posted on 2025-03-28, 22:25authored byJordan Anaya, Julia Kung, Alexander S. Baras
Simulated step data and examples with a polynomial transformation. 15 simulated survival datasets were generated for a step relationship with TMB (A). B shows the hazard ratios and associated log-likelihood ratio tests and associated cutoffs of searching for an optimal cutoff, while C shows the fits of a Cox model, FCN neural network, and a neural network comprised of a single neuron with sigmoid activation. D shows an example of a quadratic relationship with TMB (E). Generating a simulated dataset from the risk relationship in D we explored fitting a Cox model with a two degree polynomial in addition to a neural net. In F we show the fit of a two degree polynomial with non-monotonic data.
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ARTICLE ABSTRACT
Potential clinical biomarkers are often assessed with Cox regressions or their ability to differentiate two groups of patients based on a single cutoff. However, both of these approaches assume a monotonic relationship between the potential biomarker and survival. Tumor mutational burden (TMB) is currently being studied as a predictive biomarker for immunotherapy, and a single cutoff is often used to divide patients. In this study, we introduce a two-cutoff approach that allows splitting of patients when a non-monotonic relationship is present and explore the use of neural networks to model more complex relationships of TMB to outcome data. Using real-world data, we find that while in most cases the true relationship between TMB and survival appears monotonic, that is not always the case and researchers should be made aware of this possibility.
When a non-monotonic relationship to survival is present it is not possible to divide patients by a single value of a predictor. Neural networks allow for complex transformations and can be used to correctly split patients when a non-monotonic relationship is present.