Test of the function gs_design

library(tibble)
library(dplyr)
library(testthat)
library(gt)
devtools::load_all()

Test 1: verify by `gs_power_npe`

new version

x <- gs_design_npe(theta = c(.1, .2, .3), info = (1:3) * 40, beta = 0.1,
                   upper = gs_spending_bound,
                   upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                   lower = gs_spending_bound,
                   lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL), binding = TRUE)
x %>% gt()

Analysis	Bound	Z	Probability	Probability0	theta	IF	info	info0	info1
1	Upper	3.7103029	0.0010356481	0.0001035057	0.1	0.3333333	39.75157	39.75157	39.75157
1	Lower	-3.0798144	0.0001035057	0.0010356481	0.1	0.3333333	39.75157	39.75157	39.75157
2	Upper	2.5114338	0.2332751723	0.0060483891	0.2	0.6666667	79.50314	79.50314	79.50314
2	Lower	-0.7281431	0.0060483891	0.2332751723	0.2	0.6666667	79.50314	79.50314	79.50314
3	Upper	1.9930482	0.8999999998	0.0250000000	0.3	1.0000000	119.25471	119.25471	119.25471
3	Lower	1.2830660	0.0250000000	0.8999999998	0.3	1.0000000	119.25471	119.25471	119.25471

The power is 0.9. If we re-use these bounds under alternate hypothesis, then we can get a power close to 0.9.

gs_power_npe(theta = c(.1, .2, .3),info = (1:3) * 40,
             upper = gs_b, upar = (x %>% filter(Bound == "Upper"))$Z,
             lower = gs_b, lpar = -(x %>% filter(Bound == "Upper"))$Z,
             binding = TRUE # Always use binding = TRUE for power calculations
             ) %>% gt()

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1
1	Upper	3.710303	1.042508e-03	0.1	0.1	0.3333333	40	40	40
2	Upper	2.511434	2.349812e-01	0.2	0.2	0.6666667	80	80	80
3	Upper	1.993048	9.020716e-01	0.3	0.3	1.0000000	120	120	120
1	Lower	-3.710303	7.035242e-06	0.1	0.1	0.3333333	40	40	40
2	Lower	-2.511434	1.510031e-05	0.2	0.2	0.6666667	80	80	80
3	Lower	-1.993048	1.512598e-05	0.3	0.3	1.0000000	120	120	120

old version

x <- gs_design_npe_(theta = c(.1, .2, .3), info = (1:3) * 40, beta = 0.1,
                   upper = gs_spending_bound,
                   upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                   lower = gs_spending_bound,
                   lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL), binding = TRUE)
x %>% gt()

Analysis	Bound	Z	Probability	theta	theta1	info	info0	info1
1	Upper	3.7103029	0.0010356481	0.1	0.1	39.75157	39.75157	39.75157
2	Upper	2.5114338	0.2332751723	0.2	0.2	79.50314	79.50314	79.50314
3	Upper	1.9930482	0.8999999998	0.3	0.3	119.25471	119.25471	119.25471
1	Lower	-3.0798144	0.0001035057	0.1	0.1	39.75157	39.75157	39.75157
2	Lower	-0.7281431	0.0060483891	0.2	0.2	79.50314	79.50314	79.50314
3	Lower	1.2830660	0.0250000000	0.3	0.3	119.25471	119.25471	119.25471

The power is 0.9. If we re-use these bounds under alternate hypothesis, then we can get a power close to 0.9.

gs_power_npe_(theta = c(.1, .2, .3),info = (1:3) * 40,
             upper = gs_b, upar = (x %>% filter(Bound == "Upper"))$Z,
             lower = gs_b, lpar = -(x %>% filter(Bound == "Upper"))$Z,
             binding = TRUE # Always use binding = TRUE for power calculations
             ) %>% gt()

