crmPack (version 2.0.0)

mcmc: Obtaining Posterior Samples for all Model Parameters

Description

This is the function that actually runs the JAGS MCMC machinery to produce posterior samples from all model parameters and required derived values. It is a generic function, so that customized versions may be conveniently defined for specific subclasses of GeneralData, GeneralModel, and McmcOptions input.

Usage

mcmc(data, model, options, ...)
# S4 method for GeneralData,GeneralModel,McmcOptions
mcmc(data, model, options, from_prior = data@nObs == 0L, ...)
# S4 method for GeneralData,DualEndpointRW,McmcOptions
mcmc(data, model, options, from_prior = data@nObs == 0L, ...)
# S4 method for GeneralData,DualEndpointBeta,McmcOptions
mcmc(data, model, options, from_prior = data@nObs == 0L, ...)
# S4 method for GeneralData,DualEndpointEmax,McmcOptions
mcmc(data, model, options, from_prior = data@nObs == 0L, ...)
# S4 method for GeneralData,OneParLogNormalPrior,McmcOptions
mcmc(data, model, options, from_prior = data@nObs == 0L, ...)
# S4 method for GeneralData,OneParExpPrior,McmcOptions
mcmc(data, model, options, from_prior = data@nObs == 0L, ...)
# S4 method for DataMixture,GeneralModel,McmcOptions
mcmc(
  data,
  model,
  options,
  from_prior = data@nObs == 0L & data@nObsshare == 0L,
  ...
)
# S4 method for Data,LogisticIndepBeta,McmcOptions
mcmc(data, model, options, ...)
# S4 method for DataDual,Effloglog,McmcOptions
mcmc(data, model, options, ...)
# S4 method for DataDual,EffFlexi,McmcOptions
mcmc(data, model, options, ...)
# S4 method for DataOrdinal,LogisticLogNormalOrdinal,McmcOptions
mcmc(data, model, options, ...)

Value

The posterior samples, an object of class Samples.

Arguments

data

(GeneralData)
an input data.

model

(GeneralModel)
an input model.

options

(McmcOptions)
MCMC options.

...

not used.

from_prior

(flag)
sample from the prior only? Default to TRUE when number of observations in data is 0. For some models it might be necessary to specify it manually here though.

Functions

• mcmc(data = GeneralData, model = GeneralModel, options = McmcOptions): Standard method which uses JAGS.

• mcmc(data = GeneralData, model = DualEndpointRW, options = McmcOptions): Standard method which uses JAGS. For the DualEndpointRW model, it is required that there are at least two (in case of random walk prior of the first order on the biomarker level) or three doses in the grid.

• mcmc(data = GeneralData, model = DualEndpointBeta, options = McmcOptions): Standard method which uses JAGS. For the DualEndpointBeta model, it is required that the value of ref_dose_beta slot is greater than the maximum dose in a grid. This requirement comes from definition of the beta function that is used to model dose-biomarker relationship in DualEndpointBeta model. The other requirement is that there must be at least one dose in the grid.

• mcmc(data = GeneralData, model = DualEndpointEmax, options = McmcOptions): Standard method which uses JAGS. For the DualEndpointEmax model, it is required that there is at least one dose in the grid.

• mcmc(data = GeneralData, model = OneParLogNormalPrior, options = McmcOptions): Standard method which uses JAGS. For the OneParLogNormalPrior model, it is required that the length of skeleton prior probabilities vector should be equal to the length of the number of doses.

• mcmc(data = GeneralData, model = OneParExpPrior, options = McmcOptions): Standard method which uses JAGS. For the OneParExpPrior model, it is required that the length of skeleton prior probabilities vector should be equal to the length of the number of doses.

• mcmc(data = DataMixture, model = GeneralModel, options = McmcOptions): Method for DataMixture with different from_prior default. Samples from the prior only when both the number of observations and the number of shared observations are zero.

• mcmc(data = Data, model = LogisticIndepBeta, options = McmcOptions): Obtain posterior samples for the model parameters based on the pseudo LogisticIndepBeta DLE model. The joint prior and posterior probability density function of the intercept \(\phi_1\) (phi1) and the slope \(\phi_2\) (phi2) are given in WhiteheadWilliamson1998;textualcrmPack. However, since asymptotically, the joint posterior probability density will be bivariate normal, we use the bivariate normal distribution to generate posterior samples of the intercept and the slope parameters. For the prior samples of the intercept and the slope, a bivariate normal distribution with mean and the covariance matrix given in WhiteheadWilliamson1998;textualcrmPack is used.

