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SurvBregDiv: Transfer Learning for Time-to-Event Modelling via Bregman Divergence

The SurvBregDiv package implements a Bregman-divergence-based transfer learning framework for survival analysis, enabling principled borrowing of external information while explicitly accommodating population heterogeneity between the internal study and external sources.

The package supports two primary study designs: full-cohort Cox proportional hazards models and nested case–control (NCC) designs based on conditional logistic regression on sampled risk sets.

Key Features

Three external data integration modes
Depending on the type of external data available, the package supports:

  • Individual-level data: when full covariate and outcome data from an external cohort are accessible, integration is performed via a weighted pseudo-likelihood framework.
  • Coefficient-level summaries: when only external regression coefficients 𝛃̃\widetilde{\boldsymbol{\beta}} are available, integration proceeds via Kullback–Leibler divergence penalization.
  • Coefficient + curvature summaries: when an additional positive semidefinite matrix 𝐀\mathbf{A} (e.g., information matrix or variance–covariance matrix) is provided, integration proceeds via Mahalanobis distance penalization.

Robustness to clustered and tied event times data
The package accounts for two structural features common in real-world survival data. Between-cluster heterogeneity arising from multi-site enrollment, matched designs, or hierarchical sampling is accommodated via stratified partial likelihoods, which allow the baseline hazard to vary freely across strata rather than imposing a common baseline. Tied event times frequently occur when follow-up is recorded on a coarse time scale such as daily records, scheduled clinical visits, or discretized follow-up intervals, and are handled through tie-correction methods.

High-dimensional variable selection Penalized estimation with ridge, lasso, and elastic net penalties is supported for variable selection and shrinkage, with tuning parameters selected via cross-validation as default. However, cross-validation optimizes predictive performance rather than variable selection stability, and the selected predictor set can vary considerably across repeated runs or minor perturbations of the data. For settings where a reproducible and trustworthy shortlist of predictors is needed, stability selection is also available, which aggregates variable inclusion frequencies across subsamples to identify predictors that are consistently selected regardless of which subjects happen to be in the training set.

Ensemble integration via bagged estimation
Besides cross-validated LASSO and stability selection, the package supports an ensemble strategy that combines bootstrapping, external-data integration, and model aggregation—conceptually similar to bootstrap aggregation (bagging). This bagged integration approach reduces variance and improves predictive robustness compared to relying solely on a single cross-validated integrated LASSO model.

Flexible cross-validation criteria
Model tuning supports a broad range of cross-validation criteria. Discrimination- based measures include Harrell’s concordance index (C-index) [@harrell1982evaluating], and partial likelihood–based criteria include the Verweij & Van Houwelingen (V&VH) loss and the cross-validated linear predictor loss. For full details on each criterion, see Appendix: CV Criteria.

Pathwise solution for integration weights
To select the integration weight η\eta that governs the strength of external borrowing, the package provides two complementary tuning strategies: (i) a grid search approach based on a pre-specified sequence of candidate values, and (ii) an adaptive tuning strategy using Bayesian optimization to directly explore the integration weight space, which is particularly efficient when evaluating each candidate is computationally expensive.

Installation

Note: This package is currently under active development. Please report any issues or unexpected behavior.
Requires R ≥ 4.0.0.

Install from CRAN:

install.packages("SurvBregDiv")

Or install the development version from GitHub:

require("devtools")
require("remotes")
remotes::install_github("UM-KevinHe/SurvBregDiv")

Detailed Tutorial

Full package documentation and parameter explanations: here

Getting Help

If you encounter problems or bugs, please contact us: