Empirical Likelihood for the Additive Hazards Model with Current Status Data

We investigate empirical likelihood for the additive hazards model with current status data. An empirical log-likelihood ratio for a vector or subvector of regression parameters is defined and its limiting distribution is shown to be a standard chi-squared distribution. The proposed inference procedure enables us to make empirical likelihood-based inference for the regression parameters. Finite sample performance of the proposed method is assessed in simulation studies to compare with that of a normal approximation method, it shows that the empirical likelihood method provides more accurate inference than the normal approximation method. A real data example is used for illustration.     

Regression Analysis of Bivariate Current Status Data Using a Multistate Model

We consider bivariate current status data with death which often occur in animal tumorigenicity experiments. Instead of observing exact tumor onset time, the existence of tumor is known at death time or sacrifice time. Such an incomplete data structure makes it difficult to investigate the effect of treatment on tumor onset times. Furthermore, when tumor onsets occur at two sites, information for the order of their onsets is unknown. A multistate model is applied to incorporate the sequential occurrence of events. For the inference of parameters, an EM algorithm is applied and a real NTP (National Toxicology Program) dataset is analyzed as an illustrative example.     

A Corrected Pseudo-score Approach for Additive Hazards Model with Longitudinal Covariates Measured with Error

In medical studies, it is often of interest to characterize the relationship between a time-to-event and covariates, not only time-independent but also time-dependent. Time-dependent covariates are generally measured intermittently and with error. Recent interests focus on the proportional hazards framework, with longitudinal data jointly modeled through a mixed effects model. However, approaches under this framework depend on the normality assumption of the error, and might encounter intractable numerical difficulties in practice. This motivates us to consider an alternative framework, that is, the additive hazards model, about which little research has been done when time-dependent covariates are measured with error. We propose a simple corrected pseudo-score approach for the regression parameters with no assumptions on the distribution of the random effects and the error beyond those for the variance structure of the latter. The estimator has an explicit form and is shown to be consistent and asymptotically normal. We illustrate the method via simulations and by application to data from an HIV clinical trial.     

Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model

In recent years the analysis of interval-censored failure time data has attracted a great deal of attention and such data arise in many fields including demographical studies, economic and financial studies, epidemiological studies, social sciences, and tumorigenicity experiments. This is especially the case in medical studies such as clinical trials. In this article, we discuss regression analysis of one type of such data, Case I interval-censored data, in the presence of left-truncation. For the problem, the additive hazards model is employed and the maximum likelihood method is applied for estimations of unknown parameters. In particular, we adopt the sieve estimation approach that approximates the baseline cumulative hazard function by linear functions. The resulting estimates of regression parameters are shown to be consistent and efficient and have an asymptotic normal distribution. An illustrative example is provided.     

Multiple Imputation for the Cox Proportional Hazards Model with Missing Covariates

We present three multiple imputation estimates for the Cox model with missing covariates. Two of the suggested estimates are asymptotically equivalent to estimates in the literature when the number of multiple imputations approaches infinity. The third estimate can be implemented using standard software that could handle time-varying covariates. This revised version was published online in July 2006 with corrections to the Cover Date.     

Generalized Additive Models for Current Status Data

Current status data arise in studies where the target measurement is the time of occurrence of some event, but observations are limited to indicators of whether or not the event has occurred at the time the sample is collected - only the current status of each individual with respect to event occurrence is observed. Examples of such data arise in several fields, including demography, epidemiology, econometrics and bioassay. Although estimation of the marginal distribution of times of event occurrence is well understood, techniques for incorporating covariate information are not well developed. This paper proposes a semiparametric approach to estimation for regression models of current status data, using techniques from generalized additive modeling and isotonic regression. This procedure provides simultaneous estimates of the baseline distribution of event times and covariate effects. No parametric assumptions about the form of the baseline distribution are required. The results are illustrated using data from a demographic survey of breastfeeding practices in developing countries, and from an epidemiological study of heterosexual Human Immunodeficiency Virus (HIV) transmission. This revised version was published online in July 2006 with corrections to the Cover Date.     

