Nothing
inst/doc/single-continuous.R
In BayesianQDM: Bayesian Quantitative Decision-Making Framework for Binary and Continuous Endpoints
## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.width = 7,
fig.height = 4.5,
fig.path = "figures/single-cont-"
)
library(BayesianQDM)
## ----method-compare-----------------------------------------------------------
# Observed data (nMC excluded from base list; passed individually per method)
args_base <- list(
prob = 'posterior', design = 'controlled', prior = 'vague',
theta0 = 1.0,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL
)
p_ni <- do.call(pbayespostpred1cont,
c(args_base, list(CalcMethod = 'NI', nMC = NULL)))
p_mm <- do.call(pbayespostpred1cont,
c(args_base, list(CalcMethod = 'MM', nMC = NULL)))
set.seed(42)
p_mc <- do.call(pbayespostpred1cont,
c(args_base, list(CalcMethod = 'MC', nMC = 10000L)))
cat(sprintf("NI : %.6f (exact)\n", p_ni))
cat(sprintf("MM : %.6f (approx)\n", p_mm))
cat(sprintf("MC : %.6f (n_MC=10000)\n", p_mc))
## ----ctrl-post----------------------------------------------------------------
# P(mu_t - mu_c > theta_TV | data) and P(mu_t - mu_c <= theta_MAV | data)
p_tv <- pbayespostpred1cont(
prob = 'posterior', design = 'controlled', prior = 'vague',
CalcMethod = 'NI', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
p_mav <- pbayespostpred1cont(
prob = 'posterior', design = 'controlled', prior = 'vague',
CalcMethod = 'NI', theta0 = 0.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data) = %.4f -> Go criterion: >= 0.80? %s\n",
p_tv, ifelse(p_tv >= 0.80, "YES", "NO")))
cat(sprintf("P(theta <= theta_MAV | data) = %.4f -> NoGo criterion: >= 0.20? %s\n",
1 - p_mav, ifelse((1 - p_mav) >= 0.20, "YES", "NO")))
cat(sprintf("Decision: %s\n",
ifelse(p_tv >= 0.80 & (1 - p_mav) < 0.20, "Go",
ifelse(p_tv < 0.80 & (1 - p_mav) >= 0.20, "NoGo",
ifelse(p_tv >= 0.80 & (1 - p_mav) >= 0.20, "Miss", "Gray")))))
## ----ctrl-post-niChisq--------------------------------------------------------
p_tv_inf <- pbayespostpred1cont(
prob = 'posterior', design = 'controlled', prior = 'N-Inv-Chisq',
CalcMethod = 'NI', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = 5, kappa0_c = 5,
nu0_t = 5, nu0_c = 5,
mu0_t = 3.0, mu0_c = 1.0,
sigma0_t = 2.0, sigma0_c = 1.8,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data, N-Inv-Chisq prior) = %.4f\n", p_tv_inf))
## ----ctrl-pred----------------------------------------------------------------
p_pred <- pbayespostpred1cont(
prob = 'predictive', design = 'controlled', prior = 'vague',
CalcMethod = 'NI', theta0 = 1.0, nMC = NULL,
n_t = 15, n_c = 15, m_t = 60, m_c = 60,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("Predictive probability (m_t = m_c = 60) = %.4f\n", p_pred))
## ----unctrl-post--------------------------------------------------------------
p_unctrl <- pbayespostpred1cont(
prob = 'posterior', design = 'uncontrolled', prior = 'vague',
CalcMethod = 'MM', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = NULL,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = NULL, s_c = NULL,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = 1.0, # hypothetical control mean
sigma0_t = NULL, sigma0_c = NULL,
r = 1.0, # equal variance assumption
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data, uncontrolled) = %.4f\n", p_unctrl))
## ----ext-post-----------------------------------------------------------------
p_ext <- pbayespostpred1cont(
prob = 'posterior', design = 'external', prior = 'vague',
CalcMethod = 'MM', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = 20L, alpha0e_t = NULL, alpha0e_c = 0.5,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = 0.9, se_c = 1.8,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data, external control design, alpha=0.5) = %.4f\n",
p_ext))
## ----ext-borrowing------------------------------------------------------------
# alpha0e_c must be in (0, 1]; start from 0.01 to avoid validation error
alpha_seq <- c(0.01, seq(0.1, 1.0, by = 0.1))