• mcmc(data = DataDual, model = Effloglog, options = McmcOptions): Obtain the posterior samples for the model parameters in the Effloglog model. Given the value of \(\nu\), the precision of the efficacy responses, the joint prior or the posterior probability of the intercept \(\theta_1\) (theta1) and the slope \(\theta_2\) (theta2) is a bivariate normal distribution. The \(\nu\) (nu), the precision of the efficacy responses is either a fixed value or has a gamma distribution. If a gamma distribution is used, the samples of nu will be first generated. Then the mean of the nu samples will be used to generate samples of the intercept and slope parameters of the model.

• mcmc(data = DataDual, model = EffFlexi, options = McmcOptions): Obtain the posterior samples for the estimates in the EffFlexi model. This is the MCMC procedure based on what is described in LangBrezger2004;textualcrmPack such that samples of the mean efficacy responses at all dose levels, samples of sigma2 \(\sigma^2\), the variance of the efficacy response and samples of sigma2betaW \(\sigma^2_{\beta_W}\), the variance of the random walk model will be generated. Please refer to LangBrezger2004;textualcrmPack for the procedures and the form of the joint prior and posterior probability density for the mean efficacy responses. In addition, both sigma2 and sigma2betaW can be fixed or have an inverse-gamma prior and posterior distribution. Therefore, if the inverse gamma distribution(s) are used, the parameters in the distribution will be first updated and then samples of sigma2 and sigma2betaW will be generated using the updated parameters.

• mcmc( data = DataOrdinal, model = LogisticLogNormalOrdinal, options = McmcOptions ): Obtain the posterior samples for the model parameters in the LogisticLogNormalOrdinal model.

  The generic mcmc method returns a Samples object with elements of the data slot named alpha[1], alpha[2], ..., alpha[k] and beta when passed a LogisticLogNormalOrdinal object. This makes the "alpha elements" awkward to access and is inconsistent with other model objects. So rename the alpha elements to alpha1, alpha2, ..., alpha<k> for ease and consistency.

References

Examples

# Create some data from the class `Data`.
my_data <- Data(
  x = c(0.1, 0.5, 1.5, 3, 6, 10, 10, 10),
  y = c(0, 0, 0, 0, 0, 0, 1, 0),
  doseGrid = c(0.1, 0.5, 1.5, 3, 6, seq(from = 10, to = 80, by = 2))
)

# Initialize the CRM model.
my_model <- LogisticLogNormal(
  mean = c(-0.85, 1),
  cov = matrix(c(1, -0.5, -0.5, 1), nrow = 2),
  ref_dose = 56
)

# Sample from the posterior distribution.
my_options <- McmcOptions(
  burnin = 100,
  step = 2,
  samples = 1000
)

samples <- mcmc(data = my_data, model = my_model, options = my_options)
samples
# Create some data from the class `DataDual`.
plcb <- 0.001
my_data <- DataDual(
  w = c(13, 77, 86, 26, 27, 36, 37, 97, 21, 49, 87, 48),
  x = c(plcb, 25, 25, 25, plcb, 50, 50, 50, plcb, 100, 100, 100),
  y = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L),
  doseGrid = c(plcb, seq(25, 300, 25)),
  placebo = TRUE,
  ID = 1:12,
  cohort = c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L)
)

# Initialize the CRM model.
my_model <- DualEndpointRW(
  mean = c(0, 1),
  cov = matrix(c(1, 0, 0, 1), nrow = 2),
  sigma2W = c(a = 0.1, b = 0.1),
  rho = c(a = 1, b = 1),
  sigma2betaW = 0.01,
  rw1 = TRUE
)

