survival

A high-performance survival analysis library written in Rust, with a Python API powered by PyO3 and maturin.

Features

• Core survival analysis routines
• Cox proportional hazards models with frailty
• Kaplan-Meier and Aalen-Johansen (multi-state) survival curves
• Nelson-Aalen estimator
• Parametric accelerated failure time models
• Fine-Gray competing risks model
• Penalized splines (P-splines) for smooth covariate effects
• Concordance index calculations
• Person-years calculations
• Score calculations for survival models
• Residual analysis (martingale, Schoenfeld, score residuals)
• Bootstrap confidence intervals
• Cross-validation for model assessment
• Statistical tests (log-rank, likelihood ratio, Wald, score, proportional hazards)
• Sample size and power calculations
• RMST (Restricted Mean Survival Time) analysis
• Landmark analysis
• Calibration and risk stratification
• Time-dependent AUC
• Conditional logistic regression
• Time-splitting utilities

Installation

From PyPI (Recommended)

pip install survival

From Source

Prerequisites

• Python 3.11+
• Rust 1.93+ (see rustup.rs)
• maturin

Install maturin:

pip install maturin

Build and Install

Build the Python wheel:

maturin build --release

Install the wheel:

pip install target/wheels/survival-*.whl

For development:

maturin develop --release

Usage

Aalen's Additive Regression Model

from survival import AaregOptions, aareg

data = [
    [1.0, 0.0, 0.5],
    [2.0, 1.0, 1.5],
    [3.0, 0.0, 2.5],
]
variable_names = ["time", "event", "covariate1"]

# Create options with required parameters (formula, data, variable_names)
options = AaregOptions(
    formula="time + event ~ covariate1",
    data=data,
    variable_names=variable_names,
)

# Optional: modify default values via setters
# options.weights = [1.0, 1.0, 1.0]
# options.qrtol = 1e-8
# options.dfbeta = True

result = aareg(options)
print(result)

Penalized Splines (P-splines)

from survival import PSpline

x = [0.1 * i for i in range(100)]
pspline = PSpline(
    x=x,
    df=10,
    theta=1.0,
    eps=1e-6,
    method="GCV",
    boundary_knots=(0.0, 10.0),
    intercept=True,
    penalty=True,
)
pspline.fit()

Concordance Index

from survival import perform_concordance1_calculation

time_data = [1.0, 2.0, 3.0, 4.0, 5.0, 1.0, 2.0, 3.0, 4.0, 5.0]
weights = [1.0, 1.0, 1.0, 1.0, 1.0]
indices = [0, 1, 2, 3, 4]
ntree = 5

result = perform_concordance1_calculation(time_data, weights, indices, ntree)
print(f"Concordance index: {result['concordance_index']}")

Cox Regression with Frailty

from survival import perform_cox_regression_frailty

result = perform_cox_regression_frailty(
    time=[1.0, 2.0, 3.0, 4.0],
    event=[1, 1, 0, 1],
    covariates=[
        [0.2, 1.0],
        [0.1, 0.5],
        [0.4, 1.2],
        [0.3, 0.7],
    ],
    max_iter=20,
    eps=1e-5,
)
print(result["coefficients"])

Person-Years Calculation

from survival import perform_pyears_calculation

# Low-level API: inputs should match ratetable-style dimensions/cuts.
result = perform_pyears_calculation(
    time_data=[1.0, 2.0, 3.0, 1.0, 0.0, 1.0],  # [times..., events...], ny=2
    weights=[1.0, 1.0, 1.0],
    expected_dim=1,
    expected_factors=[0],
    expected_dims=[2],
    expected_cuts=[0.0, 2.0],
    expected_rates=[0.01, 0.02],
    expected_data=[0.5, 1.5, 0.5],
    observed_dim=1,
    observed_factors=[0],
    observed_dims=[2],
    observed_cuts=[0.0, 1.5, 3.0],
    method=0,
    observed_data=[0.5, 1.0, 2.0],
    do_event=1,
    ny=2,
)
print(result.keys())

Kaplan-Meier Survival Curves

from survival import survfitkm, SurvFitKMOutput

# Example survival data
time = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]
status = [1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0]  # 1 = event, 0 = censored
weights = [1.0] * len(time)  # Optional: equal weights

result = survfitkm(
    time=time,
    status=status,
    weights=weights,
    entry_times=None,  # Optional: entry times for left-truncation
    position=None,     # Optional: position flags
    reverse=False,     # Optional: reverse time order
    computation_type=0 # Optional: computation type
)

print(f"Time points: {result.time}")
print(f"Survival estimates: {result.estimate}")
print(f"Standard errors: {result.std_err}")
print(f"Number at risk: {result.n_risk}")

