Boosting methods for interval-censored data with regression and classification

TL;DR

Novel nonparametric boosting methods for regression and classification tasks with interval-censored data are introduced, which offer a robust framework for enhancing predictive accuracy in domains where interval-censored data are common.

Abstract

Boosting has garnered significant interest across both machine learning and statistical communities. Traditional boosting algorithms, designed for fully observed random samples, often struggle with real-world problems, particularly with interval-censored data. This type of data is common in survival analysis and time-to-event studies where exact event times are unobserved but fall within known intervals. Effective handling of such data is crucial in fields like medical research, reliability engineering, and social sciences. In this work, we introduce novel nonparametric boosting methods for regression and classification tasks with interval-censored data. Our approaches leverage censoring unbiased transformations to adjust loss functions and impute transformed responses while maintaining model accuracy. Implemented via functional gradient descent, these methods ensure scalability and adaptability. We rigorously establish their theoretical properties, including optimality and mean squared error trade-offs. Our proposed methods not only offer a robust framework for enhancing predictive accuracy in domains where interval-censored data are common but also complement existing work, expanding the applicability of existing boosting techniques. Empirical studies demonstrate robust performance across various finite-sample scenarios, highlighting the practical utility of our approaches.

Figures (11)

• Figure 1: Experiment results of predicting survival times. The top and bottom rows correspond to the lognormal AFT and loglogistic AFT models, respectively.
• Figure 2: Experiment results of predicting survival status.
• Figure 3: Boxplots of data analysis results.
• Figure G.1: Experiment results of SMaxAE (left), SMSqE (middle), and SKDT (right) for predicting survival times with $n=1000$, for the lognormal AFT model with $\sigma=0.25$. O, R, N, CUT, and IMP represent the oracle, reference, naive, CUT, and IMP methods, respectively, as described in Section \ref{['sec: eda']}.
• Figure G.2: Experiment results of SMaxAE (left), SMSqE (middle), and SKDT (right) for predicting survival times with different survival models. The top and bottom rows correspond to the lognormal AFT and loglogistic AFT models, respectively. O, R, N, CUT, and IMP represent the oracle, reference, naive, CUT, and IMP methods, respectively, as described in Section \ref{['sec: eda']}.

Theorems & Definitions (24)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Corollary 1
• Proposition 5
• Proposition 6
• Theorem 1
• Theorem 2
• Theorem 3