# Sample from the posterior distribution.
my_options <- McmcOptions(
  burnin = 50,
  step = 2,
  samples = 4,
  rng_kind = "Mersenne-Twister",
  rng_seed = 1
)

samples <- mcmc(data = my_data, model = my_model, options = my_options)
samples
# Create some data from the class `DataDual`.
plcb <- 0.001
my_data <- DataDual(
  w = c(13, 77, 86, 26, 27, 36, 37, 97, 21, 49, 87, 48),
  x = c(plcb, 25, 25, 25, plcb, 50, 50, 50, plcb, 100, 100, 100),
  y = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L),
  doseGrid = c(plcb, seq(25, 300, 25)),
  placebo = TRUE,
  ID = 1:12,
  cohort = c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L)
)

# Initialize the CRM model.
my_model <- DualEndpointBeta(
  mean = c(0, 1),
  cov = diag(2),
  ref_dose = 2,
  use_log_dose = FALSE,
  sigma2W = c(a = 1, b = 2),
  rho = c(a = 1.5, b = 2.5),
  E0 = 2,
  Emax = 50,
  delta1 = 6,
  mode = 9,
  ref_dose_beta = my_data@doseGrid[my_data@nGrid] + 10
)

# Sample from the posterior distribution.
my_options <- McmcOptions(
  burnin = 50,
  step = 2,
  samples = 4,
  rng_kind = "Mersenne-Twister",
  rng_seed = 1
)

samples <- mcmc(data = my_data, model = my_model, options = my_options)
samples
##obtain mcmc DLE samples given the data, LogisticIndepBeta (DLE model) and mcmc simulations options
## data must be of 'Data' class
data <- Data(
  x = c(25, 50, 50, 75, 100, 100, 225, 300),
  y = c(0, 0, 0, 0, 1, 1, 1, 1),
  doseGrid = seq(25, 300, 25)
)
## model must be of 'LogisticIndepBeta' class
model <- LogisticIndepBeta(
  binDLE = c(1.05, 1.8),
  DLEweights = c(3, 3),
  DLEdose = c(25, 300),
  data = data
)
## options must be ''McmcOptions' class
options <- McmcOptions(burnin = 100, step = 2, samples = 200)
set.seed(94)
samples <- mcmc(data = data, model = model, options = options)
# nolint start
##obtain mcmc efficacy samples given the data, 'Effloglog' model (efficacy model) and
## mcmc simulations options data must be of 'DataDual' class
data <- DataDual(
  x = c(25, 50, 25, 50, 75, 300, 250, 150),
  y = c(0, 0, 0, 0, 0, 1, 1, 0),
  w = c(0.31, 0.42, 0.59, 0.45, 0.6, 0.7, 0.6, 0.52),
  doseGrid = seq(25, 300, 25),
  placebo = FALSE
)
## model must be of 'Effloglog' class
Effmodel <- Effloglog(
  eff = c(1.223, 2.513),
  eff_dose = c(25, 300),
  nu = c(a = 1, b = 0.025),
  data = data
)

## options must be ''McmcOptions' class
options <- McmcOptions(burnin = 100, step = 2, samples = 200)
set.seed(94)
samples <- mcmc(data = data, model = Effmodel, options = options)
# nolint end
## obtain mcmc efficacy samples given the data, 'EffFlexi' model (efficacy model) and
## mcmc simulations options
## data must be of 'DataDual' class
data <- DataDual(
  x = c(25, 50, 25, 50, 75, 300, 250, 150),
  y = c(0, 0, 0, 0, 0, 1, 1, 0),
  w = c(0.31, 0.42, 0.59, 0.45, 0.6, 0.7, 0.6, 0.52),
  doseGrid = seq(25, 300, 25)
)
## model must be of 'EffFlexi' class

effmodel <- EffFlexi(
  eff = c(1.223, 2.513),
  eff_dose = c(25, 300),
  sigma2W = c(a = 0.1, b = 0.1),
  sigma2betaW = c(a = 20, b = 50),
  rw1 = FALSE,
  data = data
)

## options must be ''McmcOptions' class
options <- McmcOptions(burnin = 100, step = 2, samples = 200)
set.seed(94)
samples <- mcmc(data = data, model = effmodel, options = options)
ordinal_data <- .DefaultDataOrdinal()
ordinal_model <- .DefaultLogisticLogNormalOrdinal()
mcmc_options <- .DefaultMcmcOptions()

samples <- mcmc(ordinal_data, ordinal_model, mcmc_options)