Fine-Gray Competing Risks Model

from survival import finegray, FineGrayOutput

# Example competing risks data
tstart = [0.0, 0.0, 0.0, 0.0]
tstop = [1.0, 2.0, 3.0, 4.0]
ctime = [0.5, 1.5, 2.5, 3.5]  # Cut points
cprob = [0.1, 0.2, 0.3, 0.4]  # Cumulative probabilities
extend = [True, True, False, False]  # Whether to extend intervals
keep = [True, True, True, True]      # Which cut points to keep

result = finegray(
    tstart=tstart,
    tstop=tstop,
    ctime=ctime,
    cprob=cprob,
    extend=extend,
    keep=keep
)

print(f"Row indices: {result.row}")
print(f"Start times: {result.start}")
print(f"End times: {result.end}")
print(f"Weights: {result.wt}")

Parametric Survival Regression (Accelerated Failure Time Models)

from survival import survreg, SurvivalFit, DistributionType

# Example survival data
time = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]
status = [1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0]  # 1 = event, 0 = censored
covariates = [
    [1.0, 2.0],
    [1.5, 2.5],
    [2.0, 3.0],
    [2.5, 3.5],
    [3.0, 4.0],
    [3.5, 4.5],
    [4.0, 5.0],
    [4.5, 5.5],
]

# Fit parametric survival model
result = survreg(
    time=time,
    status=status,
    covariates=covariates,
    weights=None,          # Optional: observation weights
    offsets=None,          # Optional: offset values
    initial_beta=None,     # Optional: initial coefficient values
    strata=None,           # Optional: stratification variable
    distribution="weibull",  # "extreme_value", "logistic", "gaussian", "weibull", or "lognormal"
    max_iter=20,          # Optional: maximum iterations
    eps=1e-5,             # Optional: convergence tolerance
    tol_chol=1e-9,        # Optional: Cholesky tolerance
)

print(f"Coefficients: {result.coefficients}")
print(f"Log-likelihood: {result.log_likelihood}")
print(f"Iterations: {result.iterations}")
print(f"Variance matrix: {result.variance_matrix}")
print(f"Convergence flag: {result.convergence_flag}")

Cox Proportional Hazards Model

from survival import CoxPHModel, Subject

# Create a Cox PH model
model = CoxPHModel()

# Or create with data
covariates = [[1.0, 2.0], [2.0, 3.0], [1.5, 2.5]]
event_times = [1.0, 2.0, 3.0]
censoring = [1, 1, 0]  # 1 = event, 0 = censored

model = CoxPHModel.new_with_data(covariates, event_times, censoring)

# Fit the model
model.fit(n_iters=10)

# Get results
print(f"Baseline hazard: {model.baseline_hazard}")
print(f"Risk scores: {model.risk_scores}")
print(f"Coefficients: {model.get_coefficients()}")

# Predict on new data
new_covariates = [[1.0, 2.0], [2.0, 3.0]]
predictions = model.predict(new_covariates)
print(f"Predictions: {predictions}")

# Calculate Brier score
brier = model.brier_score()
print(f"Brier score: {brier}")

# Compute survival curves for new covariates
new_covariates = [[1.0, 2.0], [2.0, 3.0]]
time_points = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]  # Optional: specific time points
times, survival_curves = model.survival_curve(new_covariates, time_points)
print(f"Time points: {times}")
print(f"Survival curves: {survival_curves}")  # One curve per covariate set

# Create and add subjects
subject = Subject(
    id=1,
    covariates=[1.0, 2.0],
    is_case=True,
    is_subcohort=True,
    stratum=0
)
model.add_subject(subject)

Cox Martingale Residuals

from survival import coxmart

# Example survival data
time = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]
status = [1, 1, 0, 1, 0, 1, 1, 0]  # 1 = event, 0 = censored
score = [0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2]  # Risk scores

# Calculate martingale residuals
residuals = coxmart(
    time=time,
    status=status,
    score=score,
    weights=None,      # Optional: observation weights
    strata=None,       # Optional: stratification variable
    method=0,          # Optional: method (0 = Breslow, 1 = Efron)
)

print(f"Martingale residuals: {residuals}")

Survival Difference Tests (Log-Rank Test)

from survival import survdiff2, SurvDiffResult

# Example: Compare survival between two groups
time = [1.0, 2.0, 3.0, 4.0, 5.0, 1.5, 2.5, 3.5, 4.5, 5.5]
status = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1]
group = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2]  # Group 1 and Group 2

# Perform log-rank test (rho=0 for standard log-rank)
result = survdiff2(
    time=time,
    status=status,
    group=group,
    strata=None,  # Optional: stratification variable
    rho=0.0,      # 0.0 = log-rank, 1.0 = Wilcoxon, other = generalized
)

print(f"Observed events: {result.observed}")
print(f"Expected events: {result.expected}")
print(f"Chi-squared statistic: {result.chi_squared}")
print(f"Degrees of freedom: {result.degrees_of_freedom}")
print(f"Variance matrix: {result.variance}")

