Test of the function gs_power

Test 1: Examples from spec

Default

The default of gs_power_npe is a single analysis with type I error controlled.

x1 <- gs_power_npe(theta = 0) %>% filter(Bound == "Upper")
x2 <- gsDesign2:::gs_power_npe_(theta = 0) %>% filter(Bound == "Upper")

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1	Computated from
1	Upper	1.959964	0.025	0	0	1	1	1	1	new version
1	Upper	1.959964	0.025	0	0	NA	1	1	1	old version

Fixed bound

x1 <- gs_power_npe(theta = c(.1, .2, .3),
                   info = (1:3) * 40,
                   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")

x2 <- gs_power_npe_(theta = c(.1, .2, .3),
                    info = (1:3) * 40,
                    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")

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1	Computated from
1	Upper	3.710303	0.001042508	0.1	0.1	0.3333333	40	40	40	new version
2	Upper	2.511427	0.234899008	0.2	0.2	0.6666667	80	80	80	new version
3	Upper	1.993048	0.868689026	0.3	0.3	1.0000000	120	120	120	new version
1	Lower	-1.000000	0.051291779	0.1	0.1	0.3333333	40	40	40	new version
2	Lower	0.000000	0.071509147	0.2	0.2	0.6666667	80	80	80	new version
3	Lower	0.000000	0.071522125	0.3	0.3	1.0000000	120	120	120	new version
1	Upper	3.710303	0.001042508	0.1	0.1	NA	40	40	40	old version
2	Upper	2.511427	0.234899008	0.2	0.2	NA	80	80	80	old version
3	Upper	1.993048	0.868689026	0.3	0.3	NA	120	120	120	old version
1	Lower	-1.000000	0.051291779	0.1	0.1	NA	40	40	40	old version
2	Lower	0.000000	0.071509147	0.2	0.2	NA	80	80	80	old version
3	Lower	0.000000	0.071522125	0.3	0.3	NA	120	120	120	old version

Same fixed efficacy bounds, no futility bound (i.e., non-binding bound), null hypothesis

x1 <- gs_power_npe(theta = rep(0, 3),
                   info = (1:3) * 40,
                   upar = gsDesign::gsDesign(k = 3,sfu = gsDesign::sfLDOF)$upper$bound,
                   lpar = rep(-Inf, 3)) %>% mutate(`Computated from` = "new version")

x2 <- gs_power_npe_(theta = rep(0, 3),
                    info = (1:3) * 40,
                    upar = gsDesign::gsDesign(k = 3,sfu = gsDesign::sfLDOF)$upper$bound,
                    lpar = rep(-Inf, 3)) %>% mutate(`Computated from` = "old version")

Analysis	Bound	Z	Probability	IF	info	info0	info1	Computated from
1	Upper	3.710303	0.0001035057	0.3333333	40	40	40	new version
2	Upper	2.511427	0.0060485045	0.6666667	80	80	80	new version
3	Upper	1.993048	0.0250002354	1.0000000	120	120	120	new version
1	Lower	-Inf	0.0000000000	0.3333333	40	40	40	new version
2	Lower	-Inf	0.0000000000	0.6666667	80	80	80	new version
3	Lower	-Inf	0.0000000000	1.0000000	120	120	120	new version
1	Upper	3.710303	0.0001035057	NA	40	40	40	old version
2	Upper	2.511427	0.0060485045	NA	80	80	80	old version
3	Upper	1.993048	0.0250002354	NA	120	120	120	old version
1	Lower	-Inf	0.0000000000	NA	40	40	40	old version
2	Lower	-Inf	0.0000000000	NA	80	80	80	old version
3	Lower	-Inf	0.0000000000	NA	120	120	120	old version

