---
title: "SEEDS: Semi-supervised Estimation of Event Rate with Doubly-censored Survival Data"
output: pdf_document
date: "2025-09-16"
---

# SEEDS: Semi-supervised Estimation of Event Rate with Doubly-censored Survival Data

This repository contains the R implementation of the **SEEDS** (Semi-supervised Estimation of Event Rate with Doubly-censored Survival Data) method, as described in the manuscript:

> Wang, Y., Zhou, Q., Cai, T., & Wang, X. (2025). *Semi-supervised Estimation of Event Rate with Doubly-censored Survival Data*. Submitted to the *Annals of Applied Statistics*.

SEEDS is a novel semi-supervised method designed for estimating survival rates from doubly-censored survival data, commonly encountered in Electronic Health Records (EHR). It combines a small set of labeled observations (exact event times) with a larger set of unlabeled observations (surrogate proxies, e.g., diagnostic codes) to improve estimation efficiency. The method constructs three estimators (Direct, Left, Right) and optimally combines them using cross-validation, offering both semi-supervised and intrinsic versions for enhanced performance.

## Key Features
- Handles doubly-censored data with time-dependent covariates and surrogate variables.
- Implements semi-supervised and intrinsic estimators for Direct, Left, and Right censoring.
- Uses cross-validation to determine optimal weights for combining estimators.
- Provides variance estimation and confidence intervals.
- Includes simulation scripts for Cox and logistic models with varying censoring rates and correlations.
- Compares SEEDS against baseline methods: Classical Supervised Learning (CSL) and Self-Consistency (SC).

## Installation

The code requires R (version 4.0 or higher). Install the necessary packages by running the following in R:

# Define required packages
required_packages <- c(
  "survival", "dplyr", "ggplot2", "tidyr", "parallel", 
  "foreach", "doParallel", "knitr", "kableExtra", "gridExtra", 
  "viridis", "mgcv", "splines", "dblcens", "pracma", "MASS",
  "ncvreg"
)

# Install and load packages
install_and_load_packages <- function(packages) {
  for (pkg in packages) {
    if (!requireNamespace(pkg, quietly = TRUE)) {
      cat("Installing package:", pkg, "\n")
      install.packages(pkg, dependencies = TRUE)
    }
    library(pkg, character.only = TRUE)
  }
}

install_and_load_packages(required_packages)

All dependencies are available on CRAN, ensuring straightforward setup.

Repository Structure

SEEDS/
├── README.Rmd                 # This file
├── main.R                     # Main simulation script for running comparisons
├── src/
    ├── utils/
    │   ├── HelperFunctions.R  # Mathematical and utility functions (e.g., Expit, kernel smoothing)
    │   └── CV_function.R      # Cross-validation for optimal estimator combination
│   ├── estimation/
│   │   ├── Beta_estimate.R    # Parameter estimation (semi-supervised and intrinsic)
│   │   └── NewtonCLseh.R      # Newton-Raphson optimization with constraints
│   ├── methods/
│   │   ├── IntrSSL_est_ind.R  # SEEDS main estimation function
│   │   ├── Supervised_est.R   # Classical Supervised Learning (CSL) method
│   │   └── d011_new.R         # Self-Consistency (SC) method
│   ├── simulation/
│   │   ├── GenerateCoxtcor.R  # Cox model data generation
│   │   └── Generatelogbtcor.R # Logistic model data generation
├── data/
│   └── simulation_results/    # Output directory for simulation results (auto-generated)
└── docs/
    └── Supplementary.pdf      # Supplementary materials (simulation details, results)

Usage

Running Simulations

The main.R script runs simulations to compare SEEDS, CSL, and SC across different settings (Cox/logistic models, varying censoring rates, and correlations). It generates data, performs estimations, and saves results in data/simulation_results/.

To run simulations:

# Set working directory to the repository root
setwd("path/to/SEEDS")

# Source all necessary scripts
source("src/utils/HelperFunctions.R")
source("src/estimation/Beta_estimate.R")
source("src/estimation/NewtonCLseh.R")
source("src/methods/Supervised_est.R")
source("src/utils/CV_function.R")
source("src/methods/IntrSSL_est_ind.R")
source("src/methods/d011_new.R")
source("src/simulation/Generatelogbtcor.R")
source("src/simulation/GenerateCoxtcor.R")

# Run the main simulation script
source("main.R")  # Modify 'setting' (1 or 2) and 'seed' in main.R as needed

Key Parameters (in main.R):
setting: 1 (Cox model) or 2 (Logistic model).
seed: Random seed for reproducibility.
N: Number of unlabeled observations (default: 5000).
n: Number of labeled observations (default: 250 for setting 1, 100 for setting 2).
num_sims: Number of simulation replicates (default: 500).

Output: Results are saved as .RData files (e.g., setting1seed1.RData) containing survival estimates, standard deviations, and combination weights for SEEDS, CSL, and SC.


Applying SEEDS to Custom Data
To apply SEEDS to your own doubly-censored dataset, use IntrSSL_est() from IntrSSL_est_ind.R:
# Example usage
result <- IntrSSL_est(
  time = seq(0.5, 3.0, length.out = 50),  # Evaluation time points
  base_cov = matrix(rnorm(1000 * 2), ncol = 2),  # Baseline covariates
  cova_tim = your_time_dependent_times,  # List of time-dependent covariate times
  cova_ct = your_time_dependent_values,  # List of time-dependent covariate values
  lcen_ct = your_left_censoring_covariates,  # Left censoring covariates
  rcen_ct = your_right_censoring_covariates,  # Right censoring covariates
  xstar_all = your_surrogate_times,  # Surrogate observations
  deltastar_indv = your_surrogate_indicators,  # Surrogate censoring indicators (2 columns)
  label_id = your_labeled_indices,  # Indices of labeled observations
  lcen_all = your_left_censoring_times,  # Left censoring times (all subjects)
  rcen_all = your_right_censoring_times,  # Right censoring times (all subjects)
  obse = your_observed_times,  # Observed survival times (labeled)
  ldelt = your_left_indicators,  # Left censoring indicators
  rdelt = your_right_indicators,  # Right censoring indicators
  lh_labeled = 0.1,  # Left bandwidth for labeled data
  lh_unlabeled = 0.15,  # Left bandwidth for unlabeled data
  rh_labeled = 0.1,  # Right bandwidth for labeled data
  rh_unlabeled = 0.15,  # Right bandwidth for unlabeled data
  num_folds = 10  # Number of CV folds
)

# Output: 19 x length(time) matrix
# Rows: Survival estimates (Direct/Left/Right/Combined, SS/ID), SDs, and weights
print(result)
See IntrSSL_est_ind.R for detailed parameter descriptions.

Simulation Settings
The code supports two main settings in main.R:

Setting 1 (Cox model): Generates data with a Cox proportional hazards model, T* ~ Uniform(0, 0.5), and time-dependent covariates via a Poisson process (rate=0.1). Censoring: ~25% left, ~30% right.

Setting 2 (Logistic model): Uses a logistic regression model, T* ~ Uniform(-1, 1), baseline covariate Z ~ Normal(5, 1), and similar covariate/censoring structure.

Additional settings (e.g., varying correlations or censoring rates) are detailed in the supplementary materials (docs/Supplementary.pdf).