Calculates the type 2 recalibrated predictions for a logistic regression model — calculate_predictions_recalibrated_type

Calculates the type 2 recalibrated predictions for a logistic regression model. The type 2 recalibration uses two parameters to update the model predictions, the $\alpha$ parameter allow to update the model intercept and the $\beta_{overall}$ parameter allow to update the importance of the log-odds ($\beta \cdot X$) values. The log-odds function can be rewritten as

$$log(\frac{p}{1 - p}) = \alpha + \beta_{overall} \cdot (\beta_0 + \beta_1 \cdot X_1 + \beta_2 \cdot X_2 + \dots + \beta_p \cdot X_p)$$

The parameters are estimated deriving a logistic regression model in each of the imputations using the model log-odds as only covariate. The coefficients of the model represent the parameter estimations and they are aggregated using the rubin rules. Then, the recalibrated predictions are calculated using these parameters and the aggregated log-odds.

$$\frac{1}{1 + e^{(-(\alpha + \beta_{overall}(\beta \cdot X)))}}$$

Usage

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

Arguments

model: Model generated with mv_model_logreg(). Needs the predictions parameter of the model, to generate it the function calculate_predictions() must be executed over the model.
data: Data for what the predictions must be recalibrated.
.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
alpha_type_2 and beta_overall are stored in the recal_parameters.

Examples

set.seed(123)

model <- mv_model_logreg(formula = event ~ 0.5 * x + 0.3 * z - 1.2)

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),
  event = survival::Surv(rpois(9, 5), rbinom(n = 9, size = 1, prob = 0.5)),
  x = rnorm(9, 1, 0.25),
  z = rnorm(9, 2, 0.75)
)

model |>
  calculate_predictions(data) |>
  calculate_predictions_recalibrated_type_1(data) |>
  calculate_predictions_recalibrated_type_2(data)
#> 
#> ── <MiceExtVal/logreg> ─────────────────────────────────────────────────────────
#> 
#> ── formula ──
#> 
#> event ~ 0.5 * x + 0.3 * z - 1.2
#> 
#> ── predictions_imp ──
#> 
#> # A tibble: 5 × 4
#>    .imp    id    betax prediction
#>   <dbl> <dbl>    <dbl>      <dbl>
#> 1     1     1  0.00210      0.501
#> 2     1     2 -0.0534       0.487
#> 3     1     3 -0.295        0.427
#> 4     2     1 -0.0989       0.475
#> 5     2     2 -0.317        0.421
#> ── predictions_agg ──
#> 
#> # A tibble: 3 × 5
#>      id   betax prediction prediction_type_1 prediction_type_2
#>   <dbl>   <dbl>      <dbl>             <dbl>             <dbl>
#> 1     1 -0.0380      0.490             0.479             1    
#> 2     2 -0.263       0.435             0.424             1.000
#> 3     3 -0.262       0.435             0.424             1.000
#> ── recal_parameters ──
#> 
#> # A tibble: 3 × 2
#>   param           value
#>   <chr>           <dbl>
#> 1 alpha_type_1  -0.0454
#> 2 alpha_type_2 156.    
#> 3 beta_overall 529.