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Posterior Frailty Confidence Intervals

post_frailty_confint.Rd

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
)

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.

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.

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

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