TimeDepFrail (version 0.1.0)

frailty_sd: Frailty Standard Deviation and Variance for the 'Adapted Paik et Al.'s Model'

Description

The function computes both the standard deviation and the variance of the time-dependent frailty of the 'Adapted Paik et al.'s Model'.

Recalling the frailty structure \(Z_{jk} = \alpha_j + \epsilon_{jk}\) as being composed by a constant group-dependent term (\(\alpha_j\)) and a time and group dependent term (\(\epsilon_{jk}\)), the frailty variance (and standard deviation) can be computed in two different way:

• Considering only the time-dependent spread of the clusters/groups/centre: \(var(Z_{jk}) = \mu_2 * \gamma_k\). In this case, the flag_full should be FALSE and flag_variance should be TRUE.

• Considering both the time-dependent and constant spread of the clusters: \(var(Z_{jk}) = \mu_1 * \nu + \mu_2 * \gamma_k\). The new added term only moves upward the other case and the flag_full should be TRUE and flag_variance should be TRUE.

Usage

frailty_sd(object, flag_full = TRUE, flag_variance = FALSE)

Value

Numerical vector of length equal to the number of intervals of the time-domain, with the value of the frailty standard deviation or variance (either full or only the time-dependent component).

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_full

A boolean flag indicating whether to get the full standard deviation (TRUE) or only the time-dependent component (FALSE). Default to TRUE.

flag_variance

A boolean flag indicating whether to get the frailty variance (TRUE) or the frailty standard deviation (FALSE). Default to 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)

frailty_sd(result)
# }