Gradient-Boosted Survival Models for Corrosion Risk-Based Inspection of Gas Transmission Pipelines

Prediction of the time to failure of pipeline materials supports inspection scheduling within risk-based inspection (RBI) frameworks. We compare three survival models, namely the Cox proportional hazards model (Cox PH), the random survival forest (RSF), and XGBoost with the survival:cox objective, on 823 corrosion incidents from the PHMSA database (1986–2025) retained after an engineering-validity screen. The comparison turns on a point that is easy to miss at the level of implementation. For the survival:cox objective, the predict() method of XGBoost returns the hazard ratio exp(η^), whereas the Breslow estimator of the baseline cumulative hazard expects the linear predictor η^ and applies the exponential internally. Chaining the two evaluates exp(exp(η^)). Both maps are strictly increasing, so the concordance index is identical under either scale, to the last representable digit in our computation, and the defect does not appear in discrimination-based validation, while the estimated survival function is destroyed. A simulation with a known survival function isolates the magnitude: substituting the hazard ratio for the linear predictor raises the mean absolute deviation of Ŝ(t | x) from 0.073 to 0.398 and the integrated Brier score (IBS) from 0.154 to 0.395, at an unchanged concordance index of 0.723. On the pipeline corpus, the erroneous scale inflates the IBS to 0.356 ± 0.043 over 20 random splits. On the correct scale, XGBoost-Cox attains C = 0.871 ± 0.017 and IBS = 0.0614 ± 0.0056 and exceeds both reference models on both axes simultaneously (Cox PH 0.853 ± 0.018 and 0.0717 ± 0.0067; RSF 0.807 ± 0.020 and 0.0751 ± 0.0030; two-sided Wilcoxon p = 1.9 × 10−6 throughout). It also attains the lowest expected calibration error at every horizon from 10 to 40 years. No post hoc calibration is required, and adding one degrades the result. Out-of-time validation preserves the discrimination, whereas the absolute probabilities require periodic re-estimation of the baseline hazard. The feature-importance hierarchies agree with the ISO 8044 classification of corrosion factors.