Advanced Survival Models

Introduction

singleEventSurvival() supports non-parametric, semi-parametric, and parametric survival estimators through a common interface. This vignette shows how to compare those models once a survival dataset has already been prepared from Eunomia.

Example Input

All examples below assume you already created a survival dataset with the internal addCohortSurvival() helper and included age and gender columns.

library(OdysseusSurvivalModule)

survivalData <- data.frame(
  subject_id = 1:8,
  time = c(15, 21, 40, 55, 60, 74, 90, 120),
  status = c(1, 0, 1, 0, 1, 0, 1, 0),
  age_years = c(44, 51, 67, 39, 73, 58, 62, 47),
  gender = c("Female", "Male", "Female", "Male", "Female", "Male", "Female", "Male")
)

Model Choices

Supported values for model are:

• "km"
• "cox"
• "weibull"
• "exponential"
• "lognormal"
• "loglogistic"

All of them return the same high-level structure: a named list with data and summary per stratum, plus overall.

Cox Model

coxFit <- singleEventSurvival(
  survivalData = survivalData,
  timeScale = "days",
  model = "cox",
  covariates = c("age_years")
)

coxFit[["overall"]]$summary
head(coxFit[["overall"]]$data)

The Cox path uses covariates when fitting the model, but the returned object is still survival-oriented. It does not expose regression coefficients or hazard ratios.

Parametric Models

weibullFit <- singleEventSurvival(
  survivalData = survivalData,
  timeScale = "days",
  model = "weibull",
  covariates = c("age_years")
)

lognormalFit <- singleEventSurvival(
  survivalData = survivalData,
  timeScale = "days",
  model = "lognormal",
  covariates = c("age_years")
)

weibullFit[["overall"]]$summary
lognormalFit[["overall"]]$summary

Parametric models also return a data table with estimated survival, hazard, and cumulative hazard evaluated on the observed event-time grid.

Comparing Models

One practical way to compare models is to extract the same summary fields from each fit.

modelNames <- c("km", "cox", "weibull", "lognormal")

fits <- lapply(modelNames, function(modelName) {
  singleEventSurvival(
    survivalData = survivalData,
    timeScale = "days",
    model = modelName,
    covariates = if (modelName == "km") NULL else c("age_years")
  )
})
names(fits) <- modelNames

comparison <- data.frame(
  model = names(fits),
  medianSurvival = vapply(fits, function(x) x[["overall"]]$summary$medianSurvival, numeric(1)),
  meanSurvival = vapply(fits, function(x) x[["overall"]]$summary$meanSurvival, numeric(1)),
  stringsAsFactors = FALSE
)

comparison

Stratified Fitting

strata accepts "gender" and "age_group". When both are supplied, the package fits them separately, not as joint interaction strata.

stratifiedFit <- singleEventSurvival(
  survivalData = survivalData,
  timeScale = "days",
  model = "weibull",
  covariates = c("age_years"),
  strata = c("gender", "age_group"),
  ageBreaks = list(c(18, 49), c(50, 64), c(65, Inf))
)

names(stratifiedFit)
stratifiedFit[["gender=Female"]]$summary
stratifiedFit[["age_group=65+"]]$summary
stratifiedFit$logrank_test_gender
stratifiedFit$logrank_test_age_group

Working with Returned Curves

Each fitted entry can be plotted from its data component.

curveData <- weibullFit[["overall"]]$data

plot(
  curveData$time,
  curveData$survival,
  type = "l",
  xlab = "Time (days)",
  ylab = "Survival probability",
  main = "Weibull survival curve"
)

When to Use Which Model

• Use "km" for descriptive, assumption-light summaries.
• Use "cox" when covariates matter but you still want a survival-curve summary.
• Use parametric models when you want a fully specified survival shape and smoother predicted curves.

Summary

The advanced usage pattern is mostly about choosing the right model value and then extracting comparable summaries from the returned list structure. ```

Summary

This vignette covered:

1. Cox Regression - Interpreting hazard ratios and multiple covariates
2. Parametric Models - Weibull, exponential, lognormal, loglogistic
3. Model Comparison - When to use each approach
4. Stratification - Gender, age, and multi-dimension strata
5. Visualization - Plotting and comparing survival curves
6. Diagnostics - Checking modeling assumptions

For getting started, see the “Getting Started” vignette.