Penalized Cox Regression for Right-Censored or Start/Stop Survival Data

Fits an elastic-net penalized Cox proportional hazards model with [glmnet::glmnet()], through the tidymodels hardhat interface: a formula, a recipe, or predictors and outcome given separately. The outcome is a [survival::Surv()] object, either right-censored, `Surv(time, event)`, or counting-process, `Surv(start, stop, event)`, for time-varying covariates.

Usage

coxnet(x, ...)

# Default S3 method
coxnet(x, ...)

# S3 method for class 'data.frame'
coxnet(x, y, penalty = NULL, mixture = 1, path = NULL, ...)

# S3 method for class 'matrix'
coxnet(x, y, penalty = NULL, mixture = 1, path = NULL, ...)

# S3 method for class 'formula'
coxnet(formula, data, penalty = NULL, mixture = 1, path = NULL, ...)

# S3 method for class 'recipe'
coxnet(x, data, penalty = NULL, mixture = 1, path = NULL, ...)

Arguments

x

A data frame or matrix of predictors, or a [recipes::recipe()] whose outcome is a single `Surv` column.

...

Further arguments passed to [glmnet::glmnet()], such as `nlambda` or `cox.ties`. Not `x`, `y`, `family`, `alpha`, or `lambda`. `cox.ties` defaults to `"breslow"`, matching the Breslow baseline hazard used for survival predictions, so results don't depend on glmnet's own default (Breslow in glmnet 5.0, Efron from 5.1).

y

A [survival::Surv()] object with one element per row of `x`.

penalty

Default penalty (glmnet's `lambda`) used by `predict()` and `tidy()`. A single non-negative number, or `NULL` to require it there. glmnet's default path can end above a small `penalty` (it stops early once the deviance ratio saturates), so when `penalty` is below the path it is continued down to `penalty`; `0` gives the unpenalized fit. Penalties between path values are interpolated, as by [glmnet::predict.glmnet()].

mixture

Elastic-net mixing parameter (glmnet's `alpha`): 1 is the lasso, 0 is ridge regression.

path

Optional decreasing sequence of penalties to fit, instead of glmnet's default path. It is used as given: `predict()` and `tidy()` at a penalty below its smallest value warn and use the smallest.

formula

A formula with a `Surv()` outcome, such as `survival::Surv(tstart, tstop, status) ~ age + sex`.

data

A data frame containing the variables in `formula` or used by the recipe.

Value

A `coxnet_model` object: the glmnet fit, `penalty`, `mixture`, the training predictor matrix `x` and outcome `y` (kept so survival can be predicted at any penalty), and the hardhat `blueprint`.

Details

The whole regularization path is fit, as glmnet recommends; `penalty` only sets the default penalty for [predict()][predict.coxnet_model()] and [tidy()][tidy.coxnet_model()]. To choose `penalty` and `mixture` by cross-validation, use [cv_coxnet()].

Predictors must be numeric, and finite: missing values and `Inf`/`-Inf` in the predictors or the follow-up times are an error, because glmnet would give an infinite predictor a coefficient of 0 without a word. The formula interface expands factors into one indicator column per level, which suits penalized models; with a recipe, add `recipes::step_dummy()`. In a formula, write `survival::Surv()` unless survival is attached.

`strata()` and `offset()` are not supported in a formula, here or in [cv_coxnet()] and [nested_cv_coxnet()]: `strata()` would be fit as ordinary penalized indicator columns, with no stratified baseline hazard, and `offset()` would be dropped, so the model would not be the one the formula describes. A formula that uses either stops with an error; use [survival::coxph()] for stratified models and offsets.

See also

[predict.coxnet_model()], [tidy.coxnet_model()], [cv_coxnet()], [nested_cv_coxnet()]

Examples

if (requireNamespace("glmnet", quietly = TRUE) &&
    requireNamespace("survival", quietly = TRUE)) {
  lung <- stats::na.omit(survival::lung[, c("time", "status", "age", "sex", "ph.ecog", "wt.loss")])
  fit <- coxnet(survival::Surv(time, status) ~ ., data = lung, penalty = 0.05, mixture = 0.5)
  generics::tidy(fit)
  predict(fit, lung[1:3, ], type = "survival", eval_time = c(180, 365))$.pred[[1]]
}
#> TempleCBE: Pinned Cox tie-handling to 'breslow' (option 'templecbe.cox_ties').
#> # A tibble: 2 × 2
#>   .eval_time .pred_survival
#>        <dbl>          <dbl>
#> 1        180          0.793
#> 2        365          0.494