shrinkDSM: Markov Chain Monte Carlo (MCMC) for time-varying parameter survival models with shrinkage

Description

shrinkDSM samples from the joint posterior distribution of the parameters of a time-varying parameter survival model with shrinkage and returns the MCMC draws. See also shrinkTVP to see more examples of how to modify the prior setup of the time-varying component of the model.

Usage

shrinkDSM(
  formula,
  data,
  mod_type = "double",
  delta,
  S,
  group,
  subset,
  niter = 10000,
  nburn = round(niter/2),
  nthin = 1,
  learn_a_xi = TRUE,
  learn_a_tau = TRUE,
  a_xi = 0.1,
  a_tau = 0.1,
  learn_c_xi = TRUE,
  learn_c_tau = TRUE,
  c_xi = 0.1,
  c_tau = 0.1,
  a_eq_c_xi = FALSE,
  a_eq_c_tau = FALSE,
  learn_kappa2_B = TRUE,
  learn_lambda2_B = TRUE,
  kappa2_B = 20,
  lambda2_B = 20,
  hyperprior_param,
  sv_param,
  MH_tuning,
  phi_param,
  display_progress = TRUE
)

Value

The value returned is a list object of class shrinkDSM containing

beta: list object containing an mcmc.dsm.tvp object for the parameter draws from the posterior distribution of the centered states, one for each covariate. In the case that there is only one covariate, this becomes just a single mcmc.dsm.tvp object.
beta_mean: mcmc object containing the parameter draws from the posterior distribution of beta_mean.
theta_sr: mcmc object containing the parameter draws from the posterior distribution of the square root of theta.
tau2: mcmc object containing the parameter draws from the posterior distribution of tau2.
xi2: mcmc object containing the parameter draws from the posterior distribution of xi2.
lambda2: (optional) mcmc object containing the parameter draws from the posterior distribution of lambda2. Not returned if mod_type is not "triple".
kappa2: (optional) mcmc object containing the parameter draws from the posterior distribution of kappa2. Not returned if mod_type is not "triple".
a_xi: (optional) mcmc object containing the parameter draws from the posterior distribution of a_xi. Not returned if learn_a_xi is FALSE or mod_type is "ridge".
a_tau: (optional) mcmc object containing the parameter draws from the posterior distribution of a_tau. Not returned if learn_a_tau is FALSE or mod_type is "ridge".
c_xi: (optional) mcmc object containing the parameter draws from the posterior distribution of c_xi. Not returned if learn_c_xi is FALSE or mod_type is not "triple".
c_tau: (optional) mcmc object containing the parameter draws from the posterior distribution of c_tau. Not returned if learn_c_tau is FALSE or mod_type is not "triple".
lambda2_B: (optional) mcmc object containing the parameter draws from the posterior distribution of lambda2_B. Not returned if learn_lambda2_B is FALSE or mod_type is "ridge".
kappa2_B: (optional) mcmc object containing the parameter draws from the posterior distribution of kappa2_B. Not returned if learn_kappa2_B is FALSE or mod_type is "ridge".
MH_diag: (optional) named list containing statistics for assessing MH performance. Not returned if no MH steps are required or none of them are specified to be adaptive.
priorvals: list object containing hyperparameter values of the prior distributions, as specified by the user.
model: list object containing the model matrix, model response and formula used.
summaries: list object containing a collection of summary statistics of the posterior draws.

To display the output, use plot and summary. The summary method displays the specified prior values stored in priorvals and the posterior summaries stored in summaries, while the plot method calls coda's plot.mcmc

or the plot.mcmc.dsm.tvp method. Furthermore, all functions that can be applied to coda::mcmc objects (e.g. coda::acfplot) can be applied to all output elements that are coda compatible.

Arguments

formula

an object of class "formula": a symbolic representation of the model, as in the function lm. For details, see formula. The response may by a survival object as returned by the Surv function.

data

optional data frame containing the response variable and the covariates. If not found in data, the variables are taken from environment(formula), typically the environment from which shrinkDSM is called. No NAs are allowed in the response variable and the covariates.

mod_type

character string that reads either "triple", "double" or "ridge". Determines whether the triple gamma, double gamma or ridge prior are used for theta_sr and beta_mean. The default is "double".

delta

The status indicator of the last period, 0 = censored or 1 = event observed. If the formula is a survival object this parameter is ignored.