Built-in Datasets

The library includes 33 classic survival analysis datasets:

from survival import load_lung, load_aml, load_veteran

# Load the lung cancer dataset
lung = load_lung()
print(f"Columns: {lung['columns']}")
print(f"Number of rows: {len(lung['data'])}")

# Load the acute myelogenous leukemia dataset
aml = load_aml()

# Load the veteran's lung cancer dataset
veteran = load_veteran()

Available datasets:

• load_lung() - NCCTG Lung Cancer Data
• load_aml() - Acute Myelogenous Leukemia Survival Data
• load_veteran() - Veterans' Administration Lung Cancer Study
• load_ovarian() - Ovarian Cancer Survival Data
• load_colon() - Colon Cancer Data
• load_pbc() - Primary Biliary Cholangitis Data
• load_cgd() - Chronic Granulomatous Disease Data
• load_bladder() - Bladder Cancer Recurrences
• load_heart() - Stanford Heart Transplant Data
• load_kidney() - Kidney Catheter Data
• load_rats() - Rat Treatment Data
• load_stanford2() - Stanford Heart Transplant Data (Extended)
• load_udca() - UDCA Clinical Trial Data
• load_myeloid() - Acute Myeloid Leukemia Clinical Trial
• load_flchain() - Free Light Chain Data
• load_transplant() - Liver Transplant Data
• load_mgus() - Monoclonal Gammopathy Data
• load_mgus2() - Monoclonal Gammopathy Data (Updated)
• load_diabetic() - Diabetic Retinopathy Data
• load_retinopathy() - Retinopathy Data
• load_gbsg() - German Breast Cancer Study Group Data
• load_rotterdam() - Rotterdam Tumor Bank Data
• load_logan() - Logan Unemployment Data
• load_nwtco() - National Wilms Tumor Study Data
• load_solder() - Solder Joint Data
• load_tobin() - Tobin's Tobit Data
• load_rats2() - Rat Tumorigenesis Data
• load_nafld() - Non-Alcoholic Fatty Liver Disease Data
• load_cgd0() - CGD Baseline Data
• load_pbcseq() - PBC Sequential Data
• load_hoel() - Hoel's Cancer Survival Data
• load_myeloma() - Myeloma Survival Data
• load_rhdnase() - rhDNase Clinical Trial Data

API Reference

The public Python surface is broad and evolves quickly. For the most accurate, version-matched signatures, use the checked-in type stubs:

• python/survival/_survival.pyi: core PyO3 bindings exposed by survival._survival.
• python/survival/sklearn_compat.py: scikit-learn-compatible estimators and streaming wrappers.
• survival.pyi: additional typing surface used by downstream tooling.

To inspect available symbols at runtime:

import survival

public_names = [name for name in dir(survival) if not name.startswith("_")]
print(public_names)

PSpline Options

The PSpline class provides penalized spline smoothing:

Constructor Parameters:

• x: Covariate vector (list of floats)
• df: Degrees of freedom (integer)
• theta: Roughness penalty (float)
• eps: Accuracy for degrees of freedom (float)
• method: Penalty method for tuning parameter selection. Supported methods:
  • "GCV" - Generalized Cross-Validation
  • "UBRE" - Unbiased Risk Estimator
  • "REML" - Restricted Maximum Likelihood
  • "AIC" - Akaike Information Criterion
  • "BIC" - Bayesian Information Criterion
• boundary_knots: Tuple of (min, max) for the spline basis
• intercept: Whether to include an intercept in the basis
• penalty: Whether or not to apply the penalty

Methods:

• fit(): Fit the spline model, returns coefficients
• predict(new_x): Predict values at new x points

Properties:

• coefficients: Fitted coefficients (None if not fitted)
• fitted: Whether the model has been fitted
• df: Degrees of freedom
• eps: Convergence tolerance

Development

Install development dependencies:

pip install -e ".[dev,test,sklearn]"

Build the extension in your current environment:

maturin develop --release

Build the Rust library:

cargo build

Run Rust tests:

cargo test

Run Python tests:

pytest python/tests -v

Format and lint:

cargo fmt
ruff check .

The codebase is organized with:

• Core routines in src/
• Rust unit/integration tests in src/tests/
• Python binding tests in python/tests/
• R validation fixtures and archived reference cases in test/
• Python bindings using PyO3

Dependencies

Primary dependencies are defined in Cargo.toml and pyproject.toml, including:

• PyO3 and maturin for Python bindings
• numpy and ndarray for array interop
• faer, rayon, and burn for numerical compute

Compatibility

• This build is for Python only. R/extendr bindings are currently disabled.
• Python 3.11+ and Rust 1.93+ are required.
• macOS users: Ensure you are using the correct Python version and have Homebrew-installed Python if using Apple Silicon.

License

This project is licensed under the MIT License - see the LICENSE file for details.