p_alpha <- sapply(alpha_seq, function(a) {
pbayespostpred1cont(
prob = 'posterior', design = 'external', prior = 'vague',
CalcMethod = 'MM', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = 20L, alpha0e_t = NULL, alpha0e_c = a,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = 0.9, se_c = 1.8,
lower.tail = FALSE
)
})
data.frame(alpha_ec = alpha_seq, P_gt_TV = round(p_alpha, 4))
## ----oc-controlled, fig.width = 8, fig.height = 6-----------------------------
oc_ctrl <- pbayesdecisionprob1cont(
nsim = 500L,
prob = 'posterior',
design = 'controlled',
prior = 'vague',
CalcMethod = 'MM',
theta_TV = 1.5, theta_MAV = 0.5, theta_NULL = NULL,
nMC = NULL,
gamma_go = 0.80, gamma_nogo = 0.20,
n_t = 15, n_c = 15,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
mu_t = seq(1.0, 4.0, by = 0.5),
mu_c = 1.0,
sigma_t = 2.0,
sigma_c = 2.0,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
error_if_Miss = TRUE, Gray_inc_Miss = FALSE,
seed = 42L
)
print(oc_ctrl)
plot(oc_ctrl, base_size = 20)
## ----getgamma-ctrl, fig.width = 8, fig.height = 6-----------------------------
res_gamma <- getgamma1cont(
nsim = 1000L,
prob = 'posterior',
design = 'controlled',
prior = 'vague',
CalcMethod = 'MM',
theta_TV = 1.5, theta_MAV = 0.5, theta_NULL = NULL,
nMC = NULL,
mu_t_go = 1.0, mu_c_go = 1.0, # null scenario: no treatment effect
sigma_t_go = 2.0, sigma_c_go = 2.0,
mu_t_nogo = 2.5, mu_c_nogo = 1.0,
sigma_t_nogo = 2.0, sigma_c_nogo = 2.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = 15L, m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
gamma_grid = seq(0.01, 0.99, by = 0.01),
seed = 42L
)
plot(res_gamma, base_size = 20)
Try the BayesianQDM package in your browser
Any scripts or data that you put into this service are public.
BayesianQDM documentation built on April 22, 2026, 1:09 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.width = 7,
fig.height = 4.5,
fig.path = "figures/single-cont-"
)
library(BayesianQDM)
## ----method-compare-----------------------------------------------------------
# Observed data (nMC excluded from base list; passed individually per method)
args_base <- list(
prob = 'posterior', design = 'controlled', prior = 'vague',
theta0 = 1.0,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL
)
p_ni <- do.call(pbayespostpred1cont,
c(args_base, list(CalcMethod = 'NI', nMC = NULL)))
p_mm <- do.call(pbayespostpred1cont,
c(args_base, list(CalcMethod = 'MM', nMC = NULL)))
set.seed(42)
p_mc <- do.call(pbayespostpred1cont,
c(args_base, list(CalcMethod = 'MC', nMC = 10000L)))
cat(sprintf("NI : %.6f (exact)\n", p_ni))
cat(sprintf("MM : %.6f (approx)\n", p_mm))
cat(sprintf("MC : %.6f (n_MC=10000)\n", p_mc))
## ----ctrl-post----------------------------------------------------------------
# P(mu_t - mu_c > theta_TV | data) and P(mu_t - mu_c <= theta_MAV | data)
p_tv <- pbayespostpred1cont(
prob = 'posterior', design = 'controlled', prior = 'vague',
CalcMethod = 'NI', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
p_mav <- pbayespostpred1cont(
prob = 'posterior', design = 'controlled', prior = 'vague',
CalcMethod = 'NI', theta0 = 0.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data) = %.4f -> Go criterion: >= 0.80? %s\n",
p_tv, ifelse(p_tv >= 0.80, "YES", "NO")))
cat(sprintf("P(theta <= theta_MAV | data) = %.4f -> NoGo criterion: >= 0.20? %s\n",
1 - p_mav, ifelse((1 - p_mav) >= 0.20, "YES", "NO")))
cat(sprintf("Decision: %s\n",
ifelse(p_tv >= 0.80 & (1 - p_mav) < 0.20, "Go",
ifelse(p_tv < 0.80 & (1 - p_mav) >= 0.20, "NoGo",
ifelse(p_tv >= 0.80 & (1 - p_mav) >= 0.20, "Miss", "Gray")))))
## ----ctrl-post-niChisq--------------------------------------------------------
p_tv_inf <- pbayespostpred1cont(
prob = 'posterior', design = 'controlled', prior = 'N-Inv-Chisq',
CalcMethod = 'NI', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = 5, kappa0_c = 5,
