Um modelo adaptativo de sobrevivência baseado em Buckley-James e Comitê L2 Boosting de máquinas de aprendizado extremo, com abordagem automática para determinação de não linearidade e robustez a observações extremas

Abstract

Survival models are widely used in studies that analyze the time until the occurrence of an event of interest. These models deal with datasets in which, for some observations, the event may not occur during the follow-up period, resulting in censored data where the time to the event is not fully known. Traditionally, such models have been applied in the medical field for the evaluation of lifetimes, disease recurrence, and in the modeling of reliability problems, such as determining failure times in mechanical or electronic components. More recently, they have also found applications in the social sciences for modeling problems related to the internet, such as determining the time until job abandonment, evaluating the period until leaving digital platforms, and even determining the time to conclude browsing sessions. In this context, the semiparametric Buckley-James (BJ) model emerges as an alternative. It can be seen as an extension of linear regression to censored situations, thus allowing the use of ordinary least squares in estimation processes. Unlike the Cox model, BJ does not require the assumption of proportional hazards. However, the efficiency of the BJ model is compromised when the relationship between covariates and response is not linear and/or when extreme observations (outliers) are present. This work proposes an adaptive computational approach for right-censored survival models, built within the BJ framework. The proposal integrates into a learning process a committee of regressors based on Extreme Learning Machines, which are neural networks known for their computational efficiency, in an L2 Boosting scheme with case weighting based on the Student’s t-distribution. This formulation replaces the linear combination of covariates in the BJ model with the output function of the committee, allowing the developed model to automatically select between linear and nonlinear structures and, additionally, incorporate robustness in the presence of extreme observations. The choice of activation function in the ELM enables capturing different patterns of relationships between covariates and response, while the degrees of freedom of the Student’s t-distribution control the model’s sensitivity to extreme values. The results obtained from experiments with simulated data and datasets referenced in the literature, evaluated by metrics such as C-Index and IBS, demonstrate significant gains in flexibility and performance, forming the basis for the development of a general and unified method. Additionally, the proposal is applied to a dataset of Brazilian patients with chronic kidney disease, demonstrating its practical relevance and potential for analyses in real clinical scenarios.