SRtools

A comprehensive Python library for analyzing mortality and aging data using the Saturating Removal (SR) model. The SR model is a stochastic differential equation model that describes aging as a process of damage accumulation and removal, providing a mechanistic framework for understanding survival and mortality patterns.

Overview

SRtools provides tools for:

• SR Model Simulation: Simulate aging trajectories using various SR model variants
• Survival Analysis: Analyze death times, survival curves, and hazard functions
• Parameter Estimation: Fit SR model parameters to data using maximum likelihood and Bayesian methods
• Life Table Analysis: Work with aggregate survival data from life tables
• Parametric Fitting: Fit Weibull, Gompertz, and Makeham-Gompertz distributions to survival data
• Bayesian Inference: Perform MCMC sampling for parameter estimation and uncertainty quantification

Installation

Requirements

• Python 3.10+
• NumPy >= 1.21.0
• Pandas >= 1.3.0
• SciPy >= 1.7.0
• Matplotlib >= 3.4.0
• And other dependencies (see requirements.txt)

Install from source

git clone <repository-url>
cd SRtools
pip install -e ".[dev]"

Install from PyPI

The PyPI distribution name is srtools-aging because srtools is already used by an unrelated project. The Python import name remains SRtools:

pip install srtools-aging

Or install dependencies directly:

pip install -r requirements.txt

Web app

The Streamlit web app lives in app/ and is intentionally separate from the core package. Streamlit is not a dependency of SRtools.

For a deployed/stable app environment:

pip install -r app/requirements.txt
streamlit run app/streamlit_app.py

For local development against this checkout:

pip install -e ".[app]"
streamlit run app/streamlit_app.py

Quick Start

Basic SR Model Simulation

from SRtools import SR_lf

# Create an SR model simulation
# Parameters: eta, beta, kappa, epsilon, xc, npeople, nsteps, t_end
model = SR_lf(
    eta=0.5,      # Damage production rate
    beta=50,     # Damage removal parameter
    kappa=0.5,    # Removal saturation parameter
    epsilon=50, # Noise parameter
    xc=17.0,      # Critical damage threshold
    npeople=10000,
    nsteps=5000,
    t_end=110
)

# Access survival and hazard functions
survival_times, survival_values = model.getSurvival()
hazard_times, hazard_values = model.getHazard()

# Plot survival curve
model.plotSurvival()

Working with Death Times Data

from SRtools import Dataset
import numpy as np

# Create dataset from death times
death_times = np.array([...])  # Your death times data
events = np.ones_like(death_times)  # Event indicators (1 = death, 0 = censored)

dataset = Dataset(death_times, events)

# Calculate survival and hazard
survival_times, survival_values = dataset.getSurvival()
hazard_times, hazard_values = dataset.getHazard()

# Plot results
dataset.plotSurvival()
dataset.plotHazard()

Life Table Analysis

from SRtools import Life_table
import numpy as np

# Create life table from age bins and number alive
ages = np.array([0, 10, 20, 30, 40, 50, 60, 70, 80, 90])
n_alive = np.array([1000, 950, 900, 800, 600, 400, 200, 80, 20, 2])

life_table = Life_table(ages, n_alive)

# Access survival and hazard
survival_times, survival_values = life_table.getSurvival()
hazard_times, hazard_values = life_table.getHazard()

Bayesian Parameter Estimation

from SRtools import Dataset
from SRtools.sr_mcmc import run_mcmc

# Load your data
dataset = Dataset(death_times, events)

# Run MCMC to estimate SR model parameters
# See sr_mcmc.py for detailed usage

Core Components

Dataset Classes

• Dataset: Base class for working with individual death times data
• DatasetCollection: Manage multiple datasets
• Life_table: Work with aggregate survival data from life tables

SR Model Variants

• SR: Standard SR model with full parameter set and parent class for advanced models.

It is recommended to work with these:

• SR_Hetro: SR model with population heterogeneity (most advanced)
• SR_lf: SR model integrated with lifelines library (recommended for general use)

Parametric Fitters

• WeibullFitter: Fit Weibull distribution to survival data
• ExtendedWeibullFitter: Extended Weibull fitting
• GompertzFitter: Fit Gompertz distribution
• MakehamGompertzFitter: Fit Makeham-Gompertz distribution
• GompertzMakehamFitter: Alternative Makeham-Gompertz fitting

Bayesian Analysis

• Posterior: Analyze samples from MCMC to calculate and analyze posterior probabilities
• JointPosterior: Joint posterior analysis on several MCMC runs
• sr_mcmc: MCMC sampling functionality using emcee and some supporting utilities and analysis

Utilities

• Guess: Simple tool for inital parameter estimation
• plotting_utils: Visualization utilities for the comparison of parameters and CI's estimated from different runs
• distance_metrics: Distance metrics for model comparison (most of them are likelihoods and not distances)
• readResults: Read and analyze saved results
• readResultsBaysian: Read Bayesian analysis results

SR Model Description

The SR model describes the evolution of damage (X) over time:

dX/dt = eta * t - (beta * X) / (X + kappa) + sqrt(2 * epsilon) * xi

Where:

• eta: Damage production rate (linear growth)
• beta: Damage removal parameter
• kappa: Removal saturation parameter
• epsilon: Stochastic noise parameter
• xc: Critical damage threshold (death occurs when X > xc)
• xi: White noise (Wiener process)

Death occurs when the damage X exceeds the critical threshold xc.

Key Features

• Flexible Simulation: Multiple SR model variants and simulation methods
• Efficient Computation: Uses Numba JIT compilation for performance
• Comprehensive Analysis: Survival curves, hazard functions, cumulative hazards
• Statistical Fitting: Maximum likelihood and Bayesian parameter estimation
• Visualization: Built-in plotting functions for survival and hazard analysis
• Life Table Support: Work with aggregate survival data
• MCMC Integration: Full Bayesian inference using emcee

Documentation

For detailed API documentation, see the docstrings in individual modules. Key modules include:

• SRmodellib.py: Core SR model implementation
• deathTimesDataSet.py: Dataset handling and survival analysis
• life_table.py: Life table analysis
• sr_mcmc.py: MCMC sampling and Bayesian inference
• weibullFitter.py: Weibull distribution fitting
• makhamGompertzFitter.py: Gompertz-Makeham fitting

Deprecated Modules

The following modules are deprecated and should not be used in new code:

• probability.py
• prior_gen.py
• life_table_old.py

Use life_table.py instead of life_table_old.py. For prior generation and probability calculations, use the functionality in sr_mcmc.py and samples_utils.py.

Examples

See the ... notebooks for example usage.

Citation

If you use SRtools in your research, please cite the relevant papers on the SR model of aging:

• 1. Naveh Raz, Yifan Yang, Glen Pridham et al. A damage accumulation model reveals strategies of aging across species, 08 July 2025, PREPRINT (Version 1) available at Research Square [https://doi.org/10.21203/rs.3.rs-6946440/v1]
• 2. Karin, O., Agrawal, A., Porat, Z. et al. Senescent cell turnover slows with age providing an explanation for the Gompertz law. Nat Commun 10, 5495 (2019). https://doi.org/10.1038/s41467-019-13192-4

License

MIT. See LICENSE.

Contributing

[Add contributing guidelines here]

Contact

Naveh.Raz@weizmann.ac.il