from _api_doc_utils import *AndersenGill
Counting-process Cox model for recurrent events or split risk intervals
1 Where it fits
Group: Survival / event-time models
AndersenGill extends the Cox partial likelihood to counting-process style risk intervals \((s_i, t_i]\). It is the natural entry point for recurrent events, delayed entry, and time-split records with time-varying covariates.
The fitted coefficients still live on the proportional-hazards log-risk scale, so the prediction contract mirrors CoxPH: latent log hazard ratio plus relative risk.
2 Python API
Constructor: cm.AndersenGill
Use fit(x, start, stop, event). predict_lin(x) returns the log hazard ratio and predict_relative_risk(x) returns the exponentiated risk multiplier. The default predict(x) is relative risk.
print(inspect.signature(cm.AndersenGill))cls = cm.AndersenGill
display(HTML(html_table(["Public method"], public_methods(cls))))3 Minimal example
rng=np.random.default_rng(34)
x=rng.normal(size=(180,1)); rate=0.05*np.exp(0.6*x[:,0]); t_event=rng.exponential(1.0/rate); c=rng.exponential(18,size=180); stop=np.minimum(t_event,c); event=(t_event<=c).astype(float)
start=np.zeros_like(stop)
start_long=np.concatenate([start, stop/2]); stop_long=np.concatenate([stop/2, stop]); x_long=np.vstack([x,x]); event_long=np.concatenate([np.zeros_like(event), event])
model=cm.AndersenGill(); model.fit(x_long,start_long,stop_long,event_long)
print(model.predict_lin(x[:5]))
print(model.predict(x[:5]))4 summary() contract
The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.
rng=np.random.default_rng(134); x=rng.normal(size=(90,1)); rate=0.05*np.exp(0.5*x[:,0]); te=rng.exponential(1.0/rate); c=rng.exponential(15,size=90); stop=np.minimum(te,c); event=(te<=c).astype(float)
start=np.zeros_like(stop); start_long=np.concatenate([start, stop/2]); stop_long=np.concatenate([stop/2, stop]); x_long=np.vstack([x,x]); event_long=np.concatenate([np.zeros_like(event), event])
model=cm.AndersenGill(); model.fit(x_long,start_long,stop_long,event_long)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))