Weighted expectile regression for right-censored data

Right-censored models by the expectile method

Based on the expectile loss function and the adaptive LASSO penalty, the paper proposes and studies the estimation methods for the accelerated failure time (AFT) model. In this approach, we need to estimate the survival function of the censoring variable by the Kaplan-Meier estimator. The AFT model parameters are first estimated by the expectile method and afterwards, when the number of explanatory variables can be large, by the adaptive LASSO expectile method which directly carries out the automatic selection of variables. We also obtain the convergence rate and asymptotic normality for the two estimators, while showing the sparsity property for the censored adaptive LASSO expectile estimator. A numerical study using Monte Carlo simulations confirms the theoretical results and demonstrates the competitive performance of the two proposed estimators. The usefulness of these estimators is illustrated by applying them to three survival data sets.

Weighted Expectile Regression Neural Networks for Right Censored Data

As a favorable alternative to the censored quantile regression, censored expectile regression has been popular in survival analysis due to its flexibility in modeling the heterogeneous effect of covariates. The existing weighted expectile regression (WER) method assumes that the censoring variable and covariates are independent, and that the covariates effects has a global linear structure. However, these two assumptions are too restrictive to capture the complex and nonlinear pattern of the underlying covariates effects. In this article, we developed a novel weighted expectile regression neural networks (WERNN) method by incorporating the deep neural network structure into the censored expectile regression framework. To handle the random censoring, we employ the inverse probability of censoring weighting (IPCW) technique in the expectile loss function. The proposed WERNN method is flexible enough to fit nonlinear patterns and therefore achieves more accurate prediction performance than the existing WER method for right censored data. Our findings are supported by extensive Monte Carlo simulation studies and a real data application.

Flexible semiparametric mode regression for time-to-event data

The distribution of time-to-event outcomes is usually right-skewed. While for symmetric and moderately skewed data the mean and median are appropriate location measures, the mode is preferable for heavily skewed data as it better represents the center of the distribution. Mode regression has been introduced for uncensored data to model the relationship between covariates and the mode of the outcome. Starting from nonparametric kernel density based mode regression, we examine the use of inverse probability of censoring weights to extend mode regression to handle right-censored data. We add a semiparametric predictor to add further flexibility to the model and we construct a pseudo Akaike's information criterion to select the bandwidth and smoothing parameters. We use simulations to evaluate the performance of our proposed approach. We demonstrate the benefit of adding mode regression to one's toolbox for analyzing survival data on a pancreatic cancer data set from a prospectively maintained cancer registry.