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

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)

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.

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).

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)
#> Error in while (r <= n_run & actual_tol_ll > tol_ll) {    if (verbose)         message(paste("Run ", r))    RemainingIndexes <- RunIndexes[r, ]    UsedIndexes <- c()    while (length(RemainingIndexes) != 0) {        index_to_vary <- RemainingIndexes[1]        PosIndex <- which(RemainingIndexes == index_to_vary)        RemainingIndexes <- RemainingIndexes[-PosIndex]        UsedIndexes <- c(UsedIndexes, index_to_vary)        result_optimize <- suppressWarnings(optimize(ll_AdPaik_1D,             c(params_range_min[index_to_vary], params_range_max[index_to_vary]),             maximum = TRUE, tol = tol_optimize, index_to_vary,             params, dataset, centre, time_axis, dropout_matrix,             e_matrix))        params[index_to_vary] <- result_optimize$maximum    }    global_optimal_params[r, ] <- params    global_optimal_loglikelihood_run <- ll_AdPaik_eval(params,         dataset, centre, time_axis, dropout_matrix, e_matrix)    global_optimal_loglikelihood[r] <- global_optimal_loglikelihood_run    if (is.nan(global_optimal_loglikelihood_run))         stop("NaN value for the optimal log-likelihood value.")    if (print_previous_ll_values[1]) {        n_previous <- print_previous_ll_values[2]        if (r < n_previous)             if (verbose)                 message(paste(" Global log-likelihood: ", global_optimal_loglikelihood[1:r]))            else if (verbose)                 message(paste(" Global log-likelihood: ", global_optimal_loglikelihood[(r -                   n_previous + 1):r]))    }    actual_tol_ll <- abs(ll_optimal - global_optimal_loglikelihood_run)    if (ll_optimal < global_optimal_loglikelihood_run) {        ll_optimal <- global_optimal_loglikelihood_run        optimal_run <- r    }    r <- r + 1}: missing value where TRUE/FALSE needed

frailty_sd(result)
#> Error: object 'result' not found
# }