Fixed bound with futility only at analysis 1; efficacy only at analyses 2, 3

x1 <- gs_power_npe(theta = c(.1, .2, .3),
                   info = (1:3) * 40,
                   upper = gs_b,
                   upar = c(Inf, 3, 2),
                   lower = gs_b,
                   lpar = c(qnorm(.1), -Inf, -Inf)) %>% mutate(`Computated from` = "new version")

x2 <- gs_power_npe_(theta = c(.1, .2, .3),
                    info = (1:3) * 40,
                    upper = gs_b,
                    upar = c(Inf, 3, 2),
                    lower = gs_b,
                    lpar = c(qnorm(.1), -Inf, -Inf)) %>% mutate(`Computated from` = "old version")

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1	Computated from
1	Upper	Inf	0.00000000	0.1	0.1	0.3333333	40	40	40	new version
2	Upper	3.000000	0.11291848	0.2	0.2	0.6666667	80	80	80	new version
3	Upper	2.000000	0.88742529	0.3	0.3	1.0000000	120	120	120	new version
1	Lower	-1.281552	0.02780962	0.1	0.1	0.3333333	40	40	40	new version
2	Lower	-Inf	0.02780962	0.2	0.2	0.6666667	80	80	80	new version
3	Lower	-Inf	0.02780962	0.3	0.3	1.0000000	120	120	120	new version
1	Upper	Inf	0.00000000	0.1	0.1	NA	40	40	40	old version
2	Upper	3.000000	0.11291848	0.2	0.2	NA	80	80	80	old version
3	Upper	2.000000	0.88742529	0.3	0.3	NA	120	120	120	old version
1	Lower	-1.281552	0.02780962	0.1	0.1	NA	40	40	40	old version
2	Lower	-Inf	0.02780962	0.2	0.2	NA	80	80	80	old version
3	Lower	-Inf	0.02780962	0.3	0.3	NA	120	120	120	old version

Spending function bounds

# Lower spending based on non-zero effect
x1 <- gs_power_npe(theta = c(.1, .2, .3),
                   info = (1:3) * 40,
                   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")

x2 <- gs_power_npe_(theta = c(.1, .2, .3),
                    info = (1:3) * 40,
                    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")

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1	Computated from
1	Upper	3.71030287	0.001042508	0.1	0.1	0.3333333	40	40	40	new version
2	Upper	2.51143381	0.234968841	0.2	0.2	0.6666667	80	80	80	new version
3	Upper	1.99305108	0.882718886	0.3	0.3	1.0000000	120	120	120	new version
1	Lower	-1.36250263	0.023023722	0.1	0.1	0.3333333	40	40	40	new version
2	Lower	0.07264138	0.055155914	0.2	0.2	0.6666667	80	80	80	new version
3	Lower	1.85908660	0.100000000	0.3	0.3	1.0000000	120	120	120	new version
1	Upper	3.71030287	0.001042508	0.1	0.1	NA	40	40	40	old version
2	Upper	2.51143381	0.234968841	0.2	0.2	NA	80	80	80	old version
3	Upper	1.99305108	0.882718886	0.3	0.3	NA	120	120	120	old version
1	Lower	-1.36250263	0.023023722	0.1	0.1	NA	40	40	40	old version
2	Lower	0.07264138	0.055155914	0.2	0.2	NA	80	80	80	old version
3	Lower	1.85908660	0.100000000	0.3	0.3	NA	120	120	120	old version

Same bounds, but power under different theta

x1 <- gs_power_npe(theta = c(.15, .25, .35),
                   info = (1:3) * 40,
                   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")

x2 <- gs_power_npe_(theta = c(.15, .25, .35),
                    info = (1:3) * 40,
                    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")

