TemporalHazard

TemporalHazard is a pure-R implementation of the multiphase parametric hazard model of Blackstone, Naftel, and Turner (1986). It decomposes the overall hazard of an event into additive temporal phases — early, constant, and late — each governed by the generalized temporal decomposition family. This structure captures real clinical risk patterns that standard single-distribution models (Weibull, log-normal) cannot represent.

Provenance and maintenance

The original SAS/C HAZARD code was developed at the University of Alabama at Birmingham (UAB). The SAS/C code and this R package are currently developed and maintained at The Cleveland Clinic Foundation. The R code in TemporalHazard was wholly developed at The Cleveland Clinic Foundation.

Why multiphase?

After cardiac surgery, the risk of death is not constant. It starts high in the immediate post-operative period (early phase), settles to a low background rate (constant phase), and eventually rises again as patients age (late phase). A single Weibull curve forces a monotone shape; a multiphase model captures all three regimes simultaneously.

The resulting survival curve closely tracks the nonparametric Kaplan-Meier estimate while providing a smooth, parametric representation that supports covariate adjustment, prediction, and extrapolation.

Key capabilities

white_check_mark: = implemented | 🚧 = planned

Feature	Status
Multi-phase hazard modeling (early, constant, late phases)	✅
Right censoring and interval censoring	✅
Repeating events (epoch decomposition)	🚧
Time-varying covariates	✅
Weighted events	🚧
Automatic stepwise covariate selection (forward, backward, stepwise)	🚧
Conservation of Events theorem for numerically stable parameter estimation	✅
Covariance and correlation matrix estimation	✅

Installation

# Install from GitHub (requires remotes or devtools)
install.packages("remotes")
remotes::install_github("ehrlinger/temporal_hazard")

TemporalHazard requires R >= 4.1.0 and depends on the survival package. Optional packages for visualization and vignettes include ggplot2, numDeriv, and quarto.

Quick start

Single-phase model

library(TemporalHazard)
data(cabgkul)

# Intercept-only Weibull on 5,880 CABG patients
fit <- hazard(
  survival::Surv(int_dead, dead) ~ 1,
  data  = cabgkul,
  dist  = "weibull",
  theta = c(mu = 0.10, nu = 1.0),
  fit   = TRUE
)
summary(fit)

Multiphase model

# Three-phase additive hazard decomposition
fit_mp <- hazard(
  survival::Surv(int_dead, dead) ~ 1,
  data   = cabgkul,
  dist   = "multiphase",
  phases = list(
    early    = hzr_phase("cdf", t_half = 0.2, nu = 1, m = 1,
                          fixed = "shapes"),
    constant = hzr_phase("constant"),
    late     = hzr_phase("g3",  tau = 1, gamma = 3, alpha = 1, eta = 1,
                          fixed = "shapes")
  ),
  fit = TRUE
)
summary(fit_mp)

# Per-phase decomposition of cumulative hazard
t_grid <- seq(0.01, max(cabgkul$int_dead) * 0.9, length.out = 200)
predict(fit_mp, newdata = data.frame(time = t_grid),
        type = "cumulative_hazard", decompose = TRUE)

Each phase is specified with hzr_phase(), which sets the temporal shape type and starting values. The optimizer estimates both the phase-specific scale parameters and shape parameters jointly. Covariates are supported via the formula interface (see vignette("fitting-hazard-models")).

Documentation

• Clinical Analysis Walkthrough — complete end-to-end workflow from Kaplan-Meier baseline through validated multivariable model.
• Getting Started — first fit-predict workflow with visualizations.
• Fitting Hazard Models — intercept-only through multiphase and multi-endpoint models.
• Prediction & Visualization — survival curves, decomposed hazard, patient-specific risk profiles.
• Inference & Diagnostics — bootstrap CIs, decile-of-risk validation, sensitivity analysis.
• Mathematical Foundations — the generalized decomposition, additive hazard model, censoring likelihood, and time-varying covariates.
• Package Architecture — internal design, golden fixtures, and dataset catalog.
• SAS-to-R Migration — statement-by-statement mapping from SAS HAZARD syntax.

Development

install.packages(c("devtools", "roxygen2", "pkgdown", "testthat"))
devtools::install_deps(dependencies = TRUE)
devtools::test()
devtools::check()

GitHub Actions runs multi-platform R CMD check on every push and pull request. Coverage is published to Codecov and the pkgdown site deploys automatically from main.

See inst/dev/DEVELOPMENT-PLAN.md for the full roadmap covering the C/SAS migration, multiphase implementation, CRAN release, and planned feature parity work. See .github/BRANCH_PROTECTION.md for recommended required-check settings that block merges when CI fails.