Making Go/No-go decision in proof-of-concept trials
By Fenguoerbian
December 8, 2023
The gonogo package
The goal of gonogo is to provide Go/Nogo designs for binary (e.g. ORR)
or TTE (e.g. PFS) outcomes.
Supported designs and endpoints
| Design | Endpoint | Support |
|---|---|---|
| SAT | Binary | Yes |
| SAT | TTE | Yes |
| SAT | Continuous | TBA |
| RCT | Binary | TBA |
| RCT | TTE | TBA |
| RCT | Continuous | TBA |
Example - Go/Nogo design based on ORR
This is a basic example which shows you how to design go/nogo rule based
on ORR. For more details about this example, please see
vignette("ORR_Gonogo", package = "gonogo").
library(gonogo)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
nmax <- 40
n1 <- 20
eff_cut <- 0.55
fut_cut <- 0.45
fa_eff_pt <- 0.6
fa_fut_pt <- 0.5
a <- 1
b <- 1
- The total sample size at final analysis is 40.
- The sample size at interim analysis is 20.
- The efficacy boundary of ORR is 0.55.
- The futility boundary of ORR is 0.45.
- The (posterior) probability target/threshold of efficacy is 0.6. We declare efficacy if Pr(ORR > 0.55 | Data) > 0.6.
- The (posterior) probability target/threshold of futility is 0.5. We declare futility if Pr(ORR < 0.45 | Data) > 0.5.
- Prior distribution of ORR is Beta(1, 1).
About our hypothetical product, we have the following information:
tpp_tb <- tibble::tribble(
~theta, ~tpp,
0.45, "SOC",
0.55, "TPP base",
0.60, "TPP best"
)
theta_pick <- c(0.45, 0.5, 0.55, 0.6) # theta(underlying ORR) we might be interested
Rules at interim analysis
ia_eff_pt <- 0.5
ia_fut_pt <- 0.01
ia_rules <- Find_Cut(
nmax = nmax, n1 = n1, m = m,
pt = fa_eff_pt, theta0 = eff_cut,
eff_cut = eff_cut, fut_cut = fut_cut,
eff_pt = ia_eff_pt, fut_pt = ia_fut_pt,
a = a, b = b
)
If we set the rules to Go if predictive probability greater than 0.5 and to Nogo if predictive probability less than 0.01. Then we can determine the cut value for Go/Nogo as:
- Declare Go if #resp is equal to or greater than 12.
- Declare Nogo if #resp is equal to or less than 7.
Given this rule, we can compute the operating characteristics (OC) table for various observed ORR
oc_tab_s1 <- t(sapply(theta_pick, function(orr, n, go_cut, nogo_cut){
res <- ORR_Go_Nogo(n = n, orr = orr, go_cut = go_cut, nogo_cut = nogo_cut)
res <- format(res, visable = FALSE)
},
n = n1,
go_cut = as.integer(ia_rules["go_cut"]),
nogo_cut = as.integer(ia_rules["nogo_cut"])))
knitr::kable(oc_tab_s1)
| Underlying_ORR | Pr_Go | Pr_Nogo | Pr_Equivocal |
|---|---|---|---|
| 45.00% | 13.1% | 25.2% | 61.7% |
| 50.00% | 25.2% | 13.2% | 61.7% |
| 55.00% | 41.4% | 5.8% | 52.8% |
| 60.00% | 59.6% | 2.1% | 38.3% |
We can also show OC figures of different rules
rules <- data.frame(
gocut = c(ia_rules["go_cut"], ia_rules["go_cut"] - 1, ia_rules["go_cut"] + 1),
nogocut = c(ia_rules["nogo_cut"], ia_rules["nogo_cut"] + 1, ia_rules["nogo_cut"] - 1),
n = n1
)
oc_fig_s1 <- OC_Curve_Diff_Rules(rules, theta_pick,
tpp_tb = tpp_tb,
plot_params = list(
contour_vec = seq(from = 0.25, to = 1, by = 0.25)))
oc_fig_s1
Rules at final analysis
fa_rules <- Find_Cut(
nmax = nmax, n1 = nmax, m = m,
pt = fa_eff_pt, theta0 = eff_cut,
eff_cut = eff_cut, fut_cut = fut_cut,
eff_pt = fa_eff_pt, fut_pt = fa_fut_pt,
a = a, b = b
)
If we set the rules to Go if posterior Pr(ORR > 0.55) is greater than 0.6 and to Nogo if posterior Pr(ORR <= 0.45) is less than 0.5. Then we can determine the cut value for Go/Nogo as:
- Declare Go if #resp is equal to or greater than 23.
