IPCRidge

IPC-weighted ridge regression for survival data.

Usage

IPCRidge(
    alpha=1.0,
    *,
    standardize=True,
)

A linear survival model that corrects for censoring bias via inverse-probability-of-censoring (IPC) reweighting rather than the Cox partial likelihood. The model fits a weighted ridge regression on observed (uncensored) log-times:

\hat{\beta} = \arg\min_{\beta} \sum_{i:\,\delta_i=1} w_i \bigl(\log T_i - X_i \beta\bigr)^2 + \alpha \|\beta\|_2^2

where w_i = 1 / \hat{G}(T_i^-) are IPC weights from the Kaplan-Meier estimate of the censoring distribution. This eliminates censoring bias from the least-squares objective without assuming proportional hazards.

Centering and optional standardization are applied before fitting, and coefficients are returned on the original covariate scale. The intercept is always estimated.

Parameters

alpha: float = 1.0: Ridge penalty strength. 0 gives unpenalized IPC-weighted OLS.
standardize: bool = True: Standardize covariates to unit variance before penalizing (default True). Coefficients are returned on the original scale.

Examples

Fit an IPC-weighted ridge on the lung dataset:

import greenwood as gw

lung = gw.load_dataset("lung", backend="polars")

ridge = gw.IPCRidge(alpha=1.0).fit("Surv(time, status) ~ age + sex", data=lung)
ridge

IPCRidge (IPC-weighted ridge, alpha=1.0)

                 coef
(Intercept)     6.107
age          -0.02134
sex             0.573

n = 228, events = 165 (used for fitting)

Methods

Name	Description
fit()	Fit the IPC-weighted ridge regression to survival data.
predict()	Predict from the fitted IPC-weighted ridge model.
to_frame()	Return the coefficient table as a DataFrame.

fit()

Fit the IPC-weighted ridge regression to survival data.

Usage

Source

fit(
    surv,
    covariates=None,
    *,
    data=None,
)

Only uncensored subjects contribute to the fit. Each is weighted by 1/\hat{G}(T_i^-) from the Kaplan-Meier censoring estimate, so subjects who experienced events when censoring was heavy receive greater influence.

Parameters

surv: Surv | Outcome | str: A right-censored Surv response, built with gw.Surv(time=..., event=...). An Outcome or a formula string such as 'Surv(time, status == 2) ~ age + sex' is also accepted, with its columns read from data. The right-hand side sets covariates.
covariates: Any = None: A dataframe (pandas or polars), a 2-D array, or a formula string (e.g., "age + sex") evaluated against data. A list of column names in data also works.
data: Any = None: A data frame (pandas, Polars, PyArrow, DuckDB, a lazy frame, …) holding the columns named by the response and covariates. When surv is an Outcome or a formula, rows with a missing value in any column used are dropped before fitting. Covariate formula strings and lists of column names are also resolved here.

Returns

IPCRidge: The fitted estimator with cached coefficient arrays.

predict()

Predict from the fitted IPC-weighted ridge model.

Usage

Source

predict(
    newdata=None,
    *,
    type="lp",
)

Parameters

newdata: Any = None

Covariate values for prediction. None uses the training data. A data frame may also hold other columns. The covariates are picked out by name and coded as they were at fit time, so the frame the model was fit on can be passed as is.

type: str = "lp"

Prediction type:

"lp": the linear predictor \hat{\beta}_0 + X\hat{\beta} (predicted log-time). Higher values indicate longer expected survival.
"response": \exp(\text{lp}), predicted survival time on the original scale.

Returns

ndarray: Predicted values, shape (n_subjects,).

to_frame()

Return the coefficient table as a DataFrame.

Usage

Source

to_frame(
    *,
    format=None,
)

Parameters

format: str | None = None: Output format: None (default), "pandas", "polars", or "pyarrow".

Returns

DataFrame: Columns: term, estimate.