Analysis	Bound	Z	Probability	theta	theta1	info	info0	info1
1	Upper	3.710303	1.042508e-03	0.1	0.1	40	40	40
2	Upper	2.511434	2.349812e-01	0.2	0.2	80	80	80
3	Upper	1.993048	9.020716e-01	0.3	0.3	120	120	120
1	Lower	-3.710303	7.035242e-06	0.1	0.1	40	40	40
2	Lower	-2.511434	1.510031e-05	0.2	0.2	80	80	80
3	Lower	-1.993048	1.512598e-05	0.3	0.3	120	120	120

Test 1: examples in spec

difference of proportions

# Lachin book p71 
pc <- .28            # Control response rate
pe <- .40            # Experimental response rate
p0 <- (pc + pe) / 2  # Ave response rate under H0

# Information per increment of 1 in sample size
info0 <- 1 / (p0 * (1 - p0) * 4)
info <- 1 / (pc * (1 - pc) * 2 + pe * (1 - pe) * 2)

# Result should round up to next even number = 652
# Divide information needed under H1 by information per patient added
x1_a <- gs_design_npe(theta = pe - pc, info = info, info0 = info0, info_scale = 0) %>% mutate(`Computated from` = "new version", `Info scale` = 0)
x1_b <- gs_design_npe(theta = pe - pc, info = info, info0 = info0, info_scale = 1) %>% mutate(`Computated from` = "new version", `Info scale` = 1)
x1_c <- gs_design_npe(theta = pe - pc, info = info, info0 = info0, info_scale = 2) %>% mutate(`Computated from` = "new version", `Info scale` = 2)

x2 <- gs_design_npe_(theta = pe - pc, info = info, info0 = info0) %>% mutate(`Computated from` = "old version")

Analysis	Bound	Z	Probability	Probability0	theta	info	info0	info1	IF	Computated from	Info scale
1	Upper	1.959964	0.9	0.025	0.12	729.6822	729.6822	729.6822	1	new version	0
1	Upper	1.959964	0.9	0.025	0.12	729.6822	729.6822	729.6822	1	new version	1
1	Upper	1.959964	0.9	0.025	0.12	736.8641	725.0428	736.8641	1	new version	2
1	Upper	1.959964	0.9	NA	0.12	736.8641	725.0428	NA	NA	old version	NA

fixed design

`info` = `info0` = `info1`

x1_a <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 80, info_scale = 0,
                      upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                      lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "new version", `Info scale` = 0)
x1_b <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 80, info_scale = 1,
                      upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                      lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "new version", `Info scale` = 1)
x1_c <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 80, info_scale = 2,
                      upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                      lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "new version", `Info scale` = 2)
x2 <- gs_design_npe_(theta = c(.1, .2, .3), 
                     info = (1:3) * 80,
                     upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                     lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "old version")