Regression Analysis of Current Status Data Under the Additive Hazards Model with Auxiliary Covariates

This paper discusses regression analysis of current status or case I interval‐censored failure time data arising from the additive hazards model. In this situation, some covariates could be missing because of various reasons, but there may exist some auxiliary information about the missing covariates. To address the problem, we propose an estimated partial likelihood approach for estimation of regression parameters, which makes use of the available auxiliary information. The method can be easily implemented, and the asymptotic properties of the resulting estimates are established. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted and indicates that the method works well.     

Multiple Imputation of Predictor Variables Using Generalized Additive Models

The sensitivity of multiple imputation methods to deviations from their distributional assumptions is investigated using simulations, where the parameters of scientific interest are the coefficients of a linear regression model, and values in predictor variables are missing at random. The performance of a newly proposed imputation method based on generalized additive models for location, scale, and shape (GAMLSS) is investigated. Although imputation methods based on predictive mean matching are virtually unbiased, they suffer from mild to moderate under-coverage, even in the experiment where all variables are jointly normal distributed. The GAMLSS method features better coverage than currently available methods.     

A Multiple Imputation Approach to Linear Regression with Clustered Censored Data

Weextend Wei and Tanner's (1991) multiple imputation approach insemi-parametric linear regression for univariate censored datato clustered censored data. The main idea is to iterate the followingtwo steps: 1) using the data augmentation to impute for censoredfailure times; 2) fitting a linear model with imputed completedata, which takes into consideration of clustering among failuretimes. In particular, we propose using the generalized estimatingequations (GEE) or a linear mixed-effects model to implementthe second step. Through simulation studies our proposal comparesfavorably to the independence approach (Lee et al., 1993), whichignores the within-cluster correlation in estimating the regressioncoefficient. Our proposal is easy to implement by using existingsoftwares.     

A nonparametric test for current status data with unequal censoring

Nonparametric tests for the comparison of different treatments based on current status data are proposed. For this problem, most methods proposed in the literature require that observation times on all subjects follow the same distribution. In other words, censoring distributions are identical between the treatment groups. In this paper, we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given. The asymptotic distribution of the test proposed is derived. The method proposed is applied to data arising from a tumorigenicity experiment.     

A Study of Suicide Risk Using a Cox Cure Model via a Retrospective Sampling and Multiple Imputation

The incidence of suicide is an example of rare event. A Cox cure model is adopted to examine the suicide risk of a cohort study of a sample of 65,000 Personal Emergency Link users over a 10-year observation period. Our objective is to investigate the effect of personal covariates on the failure time to suicide as well as the long-term survival from suicide. Based on the Cox cure model, a new and efficient estimation approach using retrospective sampling and multiple imputation was used. Compared with the standard Cox proportional hazards model, the Cox cure model provides a new perspective on analyzing the suicide data.     

A Simple Method to Ensure Plausible Multiple Imputation for Continuous Multivariate Data

Multiple Imputation (MI) is an established approach for handling missing values. We show that MI for continuous data under the multivariate normal assumption is susceptible to generating implausible values. Our proposed remedy, is to: (1) transform the observed data into quantiles of the standard normal distribution; (2) obtain a functional relationship between the observed data and it's corresponding standard normal quantiles; (3) undertake MI using the quantiles produced in step 1; and finally, (4) use the functional relationship to transform the imputations into their original domain. In conclusion, our approach safeguards MI from imputing implausible values.     

Application of Multiple Imputation in Analysis of Data from Clinical Trials with Treatment Related Dropouts

This article develops a functional form of the generalized Poisson regression model that parametrically nests the Poisson and the two well known generalized Poisson regression models (GP-1 and GP-2). The proposed model is applied on the Malaysian motor insurance claim count data.     

Generalized Method of Moments for Additive Hazards Model with Clustered Dental Survival Data

For multivariate survival data, we study the generalized method of moments (GMM) approach to estimation and inference based on the marginal additive hazards model. We propose an efficient iterative algorithm using closed‐form solutions, which dramatically reduces the computational burden. Asymptotic normality of the proposed estimators is established, and the corresponding variance–covariance matrix can be consistently estimated. Inference procedures are derived based on the asymptotic chi‐squared distribution of the GMM objective function. Simulation studies are conducted to empirically examine the finite sample performance of the proposed method, and a real data example from a dental study is used for illustration.     

