Calculates the type 2 recalibrated predictions for a Cox model — calculate_predictions_recalibrated_type

This function calculates the type 2 recalibrated predictions for a Cox model. To help the recalibration of the model the function get_recalibrate_params_type_2_cox() is defined elsewhere in this package. Using this auxiliar function the recalibration parameters are calculated in each of the imputed datasets stored in data as a long dataset.

After estimating the recalibration parameters in each of the imputed datasets they are aggregated by their mean to use them to recalibrate the predictions of the model. The type 2 recalibration needs from two parameters S0_type_2 and beta_overall. These parameters are calculated with the get_recalibrate_params_type_2_cox() function. Once they are estimated, they are aggregated by the mean. Finally with the type 2 recalibration parameters and the aggregated predictions the type 2 recalibrated predictions are calculated.

$$S_{0, \text{type 2}}(t)^{exp(\beta_{overall}(\beta \cdot X))}$$

where $S_{0, \text{type 2}}(t)$ is estimated using a Weibull distribution and $\beta_{overall}$ is estimated deriving a Cox model with $\beta \cdot X$ as an unique covariate. Both parameters are estimated using the get_recalibrate_params_type_2_cox() function.

Usage

# S3 method for class 'cox'
calculate_predictions_recalibrated_type_2(model, data, .progress = FALSE)

Arguments

model: Model generated with mv_model_cox(). Needs the predictions parameter of the model, to generate it the function calculate_predictions() must be executed over the model.
data: External validation data. Multiple imputation dataset in long format.
.progress: TRUE to render the progress bar FALSE otherwise.

Value

A model with the parameter prediction_type_2 added to predictions_agg and the parameters S0_type_2 and beta_overall stored in recal_parameters

predictions_agg: stores now a new variable prediction_type_2
S0_type_2 and beta_overall are stored in the recal_parameters.

Examples

set.seed(123)

model <- mv_model_cox(
  formula = event ~ 0.5 * (x - 1) + 0.3 * (z - 2),
  S0 = 0.98765
)

data <- data.frame(
  .imp = c(1, 1, 1, 2, 2, 2, 3, 3, 3),
  id = c(1, 2, 3, 1, 2, 3, 1, 2, 3),
  x = rnorm(9, 1, 0.25),
  z = rnorm(9, 2, 0.75),
  event = survival::Surv(rpois(9, 5), rbinom(n = 9, size = 1, prob = 0.5))
)

model |>
  calculate_predictions(data) |>
  calculate_predictions_recalibrated_type_1(data) |>
  calculate_predictions_recalibrated_type_2(data)
#> Warning: Ran out of iterations and did not converge
#> Warning: Ran out of iterations and did not converge
#> 
#> ── <MiceExtVal/cox> ────────────────────────────────────────────────────────────
#> 
#> ── formula ──
#> 
#> event ~ 0.5 * (x - 1) + 0.3 * (z - 2)
#> 
#> ── S0 ──
#> 
#> 0.98765
#> 
#> ── predictions_imp ──
#> 
#> # A tibble: 5 × 4
#>    .imp    id   betax prediction
#>   <dbl> <dbl>   <dbl>      <dbl>
#> 1     1     1 -0.170      0.0104
#> 2     1     2  0.247      0.0158
#> 3     1     3  0.276      0.0162
#> 4     2     1  0.0990     0.0136
#> 5     2     2  0.0411     0.0129
#> ── predictions_agg ──
#> 
#> # A tibble: 3 × 5
#>      id   betax prediction prediction_type_1 prediction_type_2
#>   <dbl>   <dbl>      <dbl>             <dbl>             <dbl>
#> 1     1  0.129      0.0145                 0                NA
#> 2     2  0.0805     0.0135                 0                NA
#> 3     3 -0.0544     0.0123                 0                NA
#> ── recal_parameters ──
#> 
#> # A tibble: 3 × 2
#>   param           value
#>   <chr>           <dbl>
#> 1 alpha        -Inf    
#> 2 S0_type_2       0.829
#> 3 beta_overall   NA