S

integer vector of time points that start a new interval. Parameters are fixed within an interval and vary across intervals.

group

optional grouping indicator for latent factor.

subset

optional vector specifying a subset of observations to be used in the fitting process.

niter

positive integer, indicating the number of MCMC iterations to perform, including the burn-in. Has to be larger than or equal to nburn + 2. The default value is 10000.

nburn

non-negative integer, indicating the number of iterations discarded as burn-in. Has to be smaller than or equal to niter - 2. The default value is round(niter / 2).

nthin

positive integer, indicating the degree of thinning to be performed. Every nthin draw is kept and returned. The default value is 1, implying that every draw is kept.

learn_a_xi

logical value indicating whether to learn a_xi, the spike parameter of the state variances. The default value is TRUE.

learn_a_tau

logical value indicating whether to learn a_tau, the spike parameter of the mean of the initial values of the states. The default value is TRUE.

a_xi

positive, real number, indicating the (fixed) value for a_xi. Ignored if learn_a_xi is TRUE or mod_type is set to "ridge". The default value is 0.1.

a_tau

positive, real number, indicating the (fixed) value for a_tau. Ignored if learn_a_tau is TRUE or mod_type is set to "ridge". The default value is 0.1.

learn_c_xi

logical value indicating whether to learn c_xi, the tail parameter of the state variances. Ignored if mod_type is not set to "triple" or a_eq_c_xi is set to TRUE. The default value is TRUE.

learn_c_tau

logical value indicating whether to learn c_tau, the tail parameter of the mean of the initial values of the states. Ignored if mod_type is not set to "triple" or a_eq_c_tau is set to TRUE. The default value is TRUE.

c_xi

positive, real number, indicating the (fixed) value for c_xi. Ignored if learn_c_xi is TRUE, mod_type is not set to "triple" or a_eq_c_xi is set to TRUE. The default value is 0.1.

c_tau

positive, real number, indicating the (fixed) value for c_tau. Ignored if learn_c_xi is TRUE, mod_type is not set to "triple" or a_eq_c_tau is set to TRUE. The default value is 0.1.

a_eq_c_xi

logical value indicating whether to force a_xi and c_xi to be equal. If set to TRUE, beta_a_xi and alpha_a_xi are used as the hyperparameters and beta_c_xi and alpha_c_xi are ignored. Ignored if mod_type is not set to "triple". The default value is FALSE.

a_eq_c_tau

logical value indicating whether to force a_tau and c_tau to be equal. If set to TRUE, beta_a_tau and alpha_a_tau are used as the hyperparameters and beta_c_tau and alpha_c_tau are ignored. Ignored if mod_type is not set to "triple". The default value is FALSE.

learn_kappa2_B

logical value indicating whether to learn kappa2_B, the global level of shrinkage for the state variances. The default value is TRUE.

learn_lambda2_B

logical value indicating whether to learn the lambda2_B parameter, the global level of shrinkage for the mean of the initial values of the states. The default value is TRUE.

kappa2_B

positive, real number. Initial value of kappa2_B. The default value is 20.

lambda2_B

positive, real number. Initial value of lambda2_B. The default value is

hyperprior_param

optional named list containing hyperparameter values. Not all have to be supplied, with those missing being replaced by the default values. Any list elements that are misnamed will be ignored and a warning will be thrown. All hyperparameter values have to be positive, real numbers. The following hyperparameters can be supplied:

e1: The default value is 0.001.
e2: The default value is 0.001.
d1: The default value is 0.001.
d2: The default value is 0.001.
beta_a_xi: The default value is 10.
beta_a_tau: The default value is 10.
alpha_a_xi: The default value is 5.
alpha_a_tau: The default value is 5.

sv_param

optional named list containing hyperparameter values for the stochastic volatility parameters. Not all have to be supplied, with those missing being replaced by the default values. Any list elements that are misnamed will be ignored and a warning will be thrown. Ignored if group is missing. The following elements can be supplied:

Bsigma_sv: positive, real number. The default value is 1.
a0_sv: positive, real number. The default value is 5.
b0_sv: positive, real number. The default value is 1.5.