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1	Computated from
1	Upper	3.710303	0.002875773	0.15	0.15	0.3333333	40	40	40	new version
2	Upper	2.511434	0.391439113	0.25	0.25	0.6666667	80	80	80	new version
3	Upper	1.993051	0.931364287	0.35	0.35	1.0000000	120	120	120	new version
1	Lower	-1.046275	0.023023722	0.15	0.15	0.3333333	40	40	40	new version
2	Lower	0.519855	0.055155914	0.25	0.25	0.6666667	80	80	80	new version
3	Lower	2.408073	0.100000000	0.35	0.35	1.0000000	120	120	120	new version
1	Upper	3.710303	0.002875773	0.15	0.15	NA	40	40	40	old version
2	Upper	2.511434	0.391439113	0.25	0.25	NA	80	80	80	old version
3	Upper	1.993051	0.931364287	0.35	0.35	NA	120	120	120	old version
1	Lower	-1.046275	0.023023722	0.15	0.15	NA	40	40	40	old version
2	Lower	0.519855	0.055155914	0.25	0.25	NA	80	80	80	old version
3	Lower	2.408073	0.100000000	0.35	0.35	NA	120	120	120	old version

Two-sided symmetric spend, O’Brien-Fleming spending

Typically, 2-sided bounds are binding

x1 <- gs_power_npe(theta = rep(0, 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` = "new version")

x2 <- gs_power_npe_(theta = rep(0, 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")

Analysis	Bound	Z	Probability	IF	info	info0	info1	Computated from
1	Upper	3.710303	0.0001035057	0.3333333	40	40	40	new version
2	Upper	2.511434	0.0060483891	0.6666667	80	80	80	new version
3	Upper	1.993051	0.0250000000	1.0000000	120	120	120	new version
1	Lower	-3.710303	0.0001035057	0.3333333	40	40	40	new version
2	Lower	-2.511434	0.0060483891	0.6666667	80	80	80	new version
3	Lower	-1.993051	0.0250000000	1.0000000	120	120	120	new version
1	Upper	3.710303	0.0001035057	NA	40	40	40	old version
2	Upper	2.511434	0.0060483891	NA	80	80	80	old version
3	Upper	1.993051	0.0250000000	NA	120	120	120	old version
1	Lower	-3.710303	0.0001035057	NA	40	40	40	old version
2	Lower	-2.511434	0.0060483891	NA	80	80	80	old version
3	Lower	-1.993051	0.0250000000	NA	120	120	120	old version

Re-use these bounds under alternate hypothesis

Always use binding = TRUE for power calculations

xx1 <- gs_power_npe(theta = c(.1, .2, .3), 
                    info = (1:3) * 40,
                    binding = TRUE,
                    upar = (x1 %>% filter(Bound == "Upper"))$Z,
                    lpar = -(x1 %>% filter(Bound == "Upper"))$Z) %>% mutate(`Computated from` = "new version")

xx2 <- gs_power_npe_(theta = c(.1, .2, .3), 
                     info = (1:3) * 40,
                     binding = TRUE,
                     upar = (x1 %>% filter(Bound == "Upper"))$Z,
                     lpar = -(x1 %>% filter(Bound == "Upper"))$Z) %>% mutate(`Computated from` = "old version")

Analysis	Bound	Z	Probability	theta	theta1	IF	info	info0	info1	Computated from
1	Upper	3.710303	1.042508e-03	0.1	0.1	0.3333333	40	40	40	new version
2	Upper	2.511434	2.349812e-01	0.2	0.2	0.6666667	80	80	80	new version
3	Upper	1.993051	9.020711e-01	0.3	0.3	1.0000000	120	120	120	new version
1	Lower	-3.710303	7.035242e-06	0.1	0.1	0.3333333	40	40	40	new version
2	Lower	-2.511434	1.510031e-05	0.2	0.2	0.6666667	80	80	80	new version
3	Lower	-1.993051	1.512598e-05	0.3	0.3	1.0000000	120	120	120	new version
1	Upper	3.710303	1.042508e-03	0.1	0.1	NA	40	40	40	old version
2	Upper	2.511434	2.349812e-01	0.2	0.2	NA	80	80	80	old version
3	Upper	1.993051	9.020711e-01	0.3	0.3	NA	120	120	120	old version
1	Lower	-3.710303	7.035242e-06	0.1	0.1	NA	40	40	40	old version
2	Lower	-2.511434	1.510031e-05	0.2	0.2	NA	80	80	80	old version
3	Lower	-1.993051	1.512598e-05	0.3	0.3	NA	120	120	120	old version

