Unsupervised Clustering of Individualized Survival Curves

Tools for clustering individualized survival curves using the Partitioning Around Medoids (PAM) algorithm, with monotonic enforcement, optional smoothing, weighted distances (L1/L2), automatic K selection via silhouette width, prediction for new curves, basic stability checks, and plotting helpers. The method is described in El Badisy (2026) .

unsurv: Unsupervised Clustering of Individualized Survival Curves

unsurv

unsurv provides tools for unsupervised clustering of individualized survival curves using a medoid-based (PAM) algorithm. It is designed for applications where each observation is represented by a full survival probability trajectory over time, such as:

• survival model predictions
• individualized survival curves from Cox or deep learning models
• dynamic risk trajectories
• multi-omics prognostic profiles

The package provides:

• Medoid-based clustering of survival curves
• Automatic selection of number of clusters via silhouette
• Support for weighted L1 and L2 distances
• Prediction of cluster membership for new curves
• Stability assessment via resampling and Adjusted Rand Index
• Comparison of a curve-based partition against baseline partitions (scalar risk, covariate PCA) using unsurv_compare()
• Visualization tools

Installation

From GitHub

install.packages("remotes")
remotes::install_github("ielbadisy/unsurv")

From CRAN (after submission)

install.packages("unsurv")

Overview

The core function is:

unsurv()

which clusters survival curves represented as an n × m matrix:

• rows = individuals
• columns = survival probabilities at time points

Example: Clustering survival curves

library(unsurv)

set.seed(123)

n <- 100
Q <- 50
times <- seq(0, 5, length.out = Q)

rates <- c(0.2, 0.5, 0.9)
group <- sample(1:3, n, TRUE)

S <- sapply(times, function(t)
  exp(-rates[group] * t)
)

S <- S + matrix(rnorm(n * Q, 0, 0.01), nrow = n)
S[S < 0] <- 0
S[S > 1] <- 1

fit <- unsurv(S, times, K = NULL, K_max = 6)

fit
#> unsurv (PAM) fit
#>   K:3
#>   distance:L2 silhouette_mean:0.915
#>   n:100 Q:50

Plot cluster medoids

plot(fit)

Each line represents the medoid survival curve for a cluster.

Predict cluster membership for new curves

predict(fit, S[1:5, ])
#> [1] 1 1 1 2 1

Stability assessment

Cluster stability can be evaluated using resampling:

stab <- unsurv_stability(
  S, times, fit,
  B = 20,
  frac = 0.7,
  mode = "subsample"
)

stab$mean
#> [1] 0.9384743

Higher values indicate more stable clustering.

Using ggplot visualization

library(ggplot2)
library(unsurv)
autoplot(fit)

Methodological details

Given survival curves:

$$ S_i(t_1), S_i(t_2), \dots, S_i(t_m) $$

the algorithm:

1. Optionally enforces monotonicity
2. Applies weighted feature transformation
3. Computes pairwise distances (L1 or L2)
4. Applies PAM clustering
5. Selects optimal K via silhouette (if not specified)

Cluster medoids represent prototype survival profiles.

Typical workflow

fit <- unsurv(S, times)

clusters <- fit$clusters

pred <- predict(fit, new_S)

stab <- unsurv_stability(S, times, fit)

Vignette

A full walkthrough (simulated mechanics plus the paper’s METABRIC worked example with deep-learning survival predictions) is available in the vignette:

vignette("unsurv-intro", package = "unsurv")

Applications

unsurv is useful for:

• Patient stratification
• Risk phenotype discovery
• Prognostic subgroup identification
• Deep survival model interpretation
• Precision medicine

Relationship to other methods

Unlike clustering on covariates, unsurv clusters on the survival function itself, enabling:

• Direct interpretation of risk trajectories
• Robust clustering independent of feature space
• Model-agnostic analysis

Package structure

Core functions:

Citation

If you use unsurv, please cite:

citation("unsurv")
#> To cite package 'unsurv' in publications use:
#> 
#>   El Badisy I (2026). "unsurv: clustering individualized survival
#>   curves." _Bioinformatics Advances_, *6*(1), vbag218.
#>   doi:10.1093/bioadv/vbag218 <https://doi.org/10.1093/bioadv/vbag218>.
#> 
#> A BibTeX entry for LaTeX users is
#> 
#>   @Article{,
#>     title = {unsurv: clustering individualized survival curves},
#>     author = {Imad {El Badisy}},
#>     journal = {Bioinformatics Advances},
#>     year = {2026},
#>     volume = {6},
#>     number = {1},
#>     pages = {vbag218},
#>     doi = {10.1093/bioadv/vbag218},
#>     publisher = {Oxford University Press},
#>   }

License

MIT License © Imad El Badisy