Risk Bridge

Risk Bridge is a Python package for estimating transportable binary-risk prediction models when the available cohorts do not share identical covariate support or when observational clinic data is subject to selection bias and calibration drift.

It combines propensity-score matching, reference-cohort calibration, joint maximum likelihood estimation, and constrained maximum likelihood estimation (cMLE) into reproducible simulation and user-data workflows.

Package title: Risk Bridging through Constrained MLE.

📖 Documentation Website: https://saehwanpark.github.io/risk-bridge/

Motivation

In clinical risk prediction, models fitted on specialized clinic registries or electronic health record (EHR) databases often fail when deployed to external target populations. This calibration breakdown occurs because:

• Covariate distributions $P(X)$ drift across health systems.
• High-value intermediate risk markers $Z$ (e.g. imaging, biopsies, or genomic scores) are measured in the source study but missing in the broader target registry.
• Clinic cohorts reflect non-random testing, referral enrichment, and selection bias.

Standard unconstrained Maximum Likelihood Estimation (MLE) on source data leads to miscalibrated risk predictions in the target cohort. Risk Bridge provides a principled way to constrain model fitting using calibration information from a representative external reference study, restoring well-calibrated probabilities.

Foundation Papers

• Cao, Y., Ma, W., Zhao, G., McCarthy, A. M., & Chen, J. (2024). A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes. Lifetime Data Analysis, 30(3), 624–648. DOI: 10.1007/s10985-024-09623-6

• Wang, L., & Chen, J. (2026). Developing Accurate Risk Prediction Using Biased Electronic Health Record Data. Manuscript in preparation.

Key Features

• Simulated & Applied Workflows: Built-in Scenario 1–3 data generators for methodological experiments and a streamlined pipeline for prepared user CSV datasets.
• Dual Analysis Paths: Evaluates Propensity Score Matched (PSM) source samples alongside unadjusted Random Sampling (RS) baselines.
• Hierarchical Solver Ladder: Warm starts from unconstrained BFGS, transitions to interior-point constrained optimization (trust-constr) with analytic gradients and constraint Jacobians, and falls back to SLSQP when needed.
• Rigorous Calibration Diagnostics: Exports Calibration-in-the-Large (CITL), calibration slope, observed-to-expected (O/E) ratio, Brier score, and stratum-specific moment residuals.
• Reproducible Output Contract: Strict, versioned tabular output contract (schema_version=1.1.0) with comprehensive execution metadata and an environment.json sidecar.
• Public Python API & CLI: High-level typed configurations (UserDataRunConfig, RunConfig) and the risk-bridge command-line tool.

Installation

From PyPI (Standard Installation)

uv add risk-bridge
# or: pip install risk-bridge

The public-safe reproduction case runners are included in the wheel and source distribution. After installation, invoke them directly with python -m cases.<case>.<runner>.

From Source Repository

git clone https://github.com/SaehwanPark/risk-bridge.git
cd risk-bridge
uv sync --locked

Run the test suite and verify typing:

uv run pytest
uv run basedpyright

Quickstart

1. Simulated Scenario Run (CLI)

uv run risk-bridge \
  --mode simulated \
  --scenario 1 \
  --nsim 2 \
  --n-target 1000 \
  --n-source 500 \
  --n-reference 1000 \
  --sample-size 100 \
  --output-root data \
  --run-label quickstart

2. User-Data Cohort Run (CLI)

uv run risk-bridge \
  --mode user-data \
  --target-csv examples/target.csv \
  --source-csv examples/source.csv \
  --reference-csv examples/reference.csv \
  --x-cols X1,X2,X3,X4 \
  --y-col caseY \
  --z-origin-col zOrigin \
  --z-cat-col zCat \
  --sample-size 500 \
  --nsim 1 \
  --output-root data \
  --run-label user_data

For a five-minute walkthrough, see QUICKSTART.md or the Online Quickstart Tutorial.

Library Usage

from pathlib import Path
import polars as pl
from risk_bridge import UserDataRunConfig, UserDataSchema, run_user_data

target_df = pl.read_csv("examples/target.csv")
source_df = pl.read_csv("examples/source.csv")
reference_df = pl.read_csv("examples/reference.csv")

schema = UserDataSchema(
    x_cols=("X1", "X2", "X3", "X4"),
    y_col="caseY",
    z_origin_col="zOrigin",
    z_cat_col="zCat",
)

config = UserDataRunConfig(
    target_df=target_df,
    source_df=source_df,
    reference_df=reference_df,
    schema=schema,
    sample_size=500,
    output_root="data",
    run_label="applied_run",
)

output_dir: Path = run_user_data(config)
print(f"Results written to: {output_dir}")

Outputs

Each run writes a timestamped directory under output_root containing:

• final/run_metadata.csv: Full configuration parameters, seeds, and schema version (1.1.0).
• final/fit_diagnostics.csv: Optimizer convergence status, objective values, and feasibility violations.
• final/est_cml_psm.csv: cMLE parameter estimates ($\alpha, \beta_X, \beta_Z, \gamma_0, \gamma_X, \sigma$).
• final/calibration_metrics.csv: Target cohort CITL, slope, O/E ratio, and Brier score.
• final/calibration_residuals.csv: Stratum-specific post-fit calibration residuals.
• final/roc_metrics.csv: Area under the ROC curve (AUC).
• final/accuracy_metrics.csv: Sensitivity, specificity, and precision at target FPR.
• final/environment.json: Reproducibility metadata and numerical tolerance contract.

Replication Cases

Risk Bridge ships with four privacy-safe reproduction case studies:

• python -m cases.numerical_validation.run_suite
• python -m cases.external_calibration_validation.run_suite --profile smoke --condition matched
• python -m cases.synthetic_transport_example.run_case
• python -m cases.runtime_support_scaling.run_scaling --profile smoke

See REPRODUCTION.md and the Online Reproduction Runbook for instructions.

Documentation Links

• Documentation Website — Full online user guide, mathematical derivations, and tutorials
• Quickstart Guide — Fast setup and verification
• User Guide — Comprehensive guide to cohorts, schemas, and CLI options
• API Reference — Python library API reference
• Example Workflows — Datasets and runnable scripts
• Architecture Overview — Module map and data flow
• Contributing — Development setup and contribution standards
• Changelog — Version release history
• Citation — Software and methodology citation info
• License — Apache License 2.0