post_frailty_var: Posterior Frailty Variances

In TimeDepFrail: Time Dependent Shared Frailty Cox Model

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)

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.

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.

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)


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

post_frailty_var(result)

TimeDepFrail documentation built on April 11, 2025, 5:41 p.m.