Additive time-dependent hazard model with doubly truncated data

For doubly truncated data, i.e. the variables of interest are only observable if they lie in a certain random interval, an additive hazard model with time-dependent regression coefficients is investigated. Consistency and asymptotic normality are proven under mild assumptions. A simulation study investigates the finite sample properties and the influence of the truncation distribution on the estimation error. Finally, the method is applied to a doubly truncated data set of German companies, where the age at insolvency is of interest.     

Median regression model with doubly truncated data

We study the problem of fitting a heteroscedastic median regression model with doubly truncated data. A self-consistency equation is proposed to obtain an estimator. We set up a least absolute deviation estimating function. We establish the consistency and asymptotic normality for the case when covariates are discrete. The finite sample performance of the proposed estimators are investigated through simulation studies. The proposed method is illustrated using the AIDS Blood Transfusion Data.     

Additive hazards model with truncated and doubly censored data

In longitudinal studies, the additive hazard model is often used to analyze covariate effects on the duration time, defined as the elapsed time between the first and the second event. In this article, we consider the situation when the first event suffers partly interval censoring and the second event suffers left truncation and right-censoring. We proposed a two-step estimation procedure for estimating the regression coefficients of the additive hazards model. A simulation study is conducted to investigate the performance of the proposed estimator. The proposed method is applied to the Centers for Disease Control acquired immune deficiency syndrome blood transfusion data.     

Asymptotic properties of nonparametric M-estimation for mixing functional data

We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator.     

Semiparametric inference of proportional odds model based on randomly truncated data

This paper studies the estimation in the proportional odds model based on randomly truncated data. The proposed estimators for the regression coefficients include a class of minimum distance estimators defined through weighted empirical odds function. We have investigated the asymptotic properties like the consistency and the limiting distribution of the proposed estimators under mild conditions. The finite sample properties were investigated through simulation study making comparison of some of the estimators in the class. We conclude with an illustration of our proposed method to a well-known AIDS data.     

Confidence intervals for the scale parameter of exponential distribution based on Type II doubly censored samples

This paper deals with the problem of interval estimation of the scale parameter in the two-parameter exponential distribution subject to Type II double censoring. Base on a Type II doubly censored sample, we construct a class of interval estimators of the scale parameter which are better than the shortest length affine equivariant interval both in coverage probability and in length. The procedure can be repeated to make further improvement. The extension of the method leads to a smoothly improved confidence interval which improves the interval length with probability one. All improved intervals belong to the class of scale equivariant intervals.     

Review: Reversed low-rank ANOVA model for transforming high dimensional genetic data into low dimension

A general modeling procedure for analyzing genetic data is reviewed. We review ANOVA type model that can handle both the continuous and discrete genetic variables in one modeling framework. Unlike the regression type models which typically set the phenotype variable as a response, this ANOVA model treats the phenotype variable as an explanatory variable. By reversely treating the phenotype variable, usual high dimensional problem is turned into low dimension. Instead, the ANOVA model always includes interaction term between the genetic locations and phenotype variable to find potential association between them. The interaction term is designed to be low rank with the multiplication of bilinear terms so that the required number of parameters is kept in a manageable degree. We compare the performance of the reviewed ANOVA model to the other popular methods via microarray and SNP data sets.     

A linear transformation model for multivariate interval‐censored failure time data

This paper discusses multivariate interval‐censored failure time data observed when several correlated survival times of interest exist and only interval censoring is available for each survival time. Such data occur in many fields, for instance, studies of the development of physical symptoms or diseases in several organ systems. A marginal inference approach was used to create a linear transformation model and applied to bivariate interval‐censored data arising from a diabetic retinopathy study and an AIDS study. The results of simulation studies that were conducted to evaluate the performance of the presented approach suggest that it performs well. The Canadian Journal of Statistics 41: 275–290; 2013 © 2013 Statistical Society of Canada     

Balanced augmented empirical likelihood for regression models

This paper studies the problem of convex hull constraint in conventional empirical likelihood. Specifically, in the framework of regression, a balanced augmented empirical likelihood (BAEL) procedure through adding two synthetic data points is proposed. It can be used to resolve the under-coverage issue, especially in small-sample or high-dimension setting. Furthermore, some asymptotic properties for proposed BAEL ratio statistic are established under mild conditions. The proposed approach performs robust to different random errors by choosing a robust loss function. Extensive simulation studies and a real example are carried out to support our results.     

Bayesian methods for dealing with missing data problems

Missing data, a common but challenging issue in most studies, may lead to biased and inefficient inferences if handled inappropriately. As a natural and powerful way for dealing with missing data, Bayesian approach has received much attention in the literature. This paper reviews the recent developments and applications of Bayesian methods for dealing with ignorable and non-ignorable missing data. We firstly introduce missing data mechanisms and Bayesian framework for dealing with missing data, and then introduce missing data models under ignorable and non-ignorable missing data circumstances based on the literature. After that, important issues of Bayesian inference, including prior construction, posterior computation, model comparison and sensitivity analysis, are discussed. Finally, several future issues that deserve further research are summarized and concluded.     

Smoothed empirical likelihood confidence intervals for the relative distribution with left‐truncated and right‐censored data

The study of differences among groups is an interesting statistical topic in many applied fields. It is very common in this context to have data that are subject to mechanisms of loss of information, such as censoring and truncation. In the setting of a two‐sample problem with data subject to left truncation and right censoring, we develop an empirical likelihood method to do inference for the relative distribution. We obtain a nonparametric generalization of Wilks' theorem and construct nonparametric pointwise confidence intervals for the relative distribution. Finally, we analyse the coverage probability and length of these confidence intervals through a simulation study and illustrate their use with a real data set on gastric cancer. The Canadian Journal of Statistics 38: 453–473; 2010 © 2010 Statistical Society of Canada     

Principal weighted logistic regression for sufficient dimension reduction in binary classification

Sufficient dimension reduction (SDR) is a popular supervised machine learning technique that reduces the predictor dimension and facilitates subsequent data analysis in practice. In this article, we propose principal weighted logistic regression (PWLR), an efficient SDR method in binary classification where inverse-regression-based SDR methods often suffer. We first develop linear PWLR for linear SDR and study its asymptotic properties. We then extend it to nonlinear SDR and propose the kernel PWLR. Evaluations with both simulated and real data show the promising performance of the PWLR for SDR in binary classification.     

Aalen's linear model for doubly censored data

Double censoring often occurs in registry studies when left censoring is present in addition to right censoring. In this work, we examine estimation of Aalen's nonparametric regression coefficients based on doubly censored data. We propose two estimation techniques. The first type of estimators, including ordinary least squared (OLS) estimator and weighted least squared (WLS) estimators, are obtained using martingale arguments. The second type of estimator, the maximum likelihood estimator (MLE), is obtained via expectation-maximization (EM) algorithms that treat the survival times of left censored observations as missing. Asymptotic properties, including the uniform consistency and weak convergence, are established for the MLE. Simulation results demonstrate that the MLE is more efficient than the OLS and WLS estimators.