Fit a Neuenschwander, Branson & Gsponer logit dose-finding model

Fit Neuenschwander, Branson & Gsponer logit model for dose-finding using Stan for full Bayesian inference.

stan_nbg(
  outcome_str = NULL,
  real_doses,
  d_star,
  target,
  alpha_mean = NULL,
  alpha_sd = NULL,
  beta_mean = NULL,
  beta_sd = NULL,
  doses_given = NULL,
  tox = NULL,
  weights = NULL,
  ...
)

Arguments

outcome_str	A string representing the outcomes observed hitherto. See df_parse_outcomes for a description of syntax and examples. Alternatively, you may provide doses_given and tox parameters. See Details.
real_doses	A vector of numbers, the doses under investigation. They should be ordered from lowest to highest and be in consistent units. E.g. to conduct a dose-finding trial of doses 10mg, 20mg and 50mg, use c(10, 20, 50).
d_star	d_star, numeric reference dose-level. The linear covariate in this logit model is dose / d_star.
target	the target toxicity probability, a number between 0 and 1.
alpha_mean	Prior mean of intercept variable for normal prior. See Details.
alpha_sd	Prior standard deviation of intercept variable for normal prior. See Details.
beta_mean	Prior mean of gradient variable for normal prior. See Details.
beta_sd	Prior standard deviation of slope variable for normal prior. See Details.
doses_given	A optional vector of dose-levels given to patients 1:num_patients, where 1=lowest dose, 2=second dose, etc. Only required when outcome_str is not provided.
tox	An optional vector of toxicity outcomes for patients 1:num_patients, where 1=toxicity and 0=no toxicity. Only required when outcome_str is not provided.
weights	An optional vector of numeric weights for the observations for patients 1:num_patients, thus facilitating a time-to-event (TITE) design. Can be used with outcome_str, or with doses_given and tox. It is generally tidier to specify doses_given, tox and weights when a TITE-analysis is desired.
...	Extra parameters are passed to rstan::sampling. Commonly used options are iter, chains, warmup, cores, and control.

Value

An object of class nbg_fit, which inherits behaviour from crm_fit.

Details

The quickest and easiest way to fit this model to some observed outcomes is to describe the outcomes using trialr's syntax for dose-finding outcomes. See df_parse_outcomes for full details and examples.

The two-parameter model form is:

\(F(x_{i}, \alpha, \beta) = 1 / (1 + \exp{-(\alpha + \exp{(\beta)} log(x_i / d_star))}) \)

and the required parameters are:

• alpha_mean

• alpha_sd

• beta_mean

• beta_sd

References

Neuenschwander, B., Branson, M., & Gsponer, T. (2008). Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27, 2420–2439. https://doi.org/10.1002/sim

See also

crm_fit sampling

Examples

if (FALSE) {
# Non-TITE example:
fit1 <- stan_nbg('1NNN 2NNN 3TTT', real_doses = c(10, 20, 50, 100, 200),
                 d_star = 200, target = 0.25,
                 alpha_mean = -1, alpha_sd = 2,
                 beta_mean = 0, beta_sd = 1,
                 seed = 123)
fit1$recommended_dose

# The seed is passed to the Stan sampler. The usual Stan sampler params like
# cores, iter, chains etc are passed on too via the ellipsis operator.

# TITE-CRM example
fit2 <-stan_nbg(real_doses = c(10, 20, 50, 100, 200), d_star = 200,
                target = 0.25,
                doses_given = c(3, 3, 3, 3),
                tox = c(0, 0, 0, 0),
                weights = c(73, 66, 35, 28) / 126,
                alpha_mean = -1, alpha_sd = 2,
                beta_mean = 0, beta_sd = 1,
                seed = 123)
fit2$recommended_dose
}