Z	Probability	Probability0	theta	IF	info	info0	info1	Computated from	Info scale	theta1
1 - Upper
3.710303	0.001201556	0.0001035057	0.1	0.3333333	45.56536	45.56536	45.56536	new version	0	NA
3.710303	0.001201556	0.0001035057	0.1	0.3333333	45.56536	45.56536	45.56536	new version	1	NA
3.710303	0.001201556	0.0001035057	0.1	0.3333333	45.56536	45.56536	45.56536	new version	2	NA
3.710303	0.001201556	NA	0.1	NA	45.56536	45.56536	45.56536	old version	NA	0.1
1 - Lower
-1.000000	0.046965036	0.1586552539	0.1	0.3333333	45.56536	45.56536	45.56536	new version	0	NA
-1.000000	0.046965036	0.1586552539	0.1	0.3333333	45.56536	45.56536	45.56536	new version	1	NA
-1.000000	0.046965036	0.1586552539	0.1	0.3333333	45.56536	45.56536	45.56536	new version	2	NA
-1.000000	0.046965036	NA	0.1	NA	45.56536	45.56536	45.56536	old version	NA	0.1
2 - Upper
2.511427	0.273421987	0.0060483983	0.2	0.6666667	91.13072	91.13072	91.13072	new version	0	NA
2.511427	0.273421987	0.0060483983	0.2	0.6666667	91.13072	91.13072	91.13072	new version	1	NA
2.511427	0.273421987	0.0060483983	0.2	0.6666667	91.13072	91.13072	91.13072	new version	2	NA
2.511427	0.273421987	NA	0.2	NA	91.13072	91.13072	91.13072	old version	NA	0.2
2 - Lower
0.000000	0.061921702	0.5125857748	0.2	0.6666667	91.13072	91.13072	91.13072	new version	0	NA
0.000000	0.061921702	0.5125857748	0.2	0.6666667	91.13072	91.13072	91.13072	new version	1	NA
0.000000	0.061921702	0.5125857748	0.2	0.6666667	91.13072	91.13072	91.13072	new version	2	NA
0.000000	0.061921702	NA	0.2	NA	91.13072	91.13072	91.13072	old version	NA	0.2
3 - Upper
1.993048	0.900000000	0.0249302430	0.3	1.0000000	136.69609	136.69609	136.69609	new version	0	NA
1.993048	0.900000000	0.0249302430	0.3	1.0000000	136.69609	136.69609	136.69609	new version	1	NA
1.993048	0.900000000	0.0249302430	0.3	1.0000000	136.69609	136.69609	136.69609	new version	2	NA
1.993048	0.900000000	NA	0.3	NA	136.69609	136.69609	136.69609	old version	NA	0.3
3 - Lower
0.000000	0.061926296	0.6063477109	0.3	1.0000000	136.69609	136.69609	136.69609	new version	0	NA
0.000000	0.061926296	0.6063477109	0.3	1.0000000	136.69609	136.69609	136.69609	new version	1	NA
0.000000	0.061926296	0.6063477109	0.3	1.0000000	136.69609	136.69609	136.69609	new version	2	NA
0.000000	0.061926296	NA	0.3	NA	136.69609	136.69609	136.69609	old version	NA	0.3

`info` != `info0` != `info1`

x1_a <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 80, info0 = (1:3) * 90 + 10, info1 = (1:3) * 70 - 5, info_scale = 0,
                      upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                      lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "new version", `Info scale` = 0)
x1_b <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 80, info0 = (1:3) * 90+ 10, info1 = (1:3) * 70 - 5, info_scale = 1,
                      upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                      lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "new version", `Info scale` = 1)
x1_c <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 80, info0 = (1:3) * 90+ 10, info1 = (1:3) * 70 - 5, info_scale = 2,
                      upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                      lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "new version", `Info scale` = 2)
x2 <- gs_design_npe_(theta = c(.1, .2, .3), 
                     info = (1:3) * 80, info0 = (1:3) * 90+ 10, info1 = (1:3) * 70 - 5, 
                     upper = gs_b, upar = gsDesign::gsDesign(k = 3, sfu = gsDesign::sfLDOF)$upper$bound,
                     lower = gs_b, lpar = c(-1, 0, 0)) %>% mutate(`Computated from` = "old version")