MH_tuning

optional named list containing values used to tune the MH steps for a_xi and a_tau. Not all have to be supplied, with those missing being replaced by the default values. Any list elements that are misnamed will be ignored and a warning will be thrown. The arguments for a_xi(a_tau) are only used if learn_a_xi(learn_a_tau) is set to TRUE. Arguments ending in "adaptive" are logical values indicating whether or not to make the MH step for the respective parameter adaptive. Arguments ending in "tuning_par" serve two different purposes. If the respective MH step is not set to be adaptive, it acts as the standard deviation of the proposal distribution. If the respective MH step is set to be adaptive, it acts as the initial standard deviation. Arguments ending in "target_rate" define the acceptance rate the algorithm aims to achieve. Arguments ending in "max_adapt" set the maximum value by which the logarithm of the standard deviation of the proposal distribution is adjusted. Finally, arguments ending in "batch_size" set the batch size after which the standard deviation of the proposal distribution is adjusted. The following elements can be supplied:

a_xi_adaptive: logical value. The default is TRUE.
a_xi_tuning_par: positive, real number. The default value is 1.
a_xi_target_rate: positive, real number, between 0 and 1. The default value is 0.44.
a_xi_max_adapt: positive, real number. The default value is 0.01.
a_xi_batch_size: positive integer. The default value is 50.
a_tau_adaptive: logical value. The default is TRUE.
a_tau_tuning_par: positive, real number. The default value is 1.
a_tau_target_rate: positive, real number, between 0 and 1. The default value is 0.44.
a_tau_max_adapt: positive, real number. The default value is 0.01.
a_tau_batch_size: positive integer. The default value is 50.

phi_param

optional named list containing hyperparameter values for the grouped factor and values to tune the MH steps for a_phi and c_phi. Not all have to be supplied, with those missing being replaced by the default values. Any list elements that are misnamed will be ignored and a warning will be thrown. Ignored if group is missing. The following elements can be supplied:

mod_type_phi character string that reads either "triple", "double" or "ridge". Determines whether the triple gamma, double gamma or ridge prior are used for phi. The default is "double".
learn_a_phi: logical value. The default is TRUE.
a_phi: positive, real number. The default value is 0.1.
learn_c_phi: logical value. The default is TRUE.
c_phi: positive, real number. The default value is 0.1,
a_phi_eq_c_phi: logical value. The default is FALSE.
learn_lambda2_B_phi: logical value. The default is TRUE.
lambda2_B_phi: positive, real number. The default value is 20.
e1_phi: positive, real number. The default value is 0.001.
e2_phi: positive, real number. The default value is 0.001.
beta_a_phi: positive, real number. The default value is 10.
alpha_a_phi: positive, real number. The default value is 5.
beta_c_phi: positive, real number. The default value is 10.
alpha_c_phi: positive, real number. The default value is 5.
a_phi_adaptive: logical value. The default is TRUE.
a_phi_tuning_par: positive, real number. The default value is 1.
a_phi_target_rate: positive, real number, between 0 and 1. The default value is 0.44.
a_phi_max_adapt: positive, real number. The default value is 0.01.
a_phi_batch_size: positive integer. The default value is 50.
c_phi_adaptive: logical value. The default is TRUE.
c_phi_tuning_par: positive, real number. The default value is 1.
c_phi_target_rate: positive, real number, between 0 and 1. The default value is 0.44.
c_phi_max_adapt: positive, real number. The default value is 0.01.
c_phi_batch_size: positive integer. The default value is 50.

display_progress

logical value indicating whether the progress bar and other informative output should be displayed. The default value is TRUE.

Author

Daniel Winkler daniel.winkler@wu.ac.at

Peter Knaus peter.knaus@wu.ac.at

Examples

Run this code

# \donttest{
set.seed(123)
data("gastric")

# Create intervals for piecewise exponential model
intervals <- divisionpoints(gastric$time, gastric$status, 2)

# Estimate baseline model
mod <- shrinkDSM(time ~ radiation, gastric,
  delta = gastric$status, S = intervals
)

# Alternative formula interface
mod_surv <- shrinkDSM(Surv(time, status) ~ radiation, gastric,
  S = intervals
)

# Estimate model with different prior setup
mod2 <- shrinkDSM(time ~ radiation, gastric,
  delta = gastric$status, S = intervals,
  mod_type = "triple"
)

# Change some of the hyperparameters
mod3 <- shrinkDSM(time ~ radiation, gastric,
  delta = gastric$status, S = intervals,
  mod_type = "triple",
  hyperprior_param = list(
    beta_a_xi = 5,
    alpha_a_xi = 10
  )
)
# }

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