- Declare Nogo if #resp is equal to or less than 17.
Given this rule, we can compute the operating characteristics (OC) table for various observed ORR
oc_tab_s2 <- t(sapply(theta_pick, function(orr, n, go_cut, nogo_cut){
res <- ORR_Go_Nogo(n = n, orr = orr, go_cut = go_cut, nogo_cut = nogo_cut)
res <- format(res, visable = FALSE)
},
n = nmax,
go_cut = as.integer(fa_rules["go_cut"]),
nogo_cut = as.integer(fa_rules["nogo_cut"])))
knitr::kable(oc_tab_s2)
| Underlying_ORR | Pr_Go | Pr_Nogo | Pr_Equivocal |
|---|---|---|---|
| 45.00% | 7.7% | 43.9% | 48.4% |
| 50.00% | 21.5% | 21.5% | 57.0% |
| 55.00% | 43.9% | 7.7% | 48.4% |
| 60.00% | 68.9% | 1.9% | 29.3% |
We can also show OC figures of different rules
rules <- data.frame(
gocut = c(fa_rules["go_cut"], fa_rules["go_cut"] - 1, fa_rules["go_cut"] + 1),
nogocut = c(fa_rules["nogo_cut"], fa_rules["nogo_cut"] + 1, fa_rules["nogo_cut"] - 1),
n = nmax
)
oc_fig_s2 <- OC_Curve_Diff_Rules(rules, theta_pick,
tpp_tb = tpp_tb,
plot_params = list(
contour_vec = seq(from = 0.25, to = 1, by = 0.25)))
oc_fig_s2
This shows the marginal OC, i.e. it does not consider any previous stages’ rules’ impact on current stage. We can also compute the conditional/cumulative OC of current stage as
current_rules <- data.frame(
gocut = c(fa_rules["go_cut"], fa_rules["go_cut"] - 1, fa_rules["go_cut"] + 1),
nogocut = c(fa_rules["nogo_cut"], fa_rules["nogo_cut"] + 1, fa_rules["nogo_cut"] - 1),
n = nmax - n1 # sample size of current stage
)
previous_rules <- data.frame(
cum_num = n1,
stage_num = n1,
go_cut = as.integer(ia_rules["go_cut"]),
nogo_cut = as.integer(ia_rules["nogo_cut"])
)
if(nrow(previous_rules) > 0){
print("The previous rules are: ")
knitr::kable(previous_rules)
}
#> [1] "The previous rules are: "
| cum_num | stage_num | go_cut | nogo_cut |
|---|---|---|---|
| 20 | 20 | 12 | 7 |
oc_fig_s2 <- OC_Curve_Diff_Rules2(current_rules, theta_pick,
tpp_tb = tpp_tb,
previous_full_rules = previous_rules,
plot_params = list(
contour_vec = seq(from = 0.25, to = 1, by = 0.25)))
cowplot::plot_grid(plotlist = oc_fig_s2$gplot_list,
nrow = 1)
#> Warning: Removed 6 rows containing missing values or values outside the scale range
#> (`geom_line()`).
The proposed go/nogo rules at this stage are:
- Declare Go if #resp is equal to or greater than 23.
- Declare Nogo if #resp is equal to or less than 17.
