Calculates the type 1 recalibrated predictions for a logistic regression model. — calculate_predictions_recalibrated_type

Calculates the type 1 recalibrated predictions for a logistic regression model. The type 1 recalibration is defined by an $\alpha$ parameter that updates the value of the intercept ($\beta_0$) of the model. The log-odds function is rewritten as follows.

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

Thus, the predictions are updated by adjusting the intercept value in the model against the external validation data. The $\alpha$ parameter is estimated in each of the imputed datasets by deriving a logistic regression model using the model log-odds as offset. The coefficients in all the models are aggregated using the mean. Using the aggregated parameter and the aggregated log-odds the new predictions are calculated as follows.

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

Usage

# S3 method for class 'logreg'
calculate_predictions_recalibrated_type_1(model, data, .progress = FALSE)

Arguments

model: Model generated with mv_model_logreg(). Needs the predictions_agg and predictions_imp parameters 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_1 added to predictions_agg and the parameter alpha_type_1 stored in recal_parameters

predictions_agg: stores now a new variable prediction_type_1
alpha_type_1: stores now the $\alpha$ recalibration parameter.

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)
#> 
#> ── <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 × 4
#>      id   betax prediction prediction_type_1
#>   <dbl>   <dbl>      <dbl>             <dbl>
#> 1     1 -0.0380      0.490             0.479
#> 2     2 -0.263       0.435             0.424
#> 3     3 -0.262       0.435             0.424
#> ── recal_parameters ──
#> 
#> # A tibble: 1 × 2
#>   param          value
#>   <chr>          <dbl>
#> 1 alpha_type_1 -0.0454