nu0_t = 5, nu0_c = 5,
mu0_t = 3.0, mu0_c = 1.0,
sigma0_t = 2.0, sigma0_c = 1.8,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data, N-Inv-Chisq prior) = %.4f\n", p_tv_inf))
## ----ctrl-pred----------------------------------------------------------------
p_pred <- pbayespostpred1cont(
prob = 'predictive', design = 'controlled', prior = 'vague',
CalcMethod = 'NI', theta0 = 1.0, nMC = NULL,
n_t = 15, n_c = 15, m_t = 60, m_c = 60,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("Predictive probability (m_t = m_c = 60) = %.4f\n", p_pred))
## ----unctrl-post--------------------------------------------------------------
p_unctrl <- pbayespostpred1cont(
prob = 'posterior', design = 'uncontrolled', prior = 'vague',
CalcMethod = 'MM', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = NULL,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = NULL, s_c = NULL,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = 1.0, # hypothetical control mean
sigma0_t = NULL, sigma0_c = NULL,
r = 1.0, # equal variance assumption
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data, uncontrolled) = %.4f\n", p_unctrl))
## ----ext-post-----------------------------------------------------------------
p_ext <- pbayespostpred1cont(
prob = 'posterior', design = 'external', prior = 'vague',
CalcMethod = 'MM', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = 20L, alpha0e_t = NULL, alpha0e_c = 0.5,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = 0.9, se_c = 1.8,
lower.tail = FALSE
)
cat(sprintf("P(theta > theta_TV | data, external control design, alpha=0.5) = %.4f\n",
p_ext))
## ----ext-borrowing------------------------------------------------------------
# alpha0e_c must be in (0, 1]; start from 0.01 to avoid validation error
alpha_seq <- c(0.01, seq(0.1, 1.0, by = 0.1))
p_alpha <- sapply(alpha_seq, function(a) {
pbayespostpred1cont(
prob = 'posterior', design = 'external', prior = 'vague',
CalcMethod = 'MM', theta0 = 1.5, nMC = NULL,
n_t = 15, n_c = 15,
bar_y_t = 3.2, s_t = 2.0,
bar_y_c = 1.1, s_c = 1.8,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = 20L, alpha0e_t = NULL, alpha0e_c = a,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = 0.9, se_c = 1.8,
lower.tail = FALSE
)
})
data.frame(alpha_ec = alpha_seq, P_gt_TV = round(p_alpha, 4))
## ----oc-controlled, fig.width = 8, fig.height = 6-----------------------------
oc_ctrl <- pbayesdecisionprob1cont(
nsim = 500L,
prob = 'posterior',
design = 'controlled',
prior = 'vague',
CalcMethod = 'MM',
theta_TV = 1.5, theta_MAV = 0.5, theta_NULL = NULL,
nMC = NULL,
gamma_go = 0.80, gamma_nogo = 0.20,
n_t = 15, n_c = 15,
m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
mu_t = seq(1.0, 4.0, by = 0.5),
mu_c = 1.0,
sigma_t = 2.0,
sigma_c = 2.0,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, se_t = NULL, bar_ye_c = NULL, se_c = NULL,
error_if_Miss = TRUE, Gray_inc_Miss = FALSE,
seed = 42L
)
print(oc_ctrl)
plot(oc_ctrl, base_size = 20)
## ----getgamma-ctrl, fig.width = 8, fig.height = 6-----------------------------
res_gamma <- getgamma1cont(
nsim = 1000L,
prob = 'posterior',
design = 'controlled',
prior = 'vague',
CalcMethod = 'MM',
theta_TV = 1.5, theta_MAV = 0.5, theta_NULL = NULL,
nMC = NULL,
mu_t_go = 1.0, mu_c_go = 1.0, # null scenario: no treatment effect
sigma_t_go = 2.0, sigma_c_go = 2.0,
mu_t_nogo = 2.5, mu_c_nogo = 1.0,
sigma_t_nogo = 2.0, sigma_c_nogo = 2.0,
target_go = 0.05, target_nogo = 0.20,
n_t = 15L, n_c = 15L, m_t = NULL, m_c = NULL,
kappa0_t = NULL, kappa0_c = NULL, nu0_t = NULL, nu0_c = NULL,
mu0_t = NULL, mu0_c = NULL, sigma0_t = NULL, sigma0_c = NULL,
r = NULL,
ne_t = NULL, ne_c = NULL, alpha0e_t = NULL, alpha0e_c = NULL,
bar_ye_t = NULL, bar_ye_c = NULL, se_t = NULL, se_c = NULL,
gamma_grid = seq(0.01, 0.99, by = 0.01),
seed = 42L
)
plot(res_gamma, base_size = 20)
Try the BayesianQDM package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.