Quantile regression methods with varying-coefficient models for censored data

Considerable intellectual progress has been made to the development of various semiparametric varying-coefficient models over the past ten to fifteen years. An important advantage of these models is that they avoid much of the curse of dimensionality problem as the nonparametric functions are restricted only to some variables. More recently, varying-coefficient methods have been applied to quantile regression modeling, but all previous studies assume that the data are fully observed. The main purpose of this paper is to develop a varying-coefficient approach to the estimation of regression quantiles under random data censoring. We use a weighted inverse probability approach to account for censoring, and propose a majorize–minimize type algorithm to optimize the non-smooth objective function. The asymptotic properties of the proposed estimator of the nonparametric functions are studied, and a resampling method is developed for obtaining the estimator of the sampling variance. An important aspect of our method is that it allows the censoring time to depend on the covariates. Additionally, we show that this varying-coefficient procedure can be further improved when implemented within a composite quantile regression framework. Composite quantile regression has recently gained considerable attention due to its ability to combine information across different quantile functions. We assess the finite sample properties of the proposed procedures in simulated studies. A real data application is also considered.     

Sensitivity analysis of predictive modeling for responses from the three-parameter Weibull model with a follow-up doubly censored sample of cancer patients

The purpose of this paper is to derive the predictive densities for future responses from the three-parameter Weibull model given a doubly censored sample. The predictive density for a single future response, bivariate future response, and a set of future responses has been derived when the shape parameter α is unknown. A real data example representing 44 patients who were diagnosed with laryngeal cancer (2000-2007) at a local hospital is used to illustrate the predictive results for the four stages of cancer. The survival days of eight out of the 44 patients could not be calculated as the patients were lost to follow-up. They were the first four and the last four patients’ survival days in order. Thus, the recorded data for the survival days of 36 patients composed of 18 male and 18 female patients with cancer of the larynx are used for the predictive analysis. Furthermore, a subgroup level of the male and female patients follow-up data are considered to obtain the future survival days. A sensitivity study of the mean, standard deviation, and 95% highest predictive density (HPD) interval of the future survival days with respect to stages and doses are performed when the shape parameter α is unknown.     

An empirical study of a test for polynomial relationships in randomly right censored regression models

In this paper, a test statistic is constructed to test polynomial relationships in randomly right censored regression models based on the local polynomial smoothing technique. Two bootstrap procedures, namely the residual-based bootstrap and the naive bootstrap procedures, are suggested to derive the p-value of the test. Some simulations are conducted to empirically assess the performance of the two bootstrap procedures. The results demonstrate that the residual-based bootstrap performs much better than the naive bootstrap and the test method with the residual-based bootstrap to derive the p-value works satisfactorily. Although the limiting distribution of the test statistic and the consistency of the bootstrap approximations remain to be investigated, simulation results indicate that the proposed test method may be of some practical use. As a real example, the proposed test is applied to the Stanford heart transplant data.     

The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study

The Koul-Susarla-Van Ryzin (KSV) and weighted least squares (WLS) methods are simple to use techniques for handling linear regression models with censored data. They do not require any iterations and standard computer routines can be employed for model fitting. Emphasis has been given to the consistency and asymptotic normality for both estimators, but the finite sample performance of the WLS estimator has not been thoroughly investigated. The finite sample performance of these two estimators is compared using an extensive simulation study as well as an analysis of the Stanford heart transplant data. The results demonstrate that the WLS approach performs much better than the KSV method and is reliable for use with censored data.     

Jackknife and bootstrap methods in the identification of dynamic models

A new criterion based on a Jackknife or a Bootstrap statistic is proposed for identifying non-parsimonious dynamic models (FIR, ARX). It is applicable for selecting the number of components in latent variable regression methods or the constraining parameter in regularized least squares regression methods. These meta parameters are used to overcome ill-conditioning caused by model over-parameterization, when fitted using prediction error or least squares methods. In all cases studied, using PLS for parameter estimation, the proposed criterion led to the selection of better models, in the mean square error sense, than when selected via cross-validation. The methodology also provides approximate confidence intervals for the model parameters and the step and impulse response of the system.     

Three predictive power measures for generalized linear models: The entropy coefficient of determination, the entropy correlation coefficient and the regression correlation coefficient

In this paper, three predictive power measures for generalized linear models (GLMs) are compared, and the utility of the entropy correlation coefficient (ECC) and the entropy coefficient of determination (ECD) is demonstrated. First, ECC, ECD and the regression correlation coefficient (RCC) are briefly explained. Second, relationships of the three measures are discussed, and the necessary and sufficient condition under which ECC and RCC are equal is deduced. Third, ECC and ECD are discussed for GLMs with canonical links and polytomous response variables, and an analysis of the effects of factors in GLMs is given. Finally, a discussion of the conclusions of this study is provided.