Fit a CRM model

Fit a continual reassessment method (CRM) model for dose-finding using Stan for full Bayesian inference. There are several likelihood and prior combinations supported. See model-specific sections below.

stan_crm(
  outcome_str = NULL,
  skeleton,
  target,
  model = c("empiric", "logistic", "logistic_gamma", "logistic2"),
  a0 = NULL,
  alpha_mean = NULL,
  alpha_sd = NULL,
  beta_mean = NULL,
  beta_sd = NULL,
  beta_shape = NULL,
  beta_inverse_scale = 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.
skeleton	a vector of the prior guesses of toxicity at doses. This should be a monotonically-increasing vector of numbers between 0 and 1.
target	the target toxicity probability, a number between 0 and 1. This value would normally be one of the values in skeleton, but that is not a requirement.
model	Character string to denote desired model. One of empiric, logistic, logistic_gamma, or logistic2. The choice of model determines which parameters are required. See Details.
a0	Value of fixed intercept parameter. Only required for certain models. See Details.
alpha_mean	Prior mean of intercept variable for normal prior. Only required for certain models. See Details.
alpha_sd	Prior standard deviation of intercept variable for normal prior. Only required for certain models. See Details.
beta_mean	Prior mean of gradient variable for normal prior. Only required for certain models. See Details.
beta_sd	Prior standard deviation of slope variable for normal prior. Only required for certain models. See Details.
beta_shape	Prior shape parameter of slope variable for gamma prior. Only required for certain models. See Details.
beta_inverse_scale	Prior inverse scale parameter of slope variable for gamma prior. Only required for certain models. 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 the TITE-CRM 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-CRM 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 crm_fit

Details

The quickest and easiest way to fit a CRM 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.

Different model choices require that different parameters are provided. See sections below.

The empiric model

The model form is:

\(F(x_{i}, \beta) = x_{i}^{\exp{\beta}}\)

and the required parameters are:

• beta_sd

The logistic model

The model form is:

\(F(x_{i}, \beta) = 1 / (1 + \exp{(-a_{0} - \exp{(\beta)} x_{i}})) \)

and the required parameters are:

• a0

• beta_mean

• beta_sd

The logistic_gamma model

The model form is:

\(F(x_{i}, \beta) = 1 / (1 + \exp{(-a_{0} - \exp{(\beta)} x_{i}})) \)

and the required parameters are:

• a0

• beta_shape

• beta_inverse_scale

The logistic2 model

The model form is:

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

and the required parameters are:

• alpha_mean

• alpha_sd

• beta_mean

• beta_sd

References

O'Quigley, J., Pepe, M., & Fisher, L. (1990). Continual reassessment method: a practical design for phase 1 clinical trials in cancer. Biometrics, 46(1), 33-48. https://www.jstor.org/stable/2531628

Cheung, Y.K. (2011). Dose Finding by the Continual Reassessment Method. CRC Press. ISBN 9781420091519

See also

crm_fit sampling

Examples

if (FALSE) {
# CRM example
fit1 <- stan_crm('1N 2N 3T', skeleton = c(0.1, 0.2, 0.35, 0.6),
                 target = 0.2, model = 'empiric', beta_sd = sqrt(1.34),
                 seed = 123)

fit2 <- stan_crm('1NNN 2NNN 3TTT', skeleton = c(0.1, 0.2, 0.35, 0.6),
                 target = 0.2, model = 'logistic', a0 = 3, beta_mean = 0,
                 beta_sd = sqrt(1.34), seed = 123)

# 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, p.124 of Dose Finding by the CRM, Cheung (2010)
fit3 <-stan_crm(skeleton = c(0.05, 0.12, 0.25, 0.40, 0.55), target = 0.25,
                doses_given = c(3, 3, 3, 3),
                tox = c(0, 0, 0, 0),
                weights = c(73, 66, 35, 28) / 126,
                model = 'empiric', beta_sd = sqrt(1.34), seed = 123)
fit3$recommended_dose
}