Simulation Settings in CITIES (Figure 1 in publication)
The settings below simulates 50 datasets for a clinical trial with
two arms; control and treatment over (0,24,48,72,96,120,144) weeks. The
control arm has 120 subjects with a mean trajectory of (0,0,0,0,0,0,0)
while the treatment arm has a mean trajectory of
(0,0.1,0.2,0.4,0.6,0.8,1). The covariance structure for both arms are
described using a partial autocorrelation of (-0.2, 0.4), each with a
variance of 1. We supply no custom covariance and supply betas using the
default covariance matrix provided, i.e. one continuous and one binary
covariates. The lack of efficacy and excess efficacy functions are shown
below, alongside the behaviors of discontinuity due to adminstrative
reasons and adverse events.
Note the following
- First entry for all means must be the same, i.e. the baseline mean.
In this case, this is 0
- Length of all means and timepoints must be the same
- The length of each beta vector must the same as the number of
covariates
- prob_ae >= rate_dc_ae per arm
- z_l_loe <= z_u_loe
- z_l_ee <= z_u_ee
- pacf_vec values must be between -1 and 1, not inclusive
- reference_id must be either one of the arms. For example, if you
have 4 arms, then reference_id should be either 1,2,3 or 4.
total_data = 50
reference_id = 1
threshold = NA
timepoints = c(0,24,48,72,96,120,144)
IR_display = TRUE
delta_adjustment_in = c(0,1)
n_patient_ctrl = 120
n_patient_expt = 150
n_patient_vector = c(n_patient_ctrl, n_patient_expt)
n_total = sum(n_patient_vector)
mean_control = c(0,0,0,0,0,0,0)
mean_treatment = c(0,0.1,0.2,0.4,0.6,0.8,1)
mean_list = list(mean_control, mean_treatment)
sigma_ar_vec = c(1, 1)
pacf_list = list(c(-0.2, 0.4),
c(-0.2, 0.4))
beta_list = list(c(1.25, 1.25),
c(1.25, 1.25))
covariate_df = NA
# LoE & EE
up_good = "Up"
p_loe_max = 0.75
z_l_loe = -7
z_u_loe = -1
p_ee_max = 0.1
z_l_ee = 4
z_u_ee = 10
# Admin & AE
p_admin_ctrl = 0.02
p_admin_expt = 0.02
p_admin = c(p_admin_ctrl, p_admin_expt)
prob_ae_ctrl = 0.7
prob_ae_expt = 0.9
prob_ae = c(prob_ae_ctrl, prob_ae_expt)
rate_dc_ae_ctrl = 0.1
rate_dc_ae_expt = 0.1
rate_dc_ae = c(rate_dc_ae_ctrl, rate_dc_ae_expt)
starting_seed_val = 1
static_output = TRUE
Demonstration with custom covariance and custom covariates with 3
Arms
The settings below simulates 20 datasets for a clinical trial with
three arms over (0,24,48,72,96,120,144) weeks. Arm 1 has 120 subjects
with a mean trajectory of (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), while
arm 2 has a mean trajectory of (0, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.1, 1.2,
1.3, 1.4, 1.5), and finally arm 3 has a mean trajectory twice that of
arm 2. The covariance structure is a randomly generated positive
definite matrix, labelled Sigma. Further, a custom covariate dataframe
is generated with two continuous and one binary covariates. The lack of
efficacy and excess efficacy functions are shown below, alongside the
behaviors of discontinuity due to adminstrative reasons and adverse
events.
Note the following
- First entry for all means must be the same, i.e. the baseline mean.
In this case, this is 0
- Length of all means and timepoints must be the same
- The length of each beta vector must the same as the number of
covariates
- prob_ae >= rate_dc_ae per arm
- z_l_loe <= z_u_loe
- z_l_ee <= z_u_ee
- To submit a custom covariance, set sigma_ar_vec = NA and fill the
pacf_list with your list of custom covariance matrices per arm.
- reference_id must be either one of the arms. For example, if you
have 4 arms, then reference_id should be either 1,2,3 or 4.
