Example using a single experimental drug.
Details
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:
$$\text{logit}\, \pi(d) = \log\, \alpha + \beta \, \log\, \Bigl(\frac{d}{d^*}\Bigr),$$
where \(d^* = 250\), and the prior for
\(\boldsymbol\theta = (\log\, \alpha, \log\, \beta)\) is
$$\boldsymbol\theta \sim \text{N}(\boldsymbol m, \boldsymbol S),$$
and \(\boldsymbol m = (\text{logit}\, 0.5, \log\, 1)\) and
\(\boldsymbol S = \text{diag}(2^2, 1^2)\) are constants.
The above model is non-hierarchical. To disable the hierarchical
model structure of the blrm_exnex framework, the user can
specify the option prior_tau_dist=NULL. This will internally
set all the heterogeniety parameters (\(\tau^2_\alpha\) and
\(\tau^2_\beta\)) to zero.
References
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.
Examples
## 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,
OncoBayes2.MC.save_warmup = FALSE
)
## Example from Neuenschwander, B., et al. (2009). Stats in Medicine
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_comp = mixmvnorm(c(1, logit(1 / 2), log(1), diag(c(2^2, 1)))),
## Setting prior_tau_dist=NULL disables the hierarchical prior which is
## not required in this example as we analyze a single trial.
prior_tau_dist = NULL,
prior_PD = FALSE
)
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
## Recover user set sampling defaults
options(.user_mc_options)