Z	Probability	Probability0	theta	IF	info	info0	info1	Computated from	Info scale	theta1
1 - Upper
3.710303	0.001278699	0.0001035057	0.1	0.3571429	48.14094	48.14094	48.14094	new version	0	NA
3.710303	0.001149869	0.0001035057	0.1	0.3170732	43.79604	43.79604	43.79604	new version	1	NA
3.710303	0.004048062	0.0004523565	0.1	0.3333333	44.96523	56.20654	36.53425	new version	2	NA
3.710303	0.004048062	NA	0.1	NA	44.96523	56.20654	36.53425	old version	NA	0.1
1 - Lower
-1.000000	0.045148157	0.1586552539	0.1	0.3571429	48.14094	48.14094	48.14094	new version	0	NA
-1.000000	0.048277869	0.1586552539	0.1	0.3170732	43.79604	43.79604	43.79604	new version	1	NA
-1.000000	0.058792818	0.1855466848	0.1	0.3333333	44.96523	56.20654	36.53425	new version	2	NA
-1.000000	0.058792818	NA	0.1	NA	44.96523	56.20654	36.53425	old version	NA	0.1
2 - Upper
2.511427	0.274637453	0.0060442562	0.2	0.6785714	91.46778	91.46778	91.46778	new version	0	NA
2.511427	0.272791297	0.0060513253	0.2	0.6585366	90.96101	90.96101	90.96101	new version	1	NA
2.511427	0.272107963	0.0063972490	0.2	0.6666667	89.93046	106.79242	75.87883	new version	2	NA
2.511427	0.272107963	NA	0.2	NA	89.93046	106.79242	75.87883	old version	NA	0.2
2 - Lower
0.000000	0.059626767	0.5110855741	0.2	0.6785714	91.46778	91.46778	91.46778	new version	0	NA
0.000000	0.063543969	0.5136901172	0.2	0.6585366	90.96101	90.96101	90.96101	new version	1	NA
0.000000	0.074240014	0.5394772057	0.2	0.6666667	89.93046	106.79242	75.87883	new version	2	NA
0.000000	0.074240014	NA	0.2	NA	89.93046	106.79242	75.87883	old version	NA	0.2
3 - Upper
1.993048	0.899999988	0.0248602069	0.3	1.0000000	134.79463	134.79463	134.79463	new version	0	NA
1.993048	0.900000000	0.0249748131	0.3	1.0000000	138.12597	138.12597	138.12597	new version	1	NA
1.993048	0.899999920	0.0252790938	0.3	1.0000000	134.89569	157.37831	115.22340	new version	2	NA
1.993048	0.899999920	NA	0.3	NA	134.89569	157.37831	115.22340	old version	NA	0.3
3 - Lower
0.000000	0.059631346	0.6032976877	0.3	1.0000000	134.79463	134.79463	134.79463	new version	0	NA
0.000000	0.063548525	0.6084787927	0.3	1.0000000	138.12597	138.12597	138.12597	new version	1	NA
0.000000	0.074245152	0.6332391417	0.3	1.0000000	134.89569	157.37831	115.22340	new version	2	NA
0.000000	0.074245152	NA	0.3	NA	134.89569	157.37831	115.22340	old version	NA	0.3

futility at IA1; efficacy only at IA2 +FA

x1_a <- gs_design_npe(theta = c(.1, .2, .3),
                      info = (1:3) * 40, info0 = (1:3) * 40, info_scale = 0,
                      upper = gs_spending_bound, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_b, lpar = c(-1, -Inf, -Inf),
                      test_upper = c(FALSE, TRUE, TRUE)) %>% mutate(`Computated from` = "new version", `Info scale` = 0)

x1_b <- gs_design_npe(theta = c(.1, .2, .3),
                      info = (1:3) * 40, info0 = (1:3) * 40, info_scale = 1,
                      upper = gs_spending_bound, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_b, lpar = c(-1, -Inf, -Inf),
                      test_upper = c(FALSE, TRUE, TRUE)) %>% mutate(`Computated from` = "new version", `Info scale` = 1)

x1_c <- gs_design_npe(theta = c(.1, .2, .3),
                      info = (1:3) * 40, info0 = (1:3) * 40, info_scale = 2,
                      upper = gs_spending_bound, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_b, lpar = c(-1, -Inf, -Inf),
                      test_upper = c(FALSE, TRUE, TRUE)) %>% mutate(`Computated from` = "new version", `Info scale` = 2)

x2 <- gs_design_npe_(theta = c(.1, .2, .3),
                    info = (1:3) * 40, info0 = (1:3) * 40, 
                    upper = gs_spending_bound, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                    lower = gs_b, lpar =  c(-1, -Inf, -Inf),
                    test_upper = c(FALSE, TRUE, TRUE)) %>% mutate(`Computated from` = "old version", `Info scale` = 0)

x1_a %>% 
  union_all(x1_b) %>% 
  union_all(x1_c) %>% 
  union_all(x2) %>% 
  arrange(Analysis) %>% 
  group_by(Analysis, Bound) %>% 
  gt() %>% 
  tab_style(
    style = list(cell_fill(color = "#d3edeb")),
    locations = cells_body(rows = `Computated from` == "old version"))