And different types of OC at our interested theta are
detail_data <- oc_fig_s2$detail_data %>%
filter(pick,
stage_idx == 2,
gocut == fa_rules["go_cut"],
nogocut == fa_rules["nogo_cut"])
prob_type_vec <- detail_data %>%
distinct(prob_type) %>%
pull(prob_type)
for(prob_type in prob_type_vec){
detail_data %>%
filter(prob_type == .env$prob_type) %>%
arrange(theta) %>%
select(theta, prob_type, prob_go, prob_nogo, prob_equivocal) %>%
mutate(across(c(prob_go, prob_nogo, prob_equivocal),
.fns = \(x) paste0(round(x * 100, digits = 1), "%"))) %>%
knitr::kable(
caption = paste0(
toupper(substr(prob_type, start = 1, stop = 1)),
substr(prob_type, start = 2, stop = nchar(prob_type)),
" OC probabilities")
) %>%
print()
cat('\n\n<!-- -->\n\n')
}
| theta | prob_type | prob_go | prob_nogo | prob_equivocal |
|---|---|---|---|---|
| 0.45 | marginal | 7.7% | 43.9% | 48.4% |
| 0.50 | marginal | 21.5% | 21.5% | 57% |
| 0.55 | marginal | 43.9% | 7.7% | 48.4% |
| 0.60 | marginal | 68.9% | 1.9% | 29.3% |
Marginal OC probabilities
| theta | prob_type | prob_go | prob_nogo | prob_equivocal |
|---|---|---|---|---|
| 0.45 | conditional | 4.8% | 36.4% | 58.8% |
| 0.50 | conditional | 12.2% | 19.8% | 68% |
| 0.55 | conditional | 25.2% | 8.8% | 66% |
| 0.60 | conditional | 43.3% | 3.1% | 53.5% |
Conditional OC probabilities
| theta | prob_type | prob_go | prob_nogo | prob_equivocal |
|---|---|---|---|---|
| 0.45 | cumulative | 16% | 47.7% | 36.3% |
| 0.50 | cumulative | 32.7% | 25.4% | 41.9% |
| 0.55 | cumulative | 54.7% | 10.5% | 34.8% |
| 0.60 | cumulative | 76.2% | 3.3% | 20.5% |
Cumulative OC probabilities
Example - Go/Nogo design based on PFS
Note: The functions for TTE Go/Nogo deisgn is still under development and optimization. Hence are subject to change.
Please refer to PFS Go/Nogo vignette for a more detailed example.
Some packages that are needed for this example
# library(gonogo)
library(dplyr)
library(tidyr)
library(ggplot2)
library(ggrepel)
# require(cowplot)
# require(survival)
library(future.apply)
#> Loading required package: future
library(progressr)
# number of parallel cores,
# please adjust according to your machine's capability
# current setting is to leave (at most) 2 cores not used, since the function
# is guaranteed to return at least 1 core for later parallel computation.
worker_num <- parallelly::availableCores(omit = 2)
plan(cluster, workers = worker_num)
# progress info report settings
handlers("cli")
progress_interval <- 50
# fix the seed for random number generation
# Note that later the RNG kind will be set to a parallel safe one
random_seed <- 1024
Basic setups
First we setup the basic settings for this PFS Go/Nogo design case. We begin with settings of this trial:
# 1st is the setting of this trial
basic_settings <- list(
max_subj_num = 40,
# accrual_rate = 40 / 5,
accrual_time = 5,
n1 = 20, # number of subjects in stage1
wait_after_n1 = 0, # time to wait after `n1` subjects being enrolled
# cut_date = 9 + 2 + 5, # cutoff date = actrual accrual_time + wait time + followup time
cut_evt_num = NULL, # event number target to determine cutoff date. If `cut_date` is NULL, `cut_evt_num` will be used.
