Survival Analysis with Extended Beta-Discrete-Weibull-Logistic Model

Overview

This project implements a custom survival analysis model based on the Beta-Discrete-Weibull (BdW) distribution and extends Beta-Logistic model, originally introduced by Hubbard et al. (2021). Our extension incorporates covariate-dependent parameters through a hierarchical structure with duration dependence, enabling more expressive, personalized modeling of time-to-event data. The model supports both censored and uncensored data and is suitable for applications such as personalized risk modeling, user behavior forecasting, and event prediction.

Key Features

Extension of Hubbard et al. (2021): Builds the BdW Logistic model, allowing for duration dependence modeling.

• Custom Loss Function
  BdWLoss computes the negative log-likelihood loss for the Beta-Discrete-Weibull survival model, handling both censored and uncensored samples.

• Flexible Model Architecture
  The SurvivalModel class supports different survival distributions:

  • Weibull
  • Beta-Logistic

• Gamma Parameter Handling
  The model supports multiple strategies for handling the γ (gamma) shape parameter:

  • constant: A single gamma value for all samples.
  • partitioned: Gamma varies across defined column partitions.
  • individual: A unique gamma value for each sample.

• Survival Function Calculation
  Includes methods for computing the survival function ( S(t) ) for any time point ( t ), based on the model's learned parameters.

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Requirements

• Python 3.x
• PyTorch
• NumPy
• Matplotlib
• scikit-learn
• IPython (for interactive plots in Jupyter Notebooks)

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Model Description

The Beta-Discrete-Weibull (BdW) Logistic model integrates the flexibility of the Beta distribution with a discretized Weibull-like time-to-event distribution. It provides a likelihood-based approach to modeling survival data and supports censoring natively.

Components

• BdWLoss

  • Computes the negative log-likelihood for both censored and uncensored events.
  • Supports batching and differentiable training via PyTorch.

• SurvivalModel

  • Supports multiple survival distributions (Weibull, Beta-Logistic).
  • Includes methods for:
    • Model training
    • Evaluation and loss tracking
    • Saving/loading model checkpoints
    • Computing the survival function
    • Plotting survival curves

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Example Use Cases

• Medical Prognosis: Predicting patient survival time post-diagnosis.
• Churn Analysis: Estimating customer lifetime for subscription services.
• Industrial Maintenance: Forecasting time to equipment failure.

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Theoretical Inference

• Link

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