TimeDepFrail (version 0.1.0)

post_frailty_var: Posterior Frailty Variances

Description

Function for computing the posterior frailty variances 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 variance is \(var(\hat{Z}_{jk}) = var(\hat{\alpha}_{j}/\hat{\alpha}_{max}) + var(\hat{\epsilon}_{jk}/\hat{\epsilon}_{max}\)). This function allows to get either the entire posterior frailty variance \(var(\hat{Z}_{jk})\) or its time-independent \(var(\frac{\hat{\alpha}_{j}}{\hat{\alpha}_{\text{max}}})\) or time-dependent \(var(\frac{\hat{\epsilon}_{jk}}{\hat{\epsilon}_{\text{max}}})\) 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_var(object, flag_eps = FALSE, flag_alpha = FALSE)

Value

Vector or matrix of posterior frailty variances, depending on the flag_eps and flag_alpha values. Specifically:

• It is a vector of length equal to the N containing posterior frailty variances for \(\alpha_j, \forall j\). In this case the flag_eps must be FALSE and the flag_alpha must be TRUE.

• Matrix of dimension (N, L) containing posterior frailty variances for \(\epsilon_{jk}, \forall j,k\). In this case the flag_eps must be TRUE and the flag_alpha must be FALSE.

• Matrix of dimension (N, L) containing posterior frailty variances 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.

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_var(result)
# }