cure-sfu-project

Code accompanying "Testing and Correcting for Insufficient Follow-Up in Covariate-Dependent Cure Models: From Categorical Tests to a Heavy-Tailed Extrapolation, and Back" (Anuj Kumar, Aug 2026). The full write-up is in report/vu_project.pdf.

Project status

This repository was reconstructed from the report methodology and the available saved analyses. The numerical artifacts in the repository are the regenerated results used for the current version of the report.

The report retains its original phase numbering (Phase 1, Phase 2, Phase 5) because those labels refer to the study/report chronology. The repository itself uses a cleaner three-stage layout (01, 02, 03) so that a reader does not encounter unexplained gaps such as a missing Phase 3 or Phase 4 directory.

Repository stage	Report phase	Purpose	Status
01_sfu_tests/	Phase 1	Sufficient-follow-up hypothesis tests using cureSFUTest	Regenerated in R; verified results stored under 01_sfu_tests/results/
02_ebvk_extrapolation/	Phase 2	From-scratch EBVK extrapolation, dimensionality diagnostics, and gbex comparison	Core estimator and exploratory extensions audited
03_simulation_study/	Phase 5	Controlled simulation studies for finite-sample behavior and categorical methods	Part A and Part B regenerated

Analysis scripts

Script	What it does
01_sfu_tests/01_sfu_tests.R	Baseline SFU analysis on survival::colon; explicit 0/1 event coding and numeric covariate-matrix input
02_ebvk_extrapolation/01_synthetic_validation.R	Synthetic EBVK sanity check; 20-rep check is exploratory rather than a full Monte Carlo validation
02_ebvk_extrapolation/02_colon_age_application.R	EBVK application to colon recurrence/death data over an age grid
02_ebvk_extrapolation/03_curse_of_dimensionality.R	Multivariate product-kernel dimensionality demonstration; exploratory extension
02_ebvk_extrapolation/04_five_point_analysis.R	Reconstructed five-point covariate-space analysis
02_ebvk_extrapolation/05_bootstrap_variance.R	Bootstrap diagnostic of tail-index floor-pinning and local instability
02_ebvk_extrapolation/06_gbex_comparison.R	Small-tail gbex comparison and initialization-sensitivity diagnostic
02_ebvk_extrapolation/07_gbex_full_covariate_demo.R	Ten-covariate gbex fit; reports in-sample deviance comparison, not predictive superiority
03_simulation_study/01_bias_vs_tauc.R	Part A: bias/MSE versus censoring horizon
03_simulation_study/02_method1_vs_method2.R	Part B: parallel Method 1/Method 2 simulation study

Regenerated results

The current Part A results use the seven-point censoring-horizon sweep 4, 6, 8, 12, 20, 40, 80; the simulated uncured 99% quantile at the target covariate value is approximately 31.62.

The current Part B study uses N_REPS = 30, N_BOOT = 200, K = 2:5, and N_TOTAL = 400. Empirical power is 0.90--0.97, empirical Type-I error is 0--0.067, and Method 2 selection accuracy is 0.967--1.000 in this study. These are empirical simulation results; increasing the outer Monte Carlo count later would give more precise operating-characteristic estimates.

Layout

R/
└── beran_ebvk.R                         shared EBVK estimator core

01_sfu_tests/
├── 01_sfu_tests.R
└── results/
    └── phase1_results.rds

02_ebvk_extrapolation/
├── 01_synthetic_validation.R
├── 02_colon_age_application.R
├── 03_curse_of_dimensionality.R
├── 04_five_point_analysis.R
├── 05_bootstrap_variance.R
├── 06_gbex_comparison.R
├── 07_gbex_full_covariate_demo.R
└── results/
    ├── 01_synthetic_validation_results.rds
    ├── 02_colon_age_application_results.rds
    ├── 03_curse_of_dimensionality_results.rds
    ├── 04_five_point_results.rds
    ├── 05_bootstrap_variance_results.rds
    ├── 06_gbex_comparison_results.rds
    └── 07_gbex_full_covariate_results.rds

03_simulation_study/
├── 01_bias_vs_tauc.R
├── 02_method1_vs_method2.R
└── results/
    ├── partA_results.csv
    ├── partA_results.rds
    ├── partA_bias_vs_tauc.png
    ├── partB_results.csv
    ├── partB_results.rds
    └── partB_level_power_vs_K.png

report/
├── vu_project.tex
└── vu_project.pdf

The analysis scripts are intended to be run with the repository root as the working directory, so shared paths such as R/beran_ebvk.R resolve consistently.

Setup

Real data comes from the survival package's built-in colon dataset. Required packages include:

# CRAN packages
install.packages(c("survival", "KernSmooth", "POT", "treeClust"))

# GitHub packages
install.packages(c("remotes", "future", "furrr"))
remotes::install_github("tp-yuen/cureSFUTest")
remotes::install_github("JVelthoen/gbex")

For the parallel simulation, future, furrr, and their dependencies must be available. The Part B script automatically uses multiple workers when possible.

Reproducibility notes

Phase 1 uses bootstrap hypothesis tests. The checked result is stored in 01_sfu_tests/results/phase1_results.rds.

Phase 2's multivariate categorical/continuous product-kernel layer is an exploratory extension of the continuous-covariate EBVK construction; the report does not claim that the original EBVK asymptotic theory automatically covers this mixed-data implementation.

Phase 5 Part B records the study-level empirical power, Type-I error, and Method 2 category-selection accuracy. The present study uses 30 outer replications; that is adequate for this exploratory study, while a larger N_REPS can be used later when tighter Monte Carlo precision is desired.

Known upstream/package behaviors worked around

• cureSFUTest::sfu.cov.test() requires a numeric covariate matrix despite its potentially misleading error message.
• cureSFUTest::sfu.test() uses .Random.seed in its bootstrap path, so the analysis scripts set a seed explicitly before bootstrap-based runs.
• cureSFUTest::sfu.test() defaults to the plain Grenander estimator ("g"). This project explicitly passes method = "sg" because the study uses the smoothed-Grenander test; this is package behavior, not an upstream defect.
• gbex() takes uncensored exceedances (y) and a covariate data frame (X) rather than a status/threshold/maxit/stopcrit interface.
• gbex::predict() returns scale (s) and shape (g) rather than a type = "response" prediction.
• gbex()/predict.gbex() require real data frames with column names; bare matrices can lead to internal name mangling.
• gbex::variable_importance() requires an explicit type argument because its default vector is not resolved with match.arg() internally.

Report and repository conventions

The report's Phase 1 / Phase 2 / Phase 5 labels are retained where they are part of the written study narrative. Repository directories instead use the ordered workflow names 01_sfu_tests, 02_ebvk_extrapolation, and 03_simulation_study. This keeps the public repository navigable while preserving the report's original structure and cross-references.