Add FlexibleParametricPHFitter: Royston-Parmar flexible parametric survival model

[hass-nation]

Summary

Adds FlexibleParametricPHFitter, a flexible parametric proportional hazards model that uses restricted natural cubic splines (RCS) on log(t) to model the log cumulative hazard log(H(t)) = s(log(t); γ) + x'β.

Unlike the existing Weibull/log-normal/log-logistic fitters which impose a fixed parametric shape, the Royston-Parmar model adapts the baseline hazard to the data via a spline with user-controlled knot count.

Algorithm

• Model: log(H(t|x)) = γ₀ + γ₁·log(t) + Σⱼ γⱼ₊₁·vⱼ(log(t)) + x'β, where vⱼ are restricted cubic spline basis functions.
• Estimation: MLE via L-BFGS-B (scipy) with analytical log-likelihood gradient.
• Knot placement: percentiles of log(observed event times); user-overridable.
• Penalizer: optional L2 penalty on spline coefficients γ for regularisation.

New file

lifelines/fitters/royston_parmar_fitter.py — FlexibleParametricPHFitter class

Interface

from lifelines import FlexibleParametricPHFitter

fitter = FlexibleParametricPHFitter(n_baseline_knots=4)
fitter.fit(df, duration_col="T", event_col="E", covariates=["x1", "x2"])
fitter.predict_survival_function(X, times=np.linspace(0, 10, 100))
fitter.predict_median(X)
fitter.AIC_

Tests

17 tests — shape checks, monotone survival, concordance index above chance, custom knot locations, covariate effects, AIC computation. All pass.

Reference

Royston, P. & Parmar, M. K. B. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine, 21(15), 2175–2197.