Supervised Linear Encoding of Factors via Penalized Cox Models

step_lencode_coxnet creates a specification of a recipe step that encodes categorical predictors into a single numeric variable representing the estimated log hazard ratio from a penalized Cox proportional hazards model on a survival outcome (Surv(time, status) or Surv(tstart, tstop, status)). Inspired by embed::step_lencode_glm. Each factor is encoded on its own: a penalized Cox model with one indicator per non-reference level is fit to the training data at the single penalty, the reference level (the first level) is encoded as 0, and levels that bake() has not seen, or missing values, are encoded as 0. If a model can't be fit, a warning is raised and the factor's levels are all encoded as 0.

Usage

step_lencode_coxnet(
  recipe,
  ...,
  outcome = c("time", "status"),
  role = "predictor",
  trained = FALSE,
  penalty = 0.05,
  mixture = 1,
  mapping = NULL,
  skip = FALSE,
  id = recipes::rand_id("lencode_coxnet")
)

# S3 method for class 'step_lencode_coxnet'
tunable(x, ...)

# S3 method for class 'step_lencode_coxnet'
required_pkgs(x, ...)

Arguments

recipe: A recipe object.
...: One or more selector functions to choose variables to be encoded. Must select factor or character columns.
outcome: Character vector naming the survival outcome columns in the training data: c("time", "status") or c("tstart", "tstop", "status").
role: For model terms created by this step, what analysis role should they be assigned? By default, the function assumes that the new variables will be used as predictors in a model.
trained: A logical indicating whether the recipe has been trained.
penalty: A non-negative numeric value specifying the L1/L2 penalty for coxnet. Default is 0.05.
mixture: Elastic net mixing parameter between 0 and 1. Default is 1 (Lasso).
mapping: A named list of numeric vectors containing the level-to-score mappings, generated during prep().
skip: A logical indicating whether the step should be skipped when the recipe is baked.
id: A unique identifier for the step.
x: A step_lencode_coxnet object.

Value

An updated version of recipe with the new step added.

Missing values

A missing value in a factor counts as the reference level: in prep() it is recoded to the first level before the model is fit, so its row stays in the fit (and, with the other rows of that level, sets the baseline that the other levels are compared with), and in bake() it is encoded as 0. step_lencode_joint_model follows the same policy.

The training data are encoded with their own fit

prep() fits the encoding on the training rows, and bake(new_data = NULL), or baking the training data, encodes those same rows with the coefficients fitted to them: the encoding is not out-of-fold (cross-fitted). The encoded training column therefore carries the outcome, so it looks more predictive in the training data than it is for new subjects, and a model fit to it over-trusts it. The effect grows with the number of levels relative to the number of events, so it is worst for factors with many or rare levels, whose coefficients are fitted to a handful of subjects each: a factor with 100 levels and no relation to the outcome can show a clearly better than chance concordance in the baked training data and chance level on new data. To limit it, use a large penalty (most levels then shrink to 0) or pool rare levels before encoding (for example with recipes::step_other()). Do not evaluate a model on data that it was encoded with: estimate performance on subjects the step did not see in prep(), for example by resampling the whole recipe, so that every prep() sees only the analysis set, and not by encoding once and splitting afterwards.

Examples

if (FALSE) { # \dontrun{
if (requireNamespace("recipes", quietly = TRUE) && requireNamespace("survival", quietly = TRUE)) {
  lung <- survival::lung
  lung_df <- na.omit(lung[, c("time", "status", "sex", "ph.ecog")])
  lung_df$ph.ecog <- factor(lung_df$ph.ecog)
  lung_df$sex <- factor(lung_df$sex)

  rec <- recipes::recipe(time + status ~ ., data = lung_df) |>
    step_lencode_coxnet(ph.ecog, sex, outcome = c("time", "status"))
  prepped <- recipes::prep(rec)
  baked <- recipes::bake(prepped, new_data = NULL)
}
} # }