ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

An Additive Hazards Model for Clustered Recurrent Gap Times

In this article, clustered recurrent gap time is investigated. A marginal additive haz- ards model is proposed without specifying the association of the individuals within the same cluster. The relationship among the gap times for the same individual is also left unspecified. An estimating equation-based inference procedure is developed for the model parameters, and the asymptotic proper- ties of the resulting estimators are established. In addition, a lack-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a clinic study on chronic granulomatous disease （CGD） is illustrated.

More Efficient Estimators for Marginal Additive Hazards Model in Case-cohort Studies with Multiple Outcomes

Case-cohort study designs are widely used to reduce the cost of large cohort studies. When several diseases are of interest, we can use the same subcohort. In this paper, we will study the casecohort design of marginal additive hazards model for multiple outcomes by a more efficient version. Instead of analyzing each disease separately, ignoring the additional exposure measurements collected on subjects with other diseases, we propose a new weighted estimating equation approach to improve the efficiency by utilizing as much information collected as possible. The consistency and asymptotic normality of the resulting estimator are established. Simulation studies are conducted to examine the finite sample performance of the proposed estimator, which confirm the efficiency gains.

Analyzing Right-Censored Length-Biased Data with Additive Hazards Model

Length-biased data are often encountered in observational studies, when the survival times are left-truncated and right-censored and the truncation times follow a uniform distribution. In this article, we propose to analyze such data with the additive hazards model, which specifies that the hazard function is the sum of an arbitrary baseline hazard function and a regression function of covariates. We develop estimating equation approaches to estimate the regression parameters. The resultant estimators are shown to be consistent and asymptotically normal. Some simulation studies and a real data example are used to evaluate the finite sample properties of the proposed estimators.

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures oneach subject. The failures may be events of different natures or may be repetitions of the same kindof event. In this article, we consider the regression analysis of such multivariate failure timedata under the additive hazards model. Simple weighted estimating functions for the regressionparameters are proposed, and asymptotic distribution theory of the resulting estimators are derived.In addition, a class of generalized Wald and generalized score statistics for hypothesis testingand model selection are presented, and the asymptotic properties of these statistics are examined.

An Efficient Risk Estimator with External Information Under Additive Hazards Model

Rare event data is encountered when the events of interest occur with low frequency, and the estimators based on the cohort data only may be inefficient. However, when external information is available for the estimation, the estimators utilizing external information can be more efficient. In this paper, we propose a method to incorporate external information into the estimation of the baseline hazard function and improve efficiency for estimating the absolute risk under the additive hazards model. The resulting estimators are shown to be uniformly consistent and converge weakly to Gaussian processes. Simulation studies demonstrate that the proposed method is much more efficient. An application to a bone marrow transplant data set is provided.

A class of weighted estimating equations for additive hazards models with covariates missing at random

Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at random.Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations.Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modelling schemes.The resulting estimators have closed forms and are shown to be consistent and asymptotically normal.Simulation studies indicate that the proposed estimators perform well for practical settings.An application to a mouse leukemia study is illustrated.

Regression Analysis for the Additive Hazards Model with General Biased Survival Data

In survival analysis,data are frequently collected by some complex sampling schemes,e.g.,length biased sampling,case-cohort sampling and so on.In this paper,we consider the additive hazards model for the general biased survival data.A simple and unified estimating equation method is developed to estimate the regression parameters and baseline hazard function.The asymptotic properties of the resulting estimators are also derived.Furthermore,to check the adequacy of the fitted model with general biased survival data,we present a test statistic based on the cumulative sum of the martingale-type residuals.Simulation studies are conducted to evaluate the performance of proposed methods,and applications to the shrub and Welsh Nickel Refiners datasets are given to illustrate the methodology.

Hierarchically penalized additive hazards model with diverging number of parameters

In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.

Estimating Cumulative Treatment Effect Under an Additive Hazards Model

In clinical and epidemiologic studies of time to event,the treatment effect is often of direct interest,and the treatment effect is not constant over time.In this paper,the authors propose an estimator for the cumulative hazard difference under a stratified additive hazards model.The asymptotic properties of the resulting estimator are established,and the finite-sample properties are examined through simulation studies.An application to a liver cirrhosis data set from the Copenhagen Study Group for Liver Diseases is provided.

Estimating Differences in Restricted Mean Lifetime Using Additive Hazards Models under Dependent Censoring

In epidemiological and clinical studies,the restricted mean lifetime is often of direct interest quantity.The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times.When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring,the imbalances in confounding factors need to be accounted.We use the mixture of additive hazards model and inverse probability of censoring weighting method to estimate the differences of restricted mean lifetime.The average causal effect is then obtained by averaging the differences in fitted values based on the additive hazards models.The asymptotic properties of the proposed method are also derived and simulation studies are conducted to demonstrate their finite-sample performance.An application to the primary biliary cirrhosis(PBC)data is illustrated.

The Cox-Aalen Models as Framework for Construction of Bivariate Probability Distributions, Universal Representation

Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.

The Additive Hazard Mixing Models

This paper is concerned with the aging and dependence properties in the additive hazard mixing models including some stochastic comparisons. Further, some useful bounds of reliability functions in additive hazard mixing models are obtained.

A New Approach for Regression Analysis of Multivariate Current Status Data with Informative Censoring

Regression analysis of interval-censored failure time data has recently attracted a great deal of attention partly due to their increasing occurrences in many fields.In this paper,we discuss a type of such data,multivariate current status data,where in addition to the complex interval data structure,one also faces dependent or informative censoring.For inference,a sieve maximum likelihood estimation procedure is developed and the proposed estimators of regression parameters are shown to be asymptotically consistent and efficient.For the implementation of the method,an EM algorithm is provided,and the results from an extensive simulation study demonstrate the validity and good performance of the proposed inference procedure.For an illustