the alternative hypothesis p⁺>20% with type-I-error rate 5.0%, as described below, will achieve 90.0% power at true p⁺=40%. The drug will be tested on 24 patients in the first stage. The trial will be terminate early if 5 or fewer patients respond (early termination probability 65.6% under the null p⁺=20%). Otherwise another 21 patients will be enrolled in the second stage and the drug will be rejected if the total number of patients responding is 13 or fewer. This design requires a maximum sample size of 45 patients, with an expected sample size of 44.2 patients under the null p⁺=20%. This design is provided by <u>**`R`**</u> package <u>**`clinfun`**</u>."Sprintf.ph2simon(x, type = 'optimal')
#> [1] "Simon's optimal two-stage design for testing the null hypothesis p⁺≤20% versus the alternative hypothesis p⁺>20% with type-I-error rate 5.0%, as described below, will achieve 90.0% power at true p⁺=40%. The drug will be tested on 19 patients in the first stage. The trial will be terminate early if 4 or fewer patients respond (early termination probability 67.3% under the null p⁺=20%). Otherwise another 35 patients will be enrolled in the second stage and the drug will be rejected if the total number of patients responding is 15 or fewer. This design requires a maximum sample size of 54 patients, with an expected sample size of 51.6 patients under the null p⁺=20%. This design is provided by <u>**`R`**</u> package <u>**`clinfun`**</u>."Sprintf.ph2simon(x, type = 'n1')
#> [1] "Simon's n1 two-stage design for testing the null hypothesis p⁺≤20% versus the alternative hypothesis p⁺>20% with type-I-error rate 5.0%, as described below, will achieve 90.0% power at true p⁺=40%. The drug will be tested on 15 patients in the first stage. The trial will be terminate early if 3 or fewer patients respond (early termination probability 64.8% under the null p⁺=20%). Otherwise another 56 patients will be enrolled in the second stage and the drug will be rejected if the total number of patients responding is 19 or fewer. This design requires a maximum sample size of 71 patients, with an expected sample size of 65.9 patients under the null p⁺=20%. This design is provided by <u>**`R`**</u> package <u>**`clinfun`**</u>."Sprintf.ph2simon(x, type = 'maximax')
#> [1] "Simon's maximax two-stage design for testing the null hypothesis p⁺≤20% versus the alternative hypothesis p⁺>20% with type-I-error rate 5.0%, as described below, will achieve 90.0% power at true p⁺=40%. The drug will be tested on 27 patients in the first stage. The trial will be terminate early if 7 or fewer patients respond (early termination probability 84.4% under the null p⁺=20%). Otherwise another 73 patients will be enrolled in the second stage and the drug will be rejected if the total number of patients responding is 28 or fewer. This design requires a maximum sample size of 100 patients, with an expected sample size of 93.0 patients under the null p⁺=20%. This design is provided by <u>**`R`**</u> package <u>**`clinfun`**</u>."
operating characteristics
simon_oc(prob = c(A = .3, B = .2, C = .15), object = x, type = 'minimax')
#> We simulated 10000 trials of each of the 3 drugs 'A', 'B', 'C' with estimated response rates of 30%, 20%, 15%, respectively, using this design. The percentage of trials with each of these drugs having the highest number of responses are 82.4% for A, 13.6% for B, 4.0% for C. The percentage of trials with each of these drugs both having the highest number of responses and being accepted by the Simon's two-stage design are 47.8% for A, 2.9% for B, 0.2% for C.
simon_oc(prob = c(A = .3, B = .2, C = .15), object = x, type = 'optimal')
#> We simulated 10000 trials of each of the 3 drugs 'A', 'B', 'C' with estimated response rates of 30%, 20%, 15%, respectively, using this design. The percentage of trials with each of these drugs having the highest number of responses are 80.5% for A, 14.7% for B, 4.8% for C. The percentage of trials with each of these drugs both having the highest number of responses and being accepted by the Simon's two-stage design are 49.3% for A, 2.8% for B, 0.2% for C.
example with r1 = 0
(x1 = clinfun::ph2simon(pu = .05, pa = .3, ep1 = .05, ep2 = .2))
#>
#> Simon 2-stage Phase II design
#>
#> Unacceptable response rate: 0.05
#> Desirable response rate: 0.3
#> Error rates: alpha = 0.05 ; beta = 0.2
#>
#> r1 n1 r n EN(p0) PET(p0) qLo qHi
#> Minimax 0 7 2 14 9.112 0.6983 0.421 1.000
#> Admissible 0 6 2 15 8.384 0.7351 0.129 0.421
#> Optimal 0 5 2 18 7.941 0.7738 0.000 0.129
# works with all of our functions
autoplot(x1, type = 'optimal') # etc.