On Harmonic Oscillator Hazard Functions

Overview

This repository contains the R code and data used to reproduce the results in:

Christen, J.A. and Rubio, F.J. (2025). On harmonic oscillator hazard functions. Statistics & Probability Letters 217: 110304. DOI: 10.1016/j.spl.2024.110304 | Preprint (arXiv)

The harmonic oscillator hazard (HOH) model is a parametric survival model constructed by enforcing positivity in the solution to the damped harmonic oscillator differential equation. This produces a flexible hazard function capable of capturing a wide range of shapes, including bathtub, unimodal, and monotone, that arise naturally in applications such as cancer epidemiology and reliability analysis, while retaining a mechanistic physical interpretation.

Repository structure

HOH/
├── routinesHO.R     # Core functions required by all other scripts
├── appHO.R          # Shiny app to interactively visualise HOH shapes
├── Example.R        # Real data application from Christen & Rubio (2025)
├── Example.RData    # Saved output of Example.R
├── Example.Rmd      # R Markdown source for the real data application
├── Example.html     # Rendered tutorial with code and outputs
├── bound.R          # Upper bounds from the proof of Proposition 2
└── references.bib   # Bibliography

Requirements

The following R packages are required. Install them before running any script:

install.packages(c("shiny", "survival", "numDeriv"))

Source the core routines before running the example or the Shiny app:

source("routinesHO.R")

Shiny app

appHO.R launches an interactive Shiny app for exploring the shape of the HOH hazard function across different parameter values:

library(shiny)
source("appHO.R")

Tutorial

• On harmonic oscillator hazard functions — illustrative RPubs tutorial accompanying the paper
• Example.html — rendered R Markdown tutorial available directly in this repository

Related resources

• ODESurv — broader framework for survival modelling via ordinary differential equations
• SurvMODE — hazard-based distributional regression via ODEs (R and Julia)
• HazReg — parametric hazard-based regression models (R package)

Citation

If you use this code, please cite:

@article{christen:2025,
  author  = {Christen, J.A. and Rubio, F.J.},
  title   = {On harmonic oscillator hazard functions},
  journal = {Statistics \& Probability Letters},
  volume  = {217},
  pages   = {110304},
  year    = {2025},
  doi     = {10.1016/j.spl.2024.110304}
}