[Paper Review] Incorporating data drift to perform survival analysis on credit risk

Jianwei Peng, Stefan Lessmann|arXiv (Cornell University)|Jan 28, 2026

Financial Distress and Bankruptcy Prediction0 citations

TL;DR

The paper proposes a landmark-based dynamic joint model (LMISO) that blends a balance-based longitudinal marker with discrete-time hazard, adjusting for drift via landmark encoding and isotonic calibration to robustly predict mortgage defaults under data drift.

ABSTRACT

Survival analysis has become a standard approach for modelling time to default by time-varying covariates in credit risk. Unlike most existing methods that implicitly assume a stationary data-generating process, in practise, mortgage portfolios are exposed to various forms of data drift caused by changing borrower behaviour, macroeconomic conditions, policy regimes and so on. This study investigates the impact of data drift on survival-based credit risk models and proposes a dynamic joint modelling framework to improve robustness under non-stationary environments. The proposed model integrates a longitudinal behavioural marker derived from balance dynamics with a discrete-time hazard formulation, combined with landmark one-hot encoding and isotonic calibration. Three types of data drift (sudden, incremental and recurring) are simulated and analysed on mortgage loan datasets from Freddie Mac. Experiments and corresponding evidence show that the proposed landmark-based joint model consistently outperforms classical survival models, tree-based drift-adaptive learners and gradient boosting methods in terms of discrimination and calibration across all drift scenarios, which confirms the superiority of our model design.

Motivation & Objective

• Motivate survival analysis for credit risk under non-stationary, drift-prone environments.
• Develop a dynamic joint modelling framework that links longitudinal repayment behavior to time-to-default.
• Incorporate landmarking, landmark-specific baselines, and isotonic calibration to handle temporal drift.
• Evaluate robustness across sudden, incremental and recurring data drift using Freddie Mac mortgage data.

Proposed method

• Introduce a balance-based longitudinal marker that compares actual vs scheduled repayments to derive BD_pct(t).
• Fit a per-loan linear trajectory mi(t)=b0i + b1i t/Ni to summarize longitudinal behavior with a light ridge-regularised OLS estimator.
• Use landmarking to create a sequence of prediction tasks at fixed landmark times L with horizon H.
• Model discrete-time default probability hL via logistic regression with components X(L), mi(L), and landmark indicators ZL.
• Apply isotonic regression to calibrate raw probabilities pcal, preserving ranking while improving calibration under drift.

Experimental results

Research questions

• RQ1 How does data drift (sudden, incremental, recurring) affect survival-based credit risk models?
• RQ2 Can a landmark-based joint framework incorporating longitudinal repayment behavior improve discrimination and calibration under drift?
• RQ3 Do landmark-specific adjustments (LM) and isotonic calibration (ISO) mitigate drift-induced miscalibration in default probabilities?
• RQ4 Is the proposed LMISO approach robust across different drift scenarios compared with standard survival and drift-adaptive models?

Key findings

• LMISO consistently achieves the best discrimination, calibration and F1 across drift scenarios.
• Under sudden drift, M1-LMISO attains AUC 0.812, Brier 0.102, F1 0.924, outperforming Cox, XGBoost, HAT and ARF.
• Under incremental drift, M1-LMISO attains AUC 0.836, Brier 0.131, F1 0.876, outperforming the benchmarks.
• Under recurring drift, M1-LMISO attains AUC 0.696, Brier 0.115, F1 0.923, outperforming the benchmarks.
• The Cox model performs poorly across drift regimes, highlighting limitations of proportional-hazards under drift.