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Internal validation strategy for high dimensional prognosis model: A simulation study and application to
Antoine Dubray-Vautrin1,2, Victor Gravrand3, Grégoire Marret4
1Institut Curie, INSERM, Saint Cloud U1331, France.
Background:
Predictive models using high-dimensional data, such as genomics and transcriptomics, are increasingly used in oncology for time-to-event endpoints. Internal validation of these models is crucial to mitigate optimism bias prior to external validation. Common strategies include train-test, bootstrap, and (nested) cross-validation. However, no benchmark exists for these methods in high-dimensional settings. We aimed to compare these strategies and provide recommendations in the field of transcriptomic analysis.
Method:
A simulation study was conducted using data from the SCANDARE head and neck cohort (NCT03017573) including n = 76 patients. Simulated datasets included clinical variables (age, sex, HPV status, TNM staging), transcriptomic data (15,000 transcripts), and disease-free survival, with a realistic cumulative baseline hazard. Sample sizes of 50, 75, 100, 500, and 1000 were simulated, with 100 replicates each. Cox penalized regression was performed for model selection, followed by train-test 70 % training), bootstrap (100 iterations), 5-fold cross-validation, and nested cross-validation (5 ×5) to assess discriminative (time-dependent AUC and C-Index) and calibration (3-year integrated Brier Score) performance.
Results:
Train-test validation showed unstable performance. Conventional bootstrap was over-optimistic, while the 0.632 + bootstrap was overly pessimistic, particularly with small samples (n = 50 to n = 100). The k-fold cross-validation and nested cross-validation improved performance with larger sample sizes, with k-fold cross-validation demonstrating greater stability. Nested cross-validation showed performance fluctuations depending on the regularization method for model development.
Conclusion:
The K-fold cross-validation and nested cross-validation are recommended for internal validation of Cox penalized models in high-dimensional time-to-event settings. These methods offer greater stability and reliability compared to train-test or bootstrap approaches, particularly when sample sizes are sufficient.