基于链式方程的收入变量 缺失值的多重插补

 在经济计量分析中收入变量的缺失值是一个普遍而又较难处理的问题。传统的处理方法往往导致分析结果具有系统偏差。本文提出利用基于链式方程的多重插补方法来处理收入变量的缺失值问题。文章将此方法应用到一个实际数据集,然后通过分析插补后的数据集讨论了此方法的性质,并和其他多重插补方法进行了比较。结果表明：基于链式方程的多重插补能在一定程度上纠正推断结果的系统偏差,并且给出恰当的标准差估计。     

A Simulation Study Comparing Multiple Imputation Methods for Incomplete Longitudinal Ordinal Data

Multiple imputation (MI) is now a reference solution for handling missing data. The default method for MI is the Multivariate Normal Imputation (MNI) algorithm that is based on the multivariate normal distribution. In the presence of longitudinal ordinal missing data, where the Gaussian assumption is no longer valid, application of the MNI method is questionable. This simulation study compares the performance of the MNI and ordinal imputation regression model for incomplete longitudinal ordinal data for situations covering various numbers of categories of the ordinal outcome, time occasions, sample sizes, rates of missingness, well-balanced, and skewed data.     

Efficient Estimation of the Partly Linear Additive Hazards Model with Current Status Data

This paper focuses on efficient estimation, optimal rates of convergence and effective algorithms in the partly linear additive hazards regression model with current status data. We use polynomial splines to estimate both cumulative baseline hazard function with monotonicity constraint and nonparametric regression functions with no such constraint. We propose a simultaneous sieve maximum likelihood estimation for regression parameters and nuisance parameters and show that the resultant estimator of regression parameter vector is asymptotically normal and achieves the semiparametric information bound. In addition, we show that rates of convergence for the estimators of nonparametric functions are optimal. We implement the proposed estimation through a backfitting algorithm on generalized linear models. We conduct simulation studies to examine the finite‐sample performance of the proposed estimation method and present an analysis of renal function recovery data for illustration.     

Additive hazards regression of current status data with auxiliary covariates

This paper discusses the regression analysis of current status failure time data arising from the additive hazards model with auxiliary covariates. As often occurs in practice, it is impossible or impractical to measure the exact magnitude of covariates for all subjects in a study. To compensate the missing information, some auxiliary covariates are utilized instead. We propose two easy-to-implement procedures for estimation of regression parameters by making use of auxiliary information. The asymptotic properties of the resulting estimators are established and extensive numerical studies indicate that both procedures work well in practice.     

基于DA插补法的线性回归模型系数估计值的模拟研究

Data Augmentation(DA)插补法是最常用的MCMC多重插补法之一。利用模拟方法研究基于DA插补法的线性回归模型的系数估计值,分析估计值的统计性质受无回答机制、无回答率和插补重数的影响。模拟结果显示:在完全随机无回答机制下,选择较小插补重数常常会得到较好的回归系数估计值;在随机无回答机制下,随着无回答率增大而选择更大插补重数往往会得到更好的回归系数估计值;在非随机无回答机制下,选择更大插补重数并不一定总会得到更好的回归系数估计值。     

A transformation approach for the analysis of interval-censored failure time data

This paper discusses the analysis of interval-censored failure time data, which has recently attracted a great amount of attention (Li and Pu, Lifetime Data Anal 9:57–70, 2003; Sun, The statistical analysis of interval-censored data, 2006; Tian and Cai, Biometrika 93(2):329–342, 2006; Zhang et al., Can J Stat 33:61–70, 2005). Interval-censored data mean that the survival time of interest is observed only to belong to an interval and they occur in many fields including clinical trials, demographical studies, medical follow-up studies, public health studies and tumorgenicity experiments. A major difficulty with the analysis of interval-censored data is that one has to deal with a censoring mechanism that involves two related variables. For the inference, we present a transformation approach that transforms general interval-censored data into current status data, for which one only needs to deal with one censoring variable and the inference is thus much easy. We apply this general idea to regression analysis of interval-censored data using the additive hazards model and numerical studies indicate that the method performs well for practical situations. An illustrative example is provided.