p_admin_expt = 0.02
p_admin_ctrl = 0.03
prob_ae_expt = 0.9
rate_dc_ae_expt = 0.1
prob_ae_ctrl = 0.7
rate_dc_ae_ctrl = 0.1
n_patient_expt = 120
n_patient_expt2 = 100
n_patient_ctrl = 150
mean_treatment = c(0, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.1, 1.2, 1.3, 1.4, 1.5)
mean_treatment2 = 2*c(0, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.1, 1.2, 1.3, 1.4, 1.5)
mean_control = rep(0, length(mean_treatment))
beta_control = c(1.25, 1.25, 1)
beta_expt = c(1.25, 1.25, 1)
beta_expt2 = c(1.25, 1.25, 1)
p_loe_max = 0.6
z_l_loe = -5
z_u_loe = -1.2
p_ee_max = 0.15
z_l_ee = 2.5
z_u_ee = 4.5
timepoints = c(0:(length(mean_treatment)-1))*24
up_good = "Up"
delta_adjustment_in = NA
threshold = NA
mean_list = list(mean_control, mean_treatment, mean_treatment2)
p_admin = c(p_admin_ctrl, p_admin_expt, p_admin_expt)
rate_dc_ae = c(rate_dc_ae_ctrl, rate_dc_ae_expt, rate_dc_ae_expt)
prob_ae = c(prob_ae_ctrl, prob_ae_expt,prob_ae_expt)
n_patient_vector = c(n_patient_ctrl, n_patient_expt, n_patient_expt2)
sigma_ar_vec = NA
total_data = 20
reference_id = 1
starting_seed_val = 1
A = matrix(runif(length(timepoints)^2)*2-1, ncol=length(timepoints))
Sigma = t(A) %*% A
pacf_list = list(Sigma,
Sigma,
Sigma)
n_total = sum(n_patient_vector)
beta_list = list(beta_control, beta_expt, beta_expt2)
covariate_df = data.frame(continuous_1 = (rnorm(n = n_total, mean = 0, sd = 1)),
continuous_2 = (rnorm(n = n_total, mean = 0, sd = 1)),
binary_1 = rbinom(n = n_total, size = 1, prob = 0.5))
starting_seed_val = 1
static_output = TRUE
IR_display = TRUE
Treatment effect profiles for the four estimands in CITIES for the
custom covariate example
data_out = data_generator_loop(n_patient_vector,
p_loe_max,
z_l_loe,
z_u_loe,
p_ee_max,
z_l_ee,
z_u_ee,
timepoints,
pacf_list,
sigma_ar_vec,
mean_list,
beta_list,
p_admin,
rate_dc_ae,
prob_ae,
starting_seed_val,
reference_id,
plot_po = FALSE,
up_good,
threshold,
total_data,
delta_adjustment_in,
covariate_df)
estimates_out = plot_estimates(data_out = data_out,
total_data = total_data,
timepoints = timepoints,
IR_display = IR_display,
reference_id = reference_id,
static_output = static_output)
estimates_out %>%
mutate(mean_se = paste0(mean, " (", round(se, 2) , ")")) %>%
dplyr::select(-se, -mean) %>%
pivot_wider(names_from = Estimand, values_from = mean_se)
## # A tibble: 22 × 8
## Arm name Timepoints PP `S++` `S*+` Full IR
## <chr> <chr> <dbl> <chr> <chr> <chr> <chr> <chr>
## 1 Arm 2 1 24 0.34 (0.23) 0.08 (0.12) 0.18 (0.11) 0.08 (0.1) 0.45 …
## 2 Arm 2 2 48 0.43 (0.2) 0.18 (0.13) 0.24 (0.13) 0.18 (0.12) 0.52 …
## 3 Arm 2 3 72 0.6 (0.29) 0.4 (0.16) 0.48 (0.17) 0.41 (0.15) 0.67 …
## 4 Arm 2 4 96 0.71 (0.35) 0.51 (0.15) 0.62 (0.11) 0.58 (0.12) 0.77 …
## 5 Arm 2 5 120 0.81 (0.32) 0.68 (0.28) 0.86 (0.22) 0.77 (0.15) 0.85 …
## 6 Arm 2 6 144 0.9 (0.35) 0.87 (0.22) 0.96 (0.16) 0.99 (0.16) 0.79 …
## 7 Arm 2 7 168 0.91 (0.46) 0.91 (0.24) 1.1 (0.19) 1.09 (0.16) 0.77 …
## 8 Arm 2 8 192 1.16 (0.42) 1.21 (0.35) 1.21 (0.27) 1.22 (0.21) 0.92 …
## 9 Arm 2 9 216 1.03 (0.31) 1.21 (0.31) 1.21 (0.17) 1.3 (0.1) 0.8 (…
## 10 Arm 2 10 240 1.44 (0.35) 1.48 (0.28) 1.43 (0.22) 1.43 (0.16) 0.87 …
## # … with 12 more rows
Percentages of treatment discontinuations, and the corresponding
ICEs in CITIES for the custom covariate example
dc_out = plot_dc(data_out = data_out,
total_data = total_data,
timepoints = timepoints,
static_output = static_output)
dc_out %>%
ungroup() %>%
filter(Timepoints == max(timepoints)) %>%
select(Arm, Reason, Value) %>%
pivot_wider(names_from = Arm,
values_from = Value) %>%
arrange(factor(Reason, levels = c("AE", "LOE", "EE", "ADMIN", "OVERALL")))
## # A tibble: 5 × 4
## Reason Ctrl `Expt 1` `Expt 2`
## <chr> <dbl> <dbl> <dbl>
## 1 AE 0.1 0.1 0.1
## 2 LOE 0.39 0.26 0.18
## 3 EE 0.19 0.28 0.4
## 4 ADMIN 0.29 0.2 0.2
## 5 OVERALL 0.71 0.65 0.68