rate_diff_at = 6,
followup_time = 6
)
(basic_settings <- gonogo:::Get_Settings(basic_settings, type = 1))
#> $max_subj_num
#> [1] 40
#>
#> $accrual_time
#> [1] 5
#>
#> $n1
#> [1] 20
#>
#> $wait_after_n1
#> [1] 0
#>
#> $cut_evt_num
#> NULL
#>
#> $rate_diff_at
#> [1] 6
#>
#> $followup_time
#> [1] 6
#>
#> $accrual_rate
#> [1] 8
#>
#> $cut_date
#> [1] 11
Next we setup the underlying PFS distribution, droput rate and prior information
pfs_settings <- list(
m_ref = 7, # median reference PFS time
m_trt = 9.5, # pfs_m_ctrl,
trt_dropout = 0.1, # annual pfs dropout rate
piecewise_trt = FALSE
)
pfs_prior_shape <- 0.001
pfs_prior_rate <- 0.001
(pfs_settings <- gonogo:::Get_Settings(pfs_settings, type = 2,
prior_shape = pfs_prior_shape,
prior_rate = pfs_prior_rate))
#> $m_ref
#> [1] 7
#>
#> $m_trt
#> [1] 9.5
#>
#> $trt_dropout
#> [1] 0.1
#>
#> $piecewise_trt
#> [1] FALSE
#>
#> $hazard
#> [1] 0.07296286
#>
#> $ref_hazard
#> [1] 0.09902103
#>
#> $dropout_lambda
#> [1] 0.008780043
#>
#> $prior_shape
#> [1] 0.001
#>
#> $prior_rate
#> [1] 0.001
Thirdly is the setting of Go/Nogo design rules
# General idea:
# Declare Go if Pr(lambda <= lam_eff_cut) >= go_prob_target
# Declare Nogo if Pr(lambda > lam_fut_cut) >= nogo_prob_target
# Additionaly, for this case, we set `use_evt_cut = TRUE`
# Directly declare go when number of events at analysis <= go_evt_target
# Directly declare nogo when number of events at analysis >= nogo_evt_target
#
# Besides the Bayesian perspective, we also set a frequenter's perspective. The
# rule is based on 6M landmark pfs rate and the detailed rule is based on
# confidence interval of 6M PFS rate.
go_nogo_settings <- list(
lam_eff_cut = pfs_settings$hazard,
lam_fut_cut = pfs_settings$ref_hazard,
go_prob_target = 0.67,
nogo_prob_target = 0.1,
use_evt_cut = TRUE,
go_evt_target = 13,
nogo_evt_target = 27,
pfs_rate_diff_at = 6,
pfs_rate_eff_cut = 2 ^ (-6 / pfs_settings$m_trt),
pfs_rate_fut_cut = 2 ^ (-6 / pfs_settings$m_ref),
pfs_rate_go_prob_target = 0.67,
pfs_rate_nogo_prob_target = 0.1,
pfs_rate_use_evt_cut = TRUE,
pfs_rate_go_evt_target = 13,
pfs_rate_nogo_evt_target = 27
)
Find the rules
In this section, we compute the detailed Go/Nogo rule (without considering the “direct event number cut” mentioned in the previous section) and visualize it. Given the observed number of events, declare go if total obs time is long enough, declare nogo if total obs time is short enough. This is based on posterior distribution of lambda, the hazard parameter in exponential distribution.