Test 2: Fixed Design

The power at the following analysis is expected at 0.975.

gs_power_npe(theta = 0, 
             upper = gs_b, upar = qnorm(0.025),
             lower = gs_b, lpar = -Inf)

## # A tibble: 2 × 10
##   Analysis Bound       Z Probability theta theta1    IF  info info0 info1
##      <int> <chr>   <dbl>       <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
## 1        1 Upper   -1.96       0.975     0      0     1     1     1     1
## 2        1 Lower -Inf          0         0      0     1     1     1     1

Test 3: `info` != `info0` != `info1`

If one inputs info in upar

x1_a <- gs_power_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_power_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_power_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_power_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")

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	theta	theta1	IF	info	info0	info1	Computated from	Info scale
1 - Upper
3.710303	0.003361090	0.1	0.1	0.3571429	100	100	100	new version	0
3.710303	0.001841687	0.1	0.1	0.3170732	65	65	65	new version	1
3.710303	0.007671740	0.1	0.1	0.3333333	80	100	65	new version	2
3.710303	0.007671740	0.1	0.1	NA	80	100	65	old version	NA
1 - Lower
-1.000000	0.022750132	0.1	0.1	0.3571429	100	100	100	new version	0
-1.000000	0.035441540	0.1	0.1	0.3170732	65	65	65	new version	1
-1.000000	0.036819135	0.1	0.1	0.3333333	80	100	65	new version	2
-1.000000	0.036819135	0.1	0.1	NA	80	100	65	old version	NA
2 - Upper
2.511427	0.596459227	0.2	0.2	0.6785714	190	190	190	new version	0
2.511427	0.425190347	0.2	0.2	0.6585366	135	135	135	new version	1
2.511427	0.512129734	0.2	0.2	0.6666667	160	190	135	new version	2
2.511427	0.512129734	0.2	0.2	NA	160	190	135	old version	NA
2 - Lower
0.000000	0.023865544	0.2	0.2	0.6785714	190	190	190	new version	0
0.000000	0.040277466	0.2	0.2	0.6585366	135	135	135	new version	1
0.000000	0.039313062	0.2	0.2	0.6666667	160	190	135	new version	2
0.000000	0.039313062	0.2	0.2	NA	160	190	135	old version	NA
3 - Upper
1.993048	0.975690714	0.3	0.3	1.0000000	280	280	280	new version	0
1.993048	0.954614762	0.3	0.3	1.0000000	205	205	205	new version	1
1.993048	0.971978079	0.3	0.3	1.0000000	240	280	205	new version	2
1.993048	0.971978079	0.3	0.3	NA	240	280	205	old version	NA
3 - Lower
0.000000	0.023865545	0.3	0.3	1.0000000	280	280	280	new version	0
0.000000	0.040277546	0.3	0.3	1.0000000	205	205	205	new version	1
0.000000	0.039313070	0.3	0.3	1.0000000	240	280	205	new version	2
0.000000	0.039313070	0.3	0.3	NA	240	280	205	old version	NA

Test 3: Developer Tests

1-sided test

r = 80
x <- gs_power_npe(theta = 0, 
                  info = (1:3) * 400, 
                  binding = FALSE, r = r,
                  upper = gs_b, #gs_spending_bound, 
                  upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF)$upper$bound,
                  #list(par = list(sf = gsDesign::sfLDOF, param = NULL, total_spend = 0.025)),
                  lower = gs_b, 
                  lpar = rep(-Inf, 3)) %>% filter(Bound == "Upper")

y <- gsDesign2:::gs_power_npe_(theta = 0, 
                  info = (1:3) * 400, 
                  binding = FALSE, r = r,
                  upper = gs_b, #gs_spending_bound, 
                  upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF)$upper$bound,
                  #list(par = list(sf = gsDesign::sfLDOF, param = NULL, total_spend = 0.025)),
                  lower = gs_b, 
                  lpar = rep(-Inf, 3)) %>% filter(Bound == "Upper")

z <- gsProbability(k = 3, 
                   theta = 0, 
                   n.I = (1:3) * 400, 
                   b = gsDesign(k = 3, test.type = 1, sfu = sfLDOF)$upper$bound, a = rep(-20, 3), r = r)