Z	Probability	Probability0	theta	IF	info	info0	info1	Computated from	Info scale	theta1
1 - Upper
Inf	0.00000000	0.000000000	0.1	0.3333333	44.55554	44.55554	44.55554	new version	0	NA
Inf	0.00000000	0.000000000	0.1	0.3333333	44.55554	44.55554	44.55554	new version	1	NA
Inf	0.00000000	0.000000000	0.1	0.3333333	44.55554	44.55554	44.55554	new version	2	NA
Inf	0.00000000	NA	0.1	NA	44.55554	44.55554	44.55554	old version	0	0.1
1 - Lower
-1.000000	0.04770758	0.158655254	0.1	0.3333333	44.55554	44.55554	44.55554	new version	0	NA
-1.000000	0.04770758	0.158655254	0.1	0.3333333	44.55554	44.55554	44.55554	new version	1	NA
-1.000000	0.04770758	0.158655254	0.1	0.3333333	44.55554	44.55554	44.55554	new version	2	NA
-1.000000	0.04770758	NA	0.1	NA	44.55554	44.55554	44.55554	old version	0	0.1
2 - Upper
2.509315	0.26707709	0.006048281	0.2	0.6666667	89.11107	89.11107	89.11107	new version	0	NA
2.509315	0.26707709	0.006048281	0.2	0.6666667	89.11107	89.11107	89.11107	new version	1	NA
2.509315	0.26707709	0.006048281	0.2	0.6666667	89.11107	89.11107	89.11107	new version	2	NA
2.509315	0.26707709	NA	0.2	NA	89.11107	89.11107	89.11107	old version	0	0.2
2 - Lower
-Inf	0.04770758	0.158655254	0.2	0.6666667	89.11107	89.11107	89.11107	new version	0	NA
-Inf	0.04770758	0.158655254	0.2	0.6666667	89.11107	89.11107	89.11107	new version	1	NA
-Inf	0.04770758	0.158655254	0.2	0.6666667	89.11107	89.11107	89.11107	new version	2	NA
-Inf	0.04770758	NA	0.2	NA	89.11107	89.11107	89.11107	old version	0	0.2
3 - Upper
1.992888	0.90000000	0.024947293	0.3	1.0000000	133.66661	133.66661	133.66661	new version	0	NA
1.992888	0.90000000	0.024947293	0.3	1.0000000	133.66661	133.66661	133.66661	new version	1	NA
1.992888	0.90000000	0.024947293	0.3	1.0000000	133.66661	133.66661	133.66661	new version	2	NA
1.992888	0.90000000	NA	0.3	NA	133.66661	133.66661	133.66661	old version	0	0.3
3 - Lower
-Inf	0.04770758	0.158655254	0.3	1.0000000	133.66661	133.66661	133.66661	new version	0	NA
-Inf	0.04770758	0.158655254	0.3	1.0000000	133.66661	133.66661	133.66661	new version	1	NA
-Inf	0.04770758	0.158655254	0.3	1.0000000	133.66661	133.66661	133.66661	new version	2	NA
-Inf	0.04770758	NA	0.3	NA	133.66661	133.66661	133.66661	old version	0	0.3

spending bounds

x1_a <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 40, info0 = (1:3) * 50, info_scale = 0,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfHSD, total_spend = 0.1, param = -1, timing = NULL)) %>% mutate(`Computated from` = "new version", `Info scale` = 0)

x1_b <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 40, info0 = (1:3) * 50, info_scale = 1,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfHSD, total_spend = 0.1, param = -1, timing = NULL)) %>% mutate(`Computated from` = "new version", `Info scale` = 1)

x1_c <- gs_design_npe(theta = c(.1, .2, .3), 
                      info = (1:3) * 40, info0 = (1:3) * 50, info_scale = 2,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfHSD, total_spend = 0.1, param = -1, timing = NULL)) %>% mutate(`Computated from` = "new version", `Info scale` = 2)

x2 <- gs_design_npe_(theta = c(.1, .2, .3), 
                     info = (1:3) * 40, info0 = (1:3) * 50, 
                     upper = gs_spending_bound,
                     upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                     lower = gs_spending_bound,
                     lpar = list(sf = gsDesign::sfHSD, total_spend = 0.1, param = -1, timing = NULL)) %>% mutate(`Computated from` = "old version")