pfs_rules <- PFS_Find_Cut(basic_settings, pfs_settings, go_nogo_settings,
start_evt_num = 1)
We can print the rules as follow:
knitr::kable(pfs_rules$rules_tb)
| evt_num | sum_obs_time_Declare Go | sum_obs_time_Declare Nogo | pprob_Declare Go | pprob_Declare Nogo |
|---|---|---|---|---|
| 40 | 583 | 487 | 0.6719576 | 0.1016475 |
| 39 | 569 | 476 | 0.6727396 | 0.1013377 |
| 38 | 555 | 465 | 0.6735663 | 0.1009883 |
| 37 | 540 | 454 | 0.6702923 | 0.1005965 |
| 36 | 526 | 443 | 0.6711685 | 0.1001596 |
| 35 | 512 | 431 | 0.6720976 | 0.1022650 |
| 34 | 498 | 420 | 0.6730835 | 0.1017509 |
| 33 | 484 | 409 | 0.6741306 | 0.1011819 |
| 32 | 469 | 398 | 0.6707997 | 0.1005539 |
| 31 | 455 | 386 | 0.6719236 | 0.1026000 |
| 30 | 441 | 375 | 0.6731220 | 0.1018642 |
| 29 | 427 | 364 | 0.6744012 | 0.1010553 |
| 28 | 412 | 353 | 0.6710334 | 0.1001677 |
| 27 | 398 | 341 | 0.6724242 | 0.1020881 |
| 26 | 384 | 330 | 0.6739164 | 0.1010471 |
| 25 | 369 | 318 | 0.6705182 | 0.1029149 |
| 24 | 355 | 307 | 0.6721598 | 0.1016894 |
| 23 | 341 | 296 | 0.6739326 | 0.1003455 |
| 22 | 326 | 284 | 0.6705354 | 0.1020262 |
| 21 | 312 | 273 | 0.6725148 | 0.1004346 |
| 20 | 298 | 261 | 0.6746700 | 0.1019678 |
| 19 | 283 | 250 | 0.6713315 | 0.1000703 |
| 18 | 269 | 238 | 0.6737847 | 0.1013941 |
| 17 | 254 | 226 | 0.6704768 | 0.1026417 |
| 16 | 240 | 215 | 0.6733147 | 0.1001421 |
| 15 | 225 | 203 | 0.6700908 | 0.1010408 |
| 14 | 211 | 191 | 0.6734414 | 0.1017772 |
| 13 | 196 | 179 | 0.6703922 | 0.1023101 |
| 12 | 182 | 167 | 0.6744539 | 0.1025873 |
| 11 | 167 | 155 | 0.6717405 | 0.1025420 |
| 10 | 153 | 143 | 0.6768419 | 0.1020872 |
| 9 | 138 | 131 | 0.6747704 | 0.1011083 |
| 8 | 123 | 118 | 0.6729814 | 0.1042777 |
| 7 | 108 | 106 | 0.6716217 | 0.1018848 |
| 6 | 93 | 93 | 0.6709305 | 0.1036424 |
| 5 | 78 | 80 | 0.6713222 | 0.1042758 |
| 4 | 63 | 67 | 0.6735784 | 0.1030077 |
| 3 | 48 | 53 | 0.6793653 | 0.1053436 |
| 2 | 32 | 39 | 0.6768458 | 0.1023550 |
| 1 | 16 | 23 | 0.6884549 | 0.1027089 |
We can also visualize the rules at different number of events
cowplot::plot_grid(plotlist = pfs_rules$gplot_list,
ncol = 4)
OC Curves
Note: Remember to adjust the oc_params_sim$sim_num in your real
usage. For this readme, it is set to a quite small value to ease the
computation burden.
mpfs_pick <- c(7.0, 9.5, 11.0) # m-PFS highlighted in the figures
tpp_tb <- tribble( # additional info of some picked mPFS
~mpfs, ~tpp,
7.0, "SOC",
9.5, "TPP base",
11.0, "TPP best"
)
oc_params <- list(
mpfs_vec = seq(from = 1, to = 30, length.out = 250),
sim_num = 0
)
oc_params_sim <- oc_params
oc_params_sim$sim_num <- 500
oc_params_sim$mpfs_vec <- seq(from = 5, to = 15, length.out = 25)
plot_params <- list(
contour_vec = seq(from = 0.25, to = 1, by = 0.25),
use_smooth = FALSE)
Then we setup some rules, by “rules” we mean the data cutoff rule. Either X months after LPI, or the time when Y number of events are observed. Since we are investigating OC of this Go/Nogo design, the “rules” also include how the Go/Nogo rules are designed under various scenarios.
