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 3.10+
• Rust (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

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_data=[...],
    status_data=[...],
    covariates=[...],
    # ... other parameters
)

Person-Years Calculation

from survival import perform_pyears_calculation

result = perform_pyears_calculation(
    time_data=[...],
    weights=[...],
    # ... other parameters
)

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 30 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

API Reference

Classes

Core Models:

• AaregOptions: Configuration options for Aalen's additive regression model
• PSpline: Penalized spline class for smooth covariate effects
• CoxPHModel: Cox proportional hazards model class
• Subject: Subject data structure for Cox PH models
• ConditionalLogisticRegression: Conditional logistic regression model
• ClogitDataSet: Dataset for conditional logistic regression

Survival Curves:

• SurvFitKMOutput: Output from Kaplan-Meier survival curve fitting
• SurvfitKMOptions: Options for Kaplan-Meier fitting
• KaplanMeierConfig: Configuration for Kaplan-Meier
• SurvFitAJ: Output from Aalen-Johansen survival curve fitting
• NelsonAalenResult: Output from Nelson-Aalen estimator
• StratifiedKMResult: Output from stratified Kaplan-Meier

Parametric Models:

• SurvivalFit: Output from parametric survival regression
• SurvregConfig: Configuration for parametric survival regression
• DistributionType: Distribution types for parametric models (extreme_value, logistic, gaussian, weibull, lognormal)
• FineGrayOutput: Output from Fine-Gray competing risks model

Statistical Tests:

• SurvDiffResult: Output from survival difference tests
• LogRankResult: Output from log-rank test
• TrendTestResult: Output from trend tests
• TestResult: General test result output
• ProportionalityTest: Output from proportional hazards test
• SurvObrienResult: Output from O'Brien transformation

Validation:

• BootstrapResult: Output from bootstrap confidence interval calculations
• CVResult: Output from cross-validation
• CalibrationResult: Output from calibration analysis
• PredictionResult: Output from prediction functions
• RiskStratificationResult: Output from risk stratification
• TdAUCResult: Output from time-dependent AUC calculation

RMST and Survival Metrics:

• RMSTResult: Output from RMST calculation
• RMSTComparisonResult: Output from RMST comparison between groups
• MedianSurvivalResult: Output from median survival calculation
• CumulativeIncidenceResult: Output from cumulative incidence calculation
• NNTResult: Number needed to treat result

Landmark Analysis:

• LandmarkResult: Output from landmark analysis
• ConditionalSurvivalResult: Output from conditional survival calculation
• HazardRatioResult: Output from hazard ratio calculation
• SurvivalAtTimeResult: Output from survival at specific times
• LifeTableResult: Output from life table calculation

Power and Sample Size:

• SampleSizeResult: Output from sample size calculations
• AccrualResult: Output from accrual calculations

Utilities:

• CoxCountOutput: Output from Cox counting functions
• SplitResult: Output from time-splitting
• CondenseResult: Output from data condensing
• Surv2DataResult: Output from survival-to-data conversion
• TimelineResult: Output from timeline conversion
• IntervalResult: Output from interval calculations
• LinkFunctionParams: Link function parameters
• CchMethod: Case-cohort method specification
• CohortData: Cohort data structure

Functions

Model Fitting:

• aareg(options): Fit Aalen's additive regression model
• survreg(...): Fit parametric accelerated failure time models
• perform_cox_regression_frailty(...): Fit Cox proportional hazards model with frailty

Survival Curves:

• survfitkm(...): Fit Kaplan-Meier survival curves
• survfitkm_with_options(...): Fit Kaplan-Meier with configuration options
• survfitaj(...): Fit Aalen-Johansen survival curves (multi-state)
• nelson_aalen_estimator(...): Calculate Nelson-Aalen estimator
• stratified_kaplan_meier(...): Calculate stratified Kaplan-Meier curves
• agsurv4(...): Anderson-Gill survival calculations (version 4)
• agsurv5(...): Anderson-Gill survival calculations (version 5)

Statistical Tests:

• survdiff2(...): Perform survival difference tests (log-rank, Wilcoxon, etc.)
• logrank_test(...): Perform log-rank test
• fleming_harrington_test(...): Perform Fleming-Harrington weighted test
• logrank_trend(...): Perform log-rank trend test
• lrt_test(...): Likelihood ratio test
• wald_test_py(...): Wald test
• score_test_py(...): Score test
• ph_test(...): Proportional hazards assumption test
• survobrien(...): O'Brien transformation for survival data

Residuals:

• coxmart(...): Calculate Cox martingale residuals
• agmart(...): Calculate Anderson-Gill martingale residuals
• schoenfeld_residuals(...): Calculate Schoenfeld residuals
• cox_score_residuals(...): Calculate Cox score residuals

Concordance:

• perform_concordance1_calculation(...): Calculate concordance index (version 1)
• perform_concordance3_calculation(...): Calculate concordance index (version 3)
• perform_concordance_calculation(...): Calculate concordance index (version 5)
• compute_concordance(...): General concordance calculation

Validation:

• bootstrap_cox_ci(...): Bootstrap confidence intervals for Cox models
• bootstrap_survreg_ci(...): Bootstrap confidence intervals for parametric models
• cv_cox_concordance(...): Cross-validation for Cox model concordance
• cv_survreg_loglik(...): Cross-validation for parametric model log-likelihood
• calibration(...): Model calibration assessment
• predict_cox(...): Predictions from Cox models
• risk_stratification(...): Risk group stratification
• td_auc(...): Time-dependent AUC calculation
• brier(...): Calculate Brier score
• integrated_brier(...): Calculate integrated Brier score

RMST and Survival Metrics:

• rmst(...): Calculate restricted mean survival time
• rmst_comparison(...): Compare RMST between groups
• survival_quantile(...): Calculate survival quantiles (median, etc.)
• cumulative_incidence(...): Calculate cumulative incidence
• number_needed_to_treat(...): Calculate NNT

Landmark Analysis:

• landmark_analysis(...): Perform landmark analysis
• landmark_analysis_batch(...): Perform batch landmark analysis at multiple time points
• conditional_survival(...): Calculate conditional survival
• hazard_ratio(...): Calculate hazard ratios
• survival_at_times(...): Calculate survival at specific time points
• life_table(...): Generate life table

Power and Sample Size:

• sample_size_survival(...): Calculate required sample size
• sample_size_survival_freedman(...): Sample size using Freedman's method
• power_survival(...): Calculate statistical power
• expected_events(...): Calculate expected number of events

Utilities:

• finegray(...): Fine-Gray competing risks model data preparation
• perform_pyears_calculation(...): Calculate person-years of observation
• perform_pystep_calculation(...): Perform step calculations
• perform_pystep_simple_calculation(...): Perform simple step calculations
• perform_score_calculation(...): Calculate score statistics
• perform_agscore3_calculation(...): Calculate score statistics (version 3)
• survsplit(...): Split survival data at specified times
• survcondense(...): Condense survival data by collapsing adjacent intervals
• surv2data(...): Convert survival objects to data format
• to_timeline(...): Convert data to timeline format
• from_timeline(...): Convert from timeline format to intervals
• tmerge(...): Merge time-dependent covariates
• tmerge2(...): Merge time-dependent covariates (version 2)
• tmerge3(...): Merge time-dependent covariates (version 3)
• collapse(...): Collapse survival data
• coxcount1(...): Cox counting process calculations
• coxcount2(...): Cox counting process calculations (version 2)
• agexact(...): Exact Anderson-Gill calculations
• norisk(...): No-risk calculations
• cipoisson(...): Poisson confidence intervals
• cipoisson_exact(...): Exact Poisson confidence intervals
• cipoisson_anscombe(...): Anscombe Poisson confidence intervals
• cox_callback(...): Cox model callback for iterative fitting

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

Build the Rust library:

cargo build

Run tests:

cargo test

Format code:

cargo fmt

The codebase is organized with:

• Core routines in src/
• Tests and examples in test/
• Python bindings using PyO3

Dependencies

• PyO3 - Python bindings
• ndarray - N-dimensional arrays
• faer - Pure-Rust linear algebra
• itertools - Iterator utilities
• rayon - Parallel computation

Compatibility

• This build is for Python only. R/extendr bindings are currently disabled.
• 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.