Z	Probability	Probability0	theta	IF	info	info0	info1	Computated from	Info scale	theta1
1 - Upper
3.7103029	0.001136317	0.0001035057	0.1	0.3333333	43.32605	43.32605	43.32605	new version	0	NA
3.7103029	0.001136317	0.0001035057	0.1	0.3333333	43.32605	43.32605	43.32605	new version	1	NA
3.7103029	0.003850782	0.0004523565	0.1	0.3333333	42.73434	53.41793	42.73434	new version	2	NA
3.7103029	0.003850782	NA	0.1	NA	42.73434	53.41793	42.73434	old version	NA	0.1
1 - Lower
-1.3367329	0.023023722	0.0906549246	0.1	0.3333333	43.32605	43.32605	43.32605	new version	0	NA
-1.3367329	0.023023722	0.0906549246	0.1	0.3333333	43.32605	43.32605	43.32605	new version	1	NA
-1.3412431	0.031915434	0.1151387639	0.1	0.3333333	42.73434	53.41793	42.73434	new version	2	NA
-1.3412431	0.031915434	NA	0.1	NA	42.73434	53.41793	42.73434	old version	NA	0.1
2 - Upper
2.5114338	0.257938878	0.0060483767	0.2	0.6666667	86.65211	86.65211	86.65211	new version	0	NA
2.5114338	0.257938878	0.0060483767	0.2	0.6666667	86.65211	86.65211	86.65211	new version	1	NA
2.5114338	0.256567802	0.0063972278	0.2	0.6666667	85.46869	106.83586	85.46869	new version	2	NA
2.5114338	0.256567802	NA	0.2	NA	85.46869	106.83586	85.46869	old version	NA	0.2
2 - Lower
0.1455293	0.055155914	0.5605209895	0.2	0.6666667	86.65211	86.65211	86.65211	new version	0	NA
0.1455293	0.055155914	0.5605209895	0.2	0.6666667	86.65211	86.65211	86.65211	new version	1	NA
0.1327725	0.064047626	0.5807591379	0.2	0.6666667	85.46869	106.83586	85.46869	new version	2	NA
0.1327725	0.064047626	NA	0.2	NA	85.46869	106.83586	85.46869	old version	NA	0.2
3 - Upper
1.9930511	0.900000000	0.0249444277	0.3	1.0000000	129.97816	129.97816	129.97816	new version	0	NA
1.9930511	0.900000000	0.0249444277	0.3	1.0000000	129.97816	129.97816	129.97816	new version	1	NA
1.9930511	0.900000001	0.0252963129	0.3	1.0000000	128.20303	160.25379	128.20303	new version	2	NA
1.9930511	0.900000001	NA	0.3	NA	128.20303	160.25379	128.20303	old version	NA	0.3
3 - Lower
1.9930488	0.100000000	0.9750558052	0.3	1.0000000	129.97816	129.97816	129.97816	new version	0	NA
1.9930488	0.100000000	0.9750558052	0.3	1.0000000	129.97816	129.97816	129.97816	new version	1	NA
1.9696010	0.108891712	0.9990450865	0.3	1.0000000	128.20303	160.25379	128.20303	new version	2	NA
1.9696010	0.108891712	NA	0.3	NA	128.20303	160.25379	128.20303	old version	NA	0.3