followup_time_vec <- c(6, 9, 12, NA)
cut_evt_num_vec <- c(20, 24, 28, NA)
rules_df1 <- expand.grid(
followup_time = followup_time_vec,
cut_evt_num = cut_evt_num_vec
) %>%
filter((is.na(followup_time) & !is.na(cut_evt_num)) | (is.na(cut_evt_num) & !is.na(followup_time))) %>%
mutate(kickoff = if_else(is.na(followup_time),
paste0("event num at ", cut_evt_num),
paste0(followup_time, "m after LPI")),
idx = row_number(),
idx = c(1 : (length(followup_time_vec) - 1), 1 : (length(cut_evt_num_vec) - 1))
) %>%
mutate(go_evt_target = c(rep(0, 3), 13, 17, 20),
nogo_evt_target = c(rep(40, 3), 27, 31, 34))
rules_df2 <- tribble(
~idx, ~lam_eff_cut, ~lam_fut_cut, ~go_prob_target, ~nogo_prob_target,
1, log(2) / 10.0, log(2) / 7.0, 0.5, 0.5,
2, log(2) / 9.5, log(2) / 7.0, 0.67, 0.1,
3, log(2) / 9.5, log(2) / 7.0, 0.5, 0.15,
4, log(2) / 7.0, log(2) / 7.0, 0.9, 0.1, # BOP2: `lam_eff_cut` and `lam_fut_cut` are the same, `go_prob_target` + `nogo_prob_target` = 1
# 5, log(2) / 10.3, log(2) / 8.2, 0.5, 0.2
) %>%
mutate(
mpfs_eff_cut = log(2) / lam_eff_cut,
mpfs_fut_cut = log(2) / lam_fut_cut,
rules = paste0("Go if Pr(mPFS > ",
sprintf("%.1f", mpfs_eff_cut),
") > ",
sprintf("%.2f", go_prob_target),
".\nNogo if Pr(mPFS > ",
sprintf("%.1f", mpfs_fut_cut),
") < ",
sprintf("%.2f", 1 - nogo_prob_target), "\n"),
rules = if_else(idx == 4,
paste0("BOP2: Go if Pr(mPFS > ",
sprintf("%.1f", mpfs_eff_cut),
") > ",
sprintf("%.2f", go_prob_target),
".\n Nogo if Pr(mPFS > ",
sprintf("%.1f", mpfs_fut_cut),
") < ",
sprintf("%.2f", 1 - nogo_prob_target), "\n"),
rules)) %>%
mutate(go_evt_target = 0,
nogo_evt_target = 40)
rules_df <- bind_rows(rules_df1, rules_df2)
| followup_time | cut_evt_num | kickoff | idx | go_evt_target | nogo_evt_target | lam_eff_cut | lam_fut_cut | go_prob_target | nogo_prob_target | mpfs_eff_cut | mpfs_fut_cut | rules |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| NA | 20 | event num at 20 | 1 | 0 | 40 | NA | NA | NA | NA | NA | NA | NA |
| NA | 24 | event num at 24 | 2 | 0 | 40 | NA | NA | NA | NA | NA | NA | NA |
| NA | 28 | event num at 28 | 3 | 0 | 40 | NA | NA | NA | NA | NA | NA | NA |
| 6 | NA | 6m after LPI | 1 | 13 | 27 | NA | NA | NA | NA | NA | NA | NA |
| 9 | NA | 9m after LPI | 2 | 17 | 31 | NA | NA | NA | NA | NA | NA | NA |
| 12 | NA | 12m after LPI | 3 | 20 | 34 | NA | NA | NA | NA | NA | NA | NA |
