TimeDepFrail (version 0.1.0)

post_frailty_confint: Posterior Frailty Confidence Intervals

Description

Function for computing the posterior frailty confidence intervals of the time-dependent shared frailty Cox model.

Recalling the structure of the frailty \(Z_{jk} = \alpha_j + \epsilon_{jk}, \forall j,k\) with \(k=1,\dots,L\) and \(j=1,\dots,N\) as being composed by the sum of two independent gamma distributions:

• \(\alpha_j \sim gamma(\mu_1/\nu, 1/\nu), \forall j\)

• \(\epsilon_{jk} \sim gamma(\mu_2/\gamma_k, 1/\gamma_k), \forall j,k\)

The posterior frailty estimate is \(\hat{Z}_{jk} = \hat{\alpha}_{j}/\hat{\alpha}_{max} + \hat{\epsilon}_{jk}/\hat{\epsilon}_{max}\). This function allows to get the confidence intervals of either the entire posterior frailty estimates \(\hat{Z}_{jk}\) or its time-independent \(\frac{\hat{\alpha}_{j}}{\hat{\alpha}_{\text{max}}}\) or time-dependent \(\frac{\hat{\epsilon}_{jk}}{\hat{\epsilon}_{\text{max}}}\) components. The user can control which components to display using the flag_eps and flag_alpha parameters. Only one of these flags can be set to TRUE at a time.

Usage

post_frailty_confint(
  object,
  level = 0.95,
  flag_eps = FALSE,
  flag_alpha = FALSE
)

Value

A list for posterior frailty confidence intervals, depending on the flag_eps and flag_alpha values. Specifically:

• A list of length equal to the N containing posterior frailty confidence intervals for \(\alpha_j, \forall j\). In this case the flag_eps must be FALSE and the flag_alpha must be TRUE.

• A list of length equal to the NxL containing posterior frailty confidence intervals for \(\epsilon_{jk}, \forall j,k\). In this case the flag_eps must be TRUE and the flag_alpha must be FALSE.

• A list of length equal to the NxL containing posterior frailty confidence intervals for \(Z_{jk} \forall j,k\). In this case the flag_eps must be FALSE and the flag_alpha must be FALSE.

Arguments

object

S3 object of class 'AdPaik' returned by the main model output, that contains all the information for the computation of the frailty standard deviation.

level

A numeric value representing the confidence level for the posterior frailty confidence intervals. Default is 0.95 for 95% confidence.

flag_eps

Logical flag indicating whether to extract only the time-dependent posterior frailty estimates. Default is FALSE.

flag_alpha

Logical flag indicating whether to extract only the time-independent posterior frailty estimates. Default is FALSE.

Examples

# Consider the 'Academic Dropout dataset'
data(data_dropout)

# Define the variables needed for the model execution
formula <- time_to_event ~ Gender + CFUP + cluster(group)
time_axis <- c(1.0, 1.4, 1.8, 2.3, 3.1, 3.8, 4.3, 5.0, 5.5, 5.8, 6.0)
eps <- 1e-10
categories_range_min <- c(-8, -2, eps, eps, eps)
categories_range_max <- c(-eps, 0, 1 - eps, 1, 10)

# \donttest{
# Call the main model
result <- AdPaikModel(formula, data_dropout, time_axis,
                      categories_range_min, categories_range_max)

post_frailty_confint(result)
# }