example-single-agent {OncoBayes2}

Single Agent Example

Description

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:

\mbox{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 \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 \boldsymbol\theta \sim \mbox{N}(\boldsymbol \mu, \boldsymbol \Sigma) with additional priors on \boldsymbol\mu and \boldsymbol\Sigma, the simple prior distribution above is accomplished by fixing the diagonal elements \tau^2_\alpha and \tau^2_\beta of \boldsymbol\Sigma to zero, and taking

\boldsymbol\mu \sim \mbox{N}(\boldsymbol m, \boldsymbol S).

The arguments prior_tau_dist and prior_EX_tau_mean_comp as specified below ensure that the \tau's are fixed at 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

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)