| NA | NA | NA | 1 | 0 | 40 | 0.069 | 0.099 | 0.50 | 0.50 | 10.0 | 7 | Go if Pr(mPFS > 10.0) > 0.50. Nogo if Pr(mPFS > 7.0) < 0.50 |
| NA | NA | NA | 2 | 0 | 40 | 0.073 | 0.099 | 0.67 | 0.10 | 9.5 | 7 | Go if Pr(mPFS > 9.5) > 0.67. Nogo if Pr(mPFS > 7.0) < 0.90 |
| NA | NA | NA | 3 | 0 | 40 | 0.073 | 0.099 | 0.50 | 0.15 | 9.5 | 7 | Go if Pr(mPFS > 9.5) > 0.50. Nogo if Pr(mPFS > 7.0) < 0.85 |
| NA | NA | NA | 4 | 0 | 40 | 0.099 | 0.099 | 0.90 | 0.10 | 7.0 | 7 | BOP2: Go if Pr(mPFS > 7.0) > 0.90. Nogo if Pr(mPFS > 7.0) < 0.90 |
We can draw the theoretical OC curve
oc_fig_theory <- gonogo:::PFS_OC_Curve_Diff_Rules(rules_df[-(1 : nrow(rules_df1)), ],
mpfs_pick = mpfs_pick,
basic_settings = basic_settings,
pfs_settings = pfs_settings,
go_nogo_settings = go_nogo_settings,
tpp_tb = tpp_tb,
oc_params = oc_params,
plot_params = plot_params)
#> followup_time
#> NA
#> cut_evt_num
#> NA
#> kickoff
#> NA
#> idx
#> "1"
#> go_evt_target
#> "0"
#> nogo_evt_target
#> "40"
#> lam_eff_cut
#> "0.06931472"
#> lam_fut_cut
#> "0.09902103"
#> go_prob_target
#> "0.50"
#> nogo_prob_target
#> "0.50"
#> mpfs_eff_cut
#> "10.0"
#> mpfs_fut_cut
#> "7"
#> rules
#> "Go if Pr(mPFS > 10.0) > 0.50.\nNogo if Pr(mPFS > 7.0) < 0.50\n"
#> followup_time
#> NA
#> cut_evt_num
#> NA
#> kickoff
#> NA
#> idx
#> "2"
#> go_evt_target
#> "0"
#> nogo_evt_target
#> "40"
#> lam_eff_cut
#> "0.07296286"
#> lam_fut_cut
#> "0.09902103"
#> go_prob_target
#> "0.67"
#> nogo_prob_target
#> "0.10"
#> mpfs_eff_cut
#> " 9.5"
#> mpfs_fut_cut
#> "7"
#> rules
#> "Go if Pr(mPFS > 9.5) > 0.67.\nNogo if Pr(mPFS > 7.0) < 0.90\n"
#> followup_time
#> NA
#> cut_evt_num
#> NA
#> kickoff
#> NA
#> idx
#> "3"
#> go_evt_target
#> "0"
#> nogo_evt_target
#> "40"
#> lam_eff_cut
#> "0.07296286"
#> lam_fut_cut
#> "0.09902103"
#> go_prob_target
#> "0.50"
#> nogo_prob_target
#> "0.15"
#> mpfs_eff_cut
#> " 9.5"
#> mpfs_fut_cut
#> "7"
#> rules
#> "Go if Pr(mPFS > 9.5) > 0.50.\nNogo if Pr(mPFS > 7.0) < 0.85\n"
#> followup_time
#> NA
#> cut_evt_num
#> NA
#> kickoff
#> NA
#> idx
#> "4"
#> go_evt_target
#> "0"
#> nogo_evt_target
#> "40"
#> lam_eff_cut
#> "0.09902103"
#> lam_fut_cut
#> "0.09902103"
#> go_prob_target
#> "0.90"
#> nogo_prob_target
#> "0.10"
#> mpfs_eff_cut
#> " 7.0"
#> mpfs_fut_cut
#> "7"
#> rules
#> "BOP2: Go if Pr(mPFS > 7.0) > 0.90.\n Nogo if Pr(mPFS > 7.0) < 0.90\n"
oc_fig_theory$gplot
We can draw the OC curve under different data cutoff rules.
