fast-cindex

Fast O(N log N) concordance index (C-index) for survival analysis, with parallel Numba-accelerated bootstrapping.

Installation

pip install fast-cindex

Usage

import numpy as np
from lifelines import CoxPHFitter
from lifelines.datasets import load_rossi
from sklearn.model_selection import train_test_split
from fast_cindex import cindex, bootstrap_cindex, compare_cindex

# Load dataset and fit a Cox model
rossi = load_rossi()
train, test = train_test_split(rossi, test_size=0.2, random_state=42)

cph = CoxPHFitter()
cph.fit(train, duration_col='week', event_col='arrest')

times  = test['week'].values
events = test['arrest'].values
scores = -cph.predict_partial_hazard(test).values  # higher = higher predicted risk

Single C-index

ci = cindex(times, scores, events)
print(f"C-index: {ci:.3f}")

Bootstrap confidence interval

boot = bootstrap_cindex(times, scores, events, n_bootstraps=1000, seed=42)
lo, hi = np.percentile(boot, [2.5, 97.5])
print(f"C-index: {boot.mean():.3f} (95% CI {lo:.3f}–{hi:.3f})")

Compare two models

Bootstrap samples are shared across both models, enabling a valid paired test.

boot1, boot2 = compare_cindex(times, events, scores1, scores2, n_bootstraps=1000, seed=42)

diff = boot1 - boot2
p_value = np.mean(diff <= 0)   # one-sided: P(model1 ≤ model2)
print(f"Mean difference: {diff.mean():.4f}, p = {p_value:.4f}")

API

Score convention: higher score = higher predicted risk (e.g. a predicted hazard or negative predicted survival time).

Benchmarks

Tested on the Rossi recidivism dataset (replicated to the target size), 1000 bootstrap iterations, Apple M-series CPU.

Single C-index

Note: the 100-sample run is dominated by Numba JIT compilation on first call. Subsequent calls are fast.

Bootstrap (1000 iterations)

To reproduce:

pip install lifelines scikit-learn
python benchmark.py

import time
import numpy as np
import pandas as pd
from lifelines.utils import concordance_index
from lifelines.datasets import load_rossi
from lifelines import CoxPHFitter
from sklearn.model_selection import train_test_split
from fast_cindex import cindex, bootstrap_cindex

SIZES = [100, 1000, 5000, 10000]
N_BOOTSTRAP = 1000

# Build a large base dataset to sample from
rossi = load_rossi()
while len(rossi) < max(SIZES):
    rossi = pd.concat([rossi, rossi], axis=0)
rossi = rossi.reset_index(drop=True).iloc[:max(SIZES)]

# Fit model once on the full dataset
cph = CoxPHFitter()
train, _ = train_test_split(rossi, test_size=0.2, random_state=42)
cph.fit(train, duration_col='week', event_col='arrest')

risk_scores = -cph.predict_partial_hazard(rossi).values
durations = rossi['week'].values
events = rossi['arrest'].values

print(f"{'Size':>8}  {'lifelines cindex':>18}  {'fast cindex':>14}  {'speedup':>10}")
print(f"{'':->8}  {'':->18}  {'':->14}  {'':->10}")

for n in SIZES:
    t = durations[:n]
    e = events[:n]
    r = risk_scores[:n]

    start = time.perf_counter()
    concordance_index(t, r, e.astype(bool))
    lifelines_time = time.perf_counter() - start

    start = time.perf_counter()
    cindex(t, r, e)
    fast_time = time.perf_counter() - start

    print(f"{n:>8}  {lifelines_time:>16.4f}s  {fast_time:>12.4f}s  {lifelines_time/fast_time:>9.1f}x")

print()
print(f"{'Size':>8}  {'lifelines bootstrap':>21}  {'fast bootstrap':>17}  {'speedup':>10}")
print(f"{'':->8}  {'':->21}  {'':->17}  {'':->10}")

for n in SIZES:
    t = durations[:n]
    e = events[:n]
    r = risk_scores[:n]

    rng = np.random.RandomState(42)
    start = time.perf_counter()
    for _ in range(N_BOOTSTRAP):
        idx = rng.choice(n, n, replace=True)
        concordance_index(t[idx], r[idx], e[idx].astype(bool))
    lifelines_time = time.perf_counter() - start

    start = time.perf_counter()
    bootstrap_cindex(t, r, e, n_bootstraps=N_BOOTSTRAP, seed=42)
    fast_time = time.perf_counter() - start

    print(f"{n:>8}  {lifelines_time:>19.4f}s  {fast_time:>15.4f}s  {lifelines_time/fast_time:>9.1f}x")

License

Apache 2.0