Single Agent Example
Example using a single experimental drug.
The single agent example is described in the reference
Neuenschwander, B. et al (2008). The data are described
in the help page for hist_SA. In this case, the data
come from only one study, with the treatment being only single
agent. Hence the model specified does not involve a hierarchical
prior for the intercept and log-slope parameters. The model
described in Neuenschwander, et al (2008) is adapted as follows:
\mbox{logit}\, π(d) = \log\, α + β \, \log\, \Bigl(\frac{d}{d^*}\Bigr),
where d^* = 250, and the prior for \boldsymbolθ = (\log\, α, \log\, β) is
\boldsymbolθ \sim \mbox{N}(\boldsymbol m, \boldsymbol S),
and \boldsymbol m = (\mbox{logit}\, 0.5, \log\, 1) and \boldsymbol S = \mbox{diag}(2^2, 1^2) are constants.
In the blrm_exnex framework, in which
the prior must be specified as a hierarchical model
\boldsymbolθ \sim \mbox{N}(\boldsymbol μ, \boldsymbol Σ)
with additional priors on \boldsymbolμ and \boldsymbolΣ,
the simple prior distribution above is accomplished
by fixing the diagonal elements τ^2_α and τ^2_β
of \boldsymbolΣ to zero, and taking
\boldsymbolμ \sim \mbox{N}(\boldsymbol m, \boldsymbol S).
The arguments prior_tau_dist and prior_EX_tau_mean_comp
as specified below ensure that the τ's are fixed at zero.
Neuenschwander, B., Branson, M., & Gsponer, T. (2008). Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in medicine, 27(13), 2420-2439.
## Setting up dummy sampling for fast execution of example
## Please use 4 chains and 100x more warmup & iter in practice
.user_mc_options <- options(OncoBayes2.MC.warmup=10, OncoBayes2.MC.iter=20, OncoBayes2.MC.chains=1)
## Example from Neuenschwander, B., et al. (2009). Stats in Medicine
num_comp <- 1 # one investigational drug
num_inter <- 0 # no drug-drug interactions need to be modeled
num_groups <- nlevels(hist_SA$group_id) # no stratification needed
num_strata <- 1 # no stratification needed
dref <- 50
## Since there is no prior information the hierarchical model
## is not used in this example by setting tau to (almost) 0.
blrmfit <- blrm_exnex(
cbind(num_toxicities, num_patients - num_toxicities) ~
1 + log(drug_A / dref) |
0 |
group_id,
data = hist_SA,
prior_EX_mu_mean_comp = matrix(
c(logit(1/2), # mean of intercept on logit scale
log(1)), # mean of log-slope on logit scale
nrow = num_comp,
ncol = 2
),
prior_EX_mu_sd_comp = matrix(
c(2, # sd of intercept
1), # sd of log-slope
nrow = num_comp,
ncol = 2
),
## Here we take tau as known and as zero.
## This disables the hierarchical prior which is
## not required in this example as we analyze a
## single trial.
prior_EX_tau_mean_comp = matrix(
c(0, 0),
nrow = num_comp,
ncol = 2
),
prior_EX_tau_sd_comp = matrix(
c(1, 1),
nrow = num_comp,
ncol = 2
),
prior_EX_prob_comp = matrix(1, nrow = num_comp, ncol = 1),
prior_tau_dist = 0,
prior_PD = FALSE
)
## Recover user set sampling defaults
options(.user_mc_options)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.