First is data cut at different number of observed events:
set.seed(random_seed, kind = "L'Ecuyer-CMRG")
oc_fig <- gonogo:::PFS_OC_Curve_Diff_Rules(rules_df[1 : (length(cut_evt_num_vec) - 1), ],
mpfs_pick = mpfs_pick,
basic_settings = basic_settings,
pfs_settings = pfs_settings,
go_nogo_settings = go_nogo_settings,
tpp_tb = tpp_tb,
oc_params = oc_params_sim,
plot_params = plot_params)
#> followup_time cut_evt_num kickoff idx
#> NA "20" "event num at 20" "1"
#> go_evt_target nogo_evt_target lam_eff_cut lam_fut_cut
#> "0" "40" NA NA
#> go_prob_target nogo_prob_target mpfs_eff_cut mpfs_fut_cut
#> NA NA NA NA
#> rules
#> NA
#> followup_time cut_evt_num kickoff idx
#> NA "24" "event num at 24" "2"
#> go_evt_target nogo_evt_target lam_eff_cut lam_fut_cut
#> "0" "40" NA NA
#> go_prob_target nogo_prob_target mpfs_eff_cut mpfs_fut_cut
#> NA NA NA NA
#> rules
#> NA
#> followup_time cut_evt_num kickoff idx
#> NA "28" "event num at 28" "3"
#> go_evt_target nogo_evt_target lam_eff_cut lam_fut_cut
#> "0" "40" NA NA
#> go_prob_target nogo_prob_target mpfs_eff_cut mpfs_fut_cut
#> NA NA NA NA
#> rules
#> NA
plot_params2 <- oc_fig$plot_params
plot_params2$use_smooth <- TRUE
oc_fig_smooth <- gonogo:::PFS_OC_Curve_Draw(oc_fig$detail_data,
tpp_tb = tpp_tb,
plot_params = plot_params2)
oc_fig$gplot
oc_fig_smooth
#> `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
Second is data cut at different time after LPI:
set.seed(random_seed, kind = "L'Ecuyer-CMRG")
oc_fig <- gonogo:::PFS_OC_Curve_Diff_Rules(rules_df[(1 : (length(followup_time_vec) - 1)) + (length(cut_evt_num_vec) - 1), ],
mpfs_pick = mpfs_pick,
basic_settings = basic_settings,
pfs_settings = pfs_settings,
go_nogo_settings = go_nogo_settings,
tpp_tb = tpp_tb,
oc_params = oc_params_sim,
plot_params = plot_params)
#> followup_time cut_evt_num kickoff idx
#> " 6" NA "6m after LPI" "1"
#> go_evt_target nogo_evt_target lam_eff_cut lam_fut_cut
#> "13" "27" NA NA
#> go_prob_target nogo_prob_target mpfs_eff_cut mpfs_fut_cut
#> NA NA NA NA
#> rules
#> NA
#> followup_time cut_evt_num kickoff idx
#> " 9" NA "9m after LPI" "2"
#> go_evt_target nogo_evt_target lam_eff_cut lam_fut_cut
#> "17" "31" NA NA
#> go_prob_target nogo_prob_target mpfs_eff_cut mpfs_fut_cut
#> NA NA NA NA
#> rules
#> NA
#> followup_time cut_evt_num kickoff idx
#> "12" NA "12m after LPI" "3"
#> go_evt_target nogo_evt_target lam_eff_cut lam_fut_cut
#> "20" "34" NA NA
#> go_prob_target nogo_prob_target mpfs_eff_cut mpfs_fut_cut
#> NA NA NA NA
#> rules
#> NA
plot_params2 <- oc_fig$plot_params
plot_params2$use_smooth <- TRUE
oc_fig_smooth <- gonogo:::PFS_OC_Curve_Draw(oc_fig$detail_data,
tpp_tb = tpp_tb,
plot_params = plot_params2)
oc_fig$gplot
oc_fig_smooth
#> `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
Future work
-
(WIP) Add function for Go/Nogo design based on TTE end point.
-
(Suspend) Use
vctrsto construct output class. -
(WIP) Add rmarkdown report template and shiny app for different endpoints.
- Posted on:
- December 8, 2023
- Length:
- 16 minute read, 3259 words