Weighted Least Squares Support Vector Machine for Survival Analysis

Abstract

Background: The increasing complexity and volume of data across various disciplines have encouraged the use of machine learning methods, including in survival analysis. Given the large percentage of censored data in survival datasets, a methodological technique that can generate more precise survival probability forecasts is required. This study aims to advance survival analysis by applying the Weighted Least Squares Support Vector Machine, using a weighting approach to manage the information imbalance between censored observations and event occurrences. This strategy can yield a prognostic index that is easily categorized into low-risk and high-risk groups.Methods: This study proposes the Survival Weighted Least Squares Support Vector Machine (Surv-WLSSVM) modelthrough the integration of a weighting strategy based on the Kaplan–Meier estimator. Data with events are assigned weights that consider the value of the survival function, while censored data are given constant weights. Surv-WLSSVM was applied to both simulated and real datasets, and the results were compared with the unweighted method, namely Survival Least Squares Support Vector Machine (Surv-LSSVM). The simulation scenarios included the complexity of variable numbers, data distribution, sample size, and censoring percentage. The Real datasets used in this study consist of Breastfeeding, PBC, and Bone-Marrow data. A tuning parameters using Particle Swarm Optimization (PSO) was performed to enhance the performance of both Surv-LSSVM and Surv-WLSSVM models. Model performance was evaluated using the concordance index (c-index), where a higher c-index indicates a better model.Results: In every simulated data setting, the Surv-WLSSVM model continuously showed better performance. Similarly,on real datasets, this model outperformed the alternative and produced more diverse prognostic indices, facilitating the categorization of individuals into low-risk and high-risk groups.Conclusion: The Surv-WLSSVM represents a significant advancement in SVM-based survival modelling. This approachdemonstrates greater reliability and adaptability in handling the complexity of modern survival data.

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