trialr: stan_augbin – R documentation

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stan_augbin

Fit Wason & Seaman's Augmented Binary model for tumour response.

Description

Phase II clinical trials in oncology commonly assess response as a key outcome measure. Patients achieve a RECIST response if their tumour size post-baseline has changed in size by some threshold amount and they do not experience non-shrinkage failure. An example of non-shrinkage failure is the appearance of new lesions. As a dichtotomisation of the underlying continuous tumour size measurement, RECIST response is inefficient. Wason & Seaman introduced the Augmented Binary method to incorporate mechanisms for non-shrinkage failure whilst modelling the probability of response based on the continuous tumour size measurements. See model-specific sections below, and the references.

Usage

stan_augbin(
  tumour_size,
  non_shrinkage_failure,
  arm = NULL,
  model = c("2t-1a"),
  prior_params = list(),
  ...
)

Arguments

`tumour_size`	matrix-like object containing tumour size measures, with rows representing patients and columns representing chronological standardised assessment points. Column one is baseline.
`non_shrinkage_failure`	matrix-like object containing logical indicators of non-shrinkage failure, with rows representing patients and columns representing chronological standardised assessment points.
`arm`	optional vector of integers representing the allocated treatment arms for patients, assumed in the same order as `tumour_size` and `non_shrinkage_failure`. NULL to fit the augbin variant for single-arm trials. NULL is the default.
`model`	Character string to denote the desired model. Currently, only `2t-1a` is supported, representing the model variant with two post-baseline assessments in a single arm trial. Multi-period and multi-arm versions will be added in future releases. The model choice determines the prior parameters that must be provided. See sections below.
`prior_params`	list of prior parameters. These are combined with the data and passed to `rstan::sampling`. The parameters required depend on the model form being fit. See sections below.
`...`	Extra parameters are passed to `rstan::sampling`. Commonly used options are `iter`, `chains`, `warmup`, `cores`, `control`. See `sampling`.

Value

an instance or subclass of type augbin_fit.

Single-arm model with two post-baseline assessments

The complete model form is:

(y_{1i}, y_{2i})^T \sim N( (μ_{1i}, μ_{2i})^T, Σ)

μ_{1i} = α + γ z_{0i}

μ_{2i} = β + γ z_{0i}

logit(Pr(D_{1i} = 1 | Z_{0i})) = α_{D1} + γ_{D1} z_{0i}

logit(Pr(D_{2i} = 1 | D_{1i} = 0, Z_{0i}, Z_{1i})) = α_{D2} + γ_{D2} z_{1i}

where z_{0i}, z_{1i}, z_{2i} are tumour sizes at baseline, period 1, and period 2, for patient i; y_{1i}, y_{2i} are the log-tumour-size ratios with respect to baseline; D_{1i}, D_{2i} are indicators of non-shrinkage failure; and Σ is assumed to be unstructured covariance matrix, with associated correlation matrix having an LKJ prior.

The following prior parameters are required:

alpha_mean & alpha_sd for normal prior on α.
beta_mean & beta_sd for normal prior on β.
gamma_mean & gamma_sd for normal prior on γ.
sigma_mean & sigma_sd for normal priors on diagonal elements of Σ;
omega_lkj_eta for a LKJ prior on the two-period correlation matrix associated with Sigma. omega_lkj_eta = 1 is uniform, analogous to a Beta(1,1) prior on a binary probability.
alpha_d1_mean & alpha_d1_sd for normal prior on α_{D1}.
gamma_d1_mean & gamma_d1_sd for normal prior on γ_{D1}.
alpha_d2_mean & alpha_d2_sd for normal prior on α_{D2}.
gamma_d2_mean & gamma_d2_sd for normal prior on γ_{D2}.

Author(s)

Kristian Brock

References

Wason JMS, Seaman SR. Using continuous data on tumour measurements to improve inference in phase II cancer studies. Statistics in Medicine. 2013;32(26):4639-4650. doi:10.1002/sim.5867

Eisenhauer EA, Therasse P, Bogaerts J, et al. New response evaluation criteria in solid tumours: Revised RECIST guideline (version 1.1). European Journal of Cancer. 2009;45(2):228-247. doi:10.1016/j.ejca.2008.10.026

Examples

priors <- list(alpha_mean = 0, alpha_sd = 1,
               beta_mean = 0, beta_sd = 1,
               gamma_mean = 0, gamma_sd = 1,
               sigma_mean = 0, sigma_sd = 1,
               omega_lkj_eta = 1,
               alpha_d1_mean = 0, alpha_d1_sd = 1,
               gamma_d1_mean = 0, gamma_d1_sd = 1,
               alpha_d2_mean = 0, alpha_d2_sd = 1,
               gamma_d2_mean = 0, gamma_d2_sd = 1)
# Scenario 1 of Table 1 in Wason & Seaman (2013)
N <- 50
sigma <- 1
delta1 <- -0.356
mu <- c(0.5 * delta1, delta1)
Sigma = matrix(c(0.5 * sigma^2, 0.5 * sigma^2, 0.5 * sigma^2, sigma^2),
               ncol = 2)
alphaD <- -1.5
gammaD <- 0
set.seed(123456)
y <- MASS::mvrnorm(n = N, mu, Sigma)
z0 <- runif(N, min = 5, max = 10)
z1 <- exp(y[, 1]) * z0
z2 <- exp(y[, 2]) * z0
d1 <- rbinom(N, size = 1, prob = gtools::inv.logit(alphaD + gammaD * z0))
d2 <- rbinom(N, size = 1, prob = gtools::inv.logit(alphaD + gammaD * z1))
tumour_size <- data.frame(z0, z1, z2) # Sizes in cm
non_shrinkage_failure <- data.frame(d1, d2)
# Fit
## Not run: 
fit <- stan_augbin(tumour_size, non_shrinkage_failure,
                   prior_params = priors, model = '2t-1a', seed = 123)

## End(Not run)

trialr

Clinical Trial Designs in 'rstan'

v0.1.5

GPL (>= 3)

Authors

Kristian Brock [aut, cre] (<https://orcid.org/0000-0002-3921-0166>), Trustees of Columbia University [cph]

Initial release

2020-10-14