Calculated from	upper bound	upper prob
1
new version	3.710303	0.0001035057
old version	3.710303	0.0001035057
gsDesign	3.710303	0.0001035057
2
new version	2.511427	0.0060483973
old version	2.511427	0.0060483973
gsDesign	2.511427	0.0060483970
3
new version	1.993048	0.0250000020
old version	1.993048	0.0250000020
gsDesign	1.993048	0.0250000013

Test 4: Independent Tests

Expect equal with mvtnorm for efficacy and futility bounds

info <- c(40, 100)
r <- info[1] / info[2]

test<-gs_power_npe(theta = 0,
                   info = info,
                   info0 = NULL,
                   binding = FALSE,
                   upper = gs_spending_bound,
                   upar = list(sf = gsDesign::sfLDOF, param = NULL, total_spend = 0.025),
                   lower = gs_spending_bound,
                   lpar = list(sf = gsDesign::sfLDOF, param = NULL, total_spend = 0.02)
)

test1 <- test%>% filter(Bound == "Upper")
test2 <- test%>% filter(Bound == "Lower")

alpha.t <- 0.025
b.ia <- gsDesign::sfLDOF(alpha = alpha.t, t = r)
alpha.ia <- b.ia$spend

Pb <- function(alpha.t, alpha.ia, r, b){
  temp = mvtnorm::pmvnorm(lower = c(-Inf, b), 
                          upper = c(qnorm(1-alpha.ia), Inf),
                          corr = rbind(c(1, sqrt(r)), c(sqrt(r), 1)))
  return(alpha.t - alpha.ia - temp)
}

b <- uniroot(Pb, c(1.96, 4), alpha.t = alpha.t, alpha.ia = alpha.ia, r = r)

pb <- 1- pnorm(b$root)

expect_equal(object = test1$Z, expected = c(qnorm(1-alpha.ia),b$root), tolerance = 0.001)
expect_equal(object = test1$Probability, expected = cumsum(c(b.ia$spend,pb)), tolerance = 0.001)

  beta.t <- 0.02
  a.ia <- gsDesign::sfLDOF(alpha = beta.t, t = r)
  beta.ia <- a.ia$spend

  Pa <- function(beta.t, beta.ia,  r, a){
    temp <- mvtnorm::pmvnorm(lower = c(-Inf, qnorm(beta.ia)),
                             upper = c(a, Inf),
                             corr = rbind(c(1, sqrt(r)), c(sqrt(r), 1)))
    return(beta.t -  beta.ia - temp)
  }

  a <- uniroot(Pa, c(-4, 1.96), beta.t = beta.t, beta.ia = beta.ia, r = r)

  pa <- pnorm(a$root)

  expect_equal(object = test2$Z, expected = c(qnorm(beta.ia), a$root), tolerance = 0.001)
  expect_equal(object = test2$Probability, expected = cumsum(c(a.ia$spend,pa)), tolerance = 0.001)