2-sided symmetric spend

x1_a <- gs_design_npe(theta = c(.1, .2, .3),
                      info = (1:3) * 40, info_scale = 0,
                      binding = TRUE,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)) %>% mutate(`Computated from` = "new version", `Info scale` = 0)

x1_b <- gs_design_npe(theta = c(.1, .2, .3),
                      info = (1:3) * 40, info_scale = 1,
                      binding = TRUE,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)) %>% mutate(`Computated from` = "new version", `Info scale` = 1)

x1_c <- gs_design_npe(theta = c(.1, .2, .3),
                      info = (1:3) * 40, info_scale = 2,
                      binding = TRUE,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)) %>% mutate(`Computated from` = "new version", `Info scale` = 2)

x2 <- gs_design_npe_(theta = c(.1, .2, .3),
                      info = (1:3) * 40, 
                      binding = TRUE,
                      upper = gs_spending_bound,
                      upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                      lower = gs_spending_bound,
                      lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)) %>% mutate(`Computated from` = "old version")

Z	Probability	Probability0	theta	IF	info	info0	info1	Computated from	Info scale	theta1
1 - Upper
3.7103029	0.0010356481	0.0001035057	0.1	0.3333333	39.75157	39.75157	39.75157	new version	0	NA
3.7103029	0.0010356481	0.0001035057	0.1	0.3333333	39.75157	39.75157	39.75157	new version	1	NA
3.7103029	0.0010356481	0.0001035057	0.1	0.3333333	39.75157	39.75157	39.75157	new version	2	NA
3.7103029	0.0010356481	NA	0.1	NA	39.75157	39.75157	39.75157	old version	NA	0.1
1 - Lower
-3.0798144	0.0001035057	0.0010356481	0.1	0.3333333	39.75157	39.75157	39.75157	new version	0	NA
-3.0798144	0.0001035057	0.0010356481	0.1	0.3333333	39.75157	39.75157	39.75157	new version	1	NA
-3.0798144	0.0001035057	0.0010356481	0.1	0.3333333	39.75157	39.75157	39.75157	new version	2	NA
-3.0798144	0.0001035057	NA	0.1	NA	39.75157	39.75157	39.75157	old version	NA	0.1
2 - Upper
2.5114338	0.2332751723	0.0060483891	0.2	0.6666667	79.50314	79.50314	79.50314	new version	0	NA
2.5114338	0.2332751723	0.0060483891	0.2	0.6666667	79.50314	79.50314	79.50314	new version	1	NA
2.5114338	0.2332751723	0.0060483891	0.2	0.6666667	79.50314	79.50314	79.50314	new version	2	NA
2.5114338	0.2332751723	NA	0.2	NA	79.50314	79.50314	79.50314	old version	NA	0.2
2 - Lower
-0.7281431	0.0060483891	0.2332751723	0.2	0.6666667	79.50314	79.50314	79.50314	new version	0	NA
-0.7281431	0.0060483891	0.2332751723	0.2	0.6666667	79.50314	79.50314	79.50314	new version	1	NA
-0.7281431	0.0060483891	0.2332751723	0.2	0.6666667	79.50314	79.50314	79.50314	new version	2	NA
-0.7281431	0.0060483891	NA	0.2	NA	79.50314	79.50314	79.50314	old version	NA	0.2
3 - Upper
1.9930482	0.8999999998	0.0250000000	0.3	1.0000000	119.25471	119.25471	119.25471	new version	0	NA
1.9930482	0.8999999998	0.0250000000	0.3	1.0000000	119.25471	119.25471	119.25471	new version	1	NA
1.9930482	0.8999999998	0.0250000000	0.3	1.0000000	119.25471	119.25471	119.25471	new version	2	NA
1.9930482	0.8999999998	NA	0.3	NA	119.25471	119.25471	119.25471	old version	NA	0.3
3 - Lower
1.2830660	0.0250000000	0.8999999998	0.3	1.0000000	119.25471	119.25471	119.25471	new version	0	NA
1.2830660	0.0250000000	0.8999999998	0.3	1.0000000	119.25471	119.25471	119.25471	new version	1	NA
1.2830660	0.0250000000	0.8999999998	0.3	1.0000000	119.25471	119.25471	119.25471	new version	2	NA
1.2830660	0.0250000000	NA	0.3	NA	119.25471	119.25471	119.25471	old version	NA	0.3

Test of the function gs_design_npe

Test 1: verify by gs_power_npe