Expect equal with `gsDesign::gsProbability` outcome for efficacy bounds

info <- c(40, 150, 200)

x <- gs_power_npe(theta = .1,
                  info = info, binding = FALSE,
                  upper = gs_spending_bound,
                  upar = list(sf = gsDesign::sfLDOF, param = NULL, total_spend = 0.025),
                  lower = gs_b,
                  lpar = rep(-Inf, 3)) %>% filter(Bound == "Upper")

y <- gs_power_npe(theta = .1,
                  info = info, binding = FALSE,
                  upper = gs_spending_bound,
                  upar = list(sf = gsDesign::sfLDOF, param = NULL, total_spend = 0.025),
                  lower = gs_b,
                  lpar = rep(-Inf, 3)) %>% filter(Bound == "Upper")

z <- gsDesign::gsProbability(k = 3, theta = .1,
                             n.I = info,
                             a = rep(-20, 3),
                             b = gsDesign(k = 3, test.type=1, sfu = sfLDOF, n.I = info)$upper$bound)

Calculated from	upper bound	upper prob
1
new version	4.876885	1.095752e-05
old version	4.876885	1.095752e-05
gsDesign	4.876885	1.095752e-05
2
new version	2.339724	1.324308e-01
old version	2.339724	1.324308e-01
gsDesign	2.339719	1.324317e-01
3
new version	2.011782	2.870640e-01
old version	2.011782	2.870640e-01
gsDesign	2.011778	2.870653e-01

Test 5: Compare with `gsDesign` under information-based design

Information-based design is useful when testing for a natural parameter \(\delta\) (e.g., treatment difference on a relevant scale such as risk difference) where the variance of the estimate of \(\delta\) is unknown. The basic canonical form of represents information-based design, so it is a particularly simple way to check corresponding basic calculations for sample size, bounds and power in gs_power_npe() and gs_design_npe().

Step 1: set the design assumptions

k <- 2           # Number of analyses
test.type <- 4
alpha <- 0.025   # 1-sided Type I error
beta <- 0.15     # Type 2 error (1 - targeted power)
astar <- .1
timing <- 0.4    # Timing (information fraction) at interim analyses
sfu <- sfHSD     # Efficacy bound spending function
sfupar <- -1     # Upper bound spending function parameters, if any
sfl <- sfLDPocock# Lower bound spending function, if used (test.type > 2)
sflpar <- 0      # Lower bound spending function parameters, if any
delta <- 0.1     # Natural parameter difference (assumed value - H0 value)
delta1 <- 0.1    # Natural parameter assumed value
delta0 <- 0      # Natural parameter difference under H0
endpoint <- 'info'
n.fix <- 0

Test of the function gs_power_npe

Test 1: Examples from spec

Default

Fixed bound

Same fixed efficacy bounds, no futility bound (i.e., non-binding bound), null hypothesis

Fixed bound with futility only at analysis 1; efficacy only at analyses 2, 3

Spending function bounds

Same bounds, but power under different theta

Two-sided symmetric spend, O’Brien-Fleming spending

Re-use these bounds under alternate hypothesis

Test 2: Fixed Design

Test 3: `info` != `info0` != `info1`

Test 3: Developer Tests

1-sided test

Test 4: Independent Tests

Expect equal with mvtnorm for efficacy and futility bounds

Expect equal with `gsDesign::gsProbability` outcome for efficacy bounds

Test 5: Compare with `gsDesign` under information-based design

Step 1: set the design assumptions

References

Test of the function gs_power_npe

Test 1: Examples from spec

Default

Fixed bound

Same fixed efficacy bounds, no futility bound (i.e., non-binding bound), null hypothesis

Fixed bound with futility only at analysis 1; efficacy only at analyses 2, 3

Spending function bounds

Same bounds, but power under different theta

Two-sided symmetric spend, O’Brien-Fleming spending

Re-use these bounds under alternate hypothesis

Test 2: Fixed Design

Test 3: info != info0 != info1

Test 3: Developer Tests

1-sided test

Test 4: Independent Tests

Expect equal with mvtnorm for efficacy and futility bounds

Expect equal with gsDesign::gsProbability outcome for efficacy bounds

Test 5: Compare with gsDesign under information-based design

Step 1: set the design assumptions

References

Test 3: `info` != `info0` != `info1`

Expect equal with `gsDesign::gsProbability` outcome for efficacy bounds

Test 5: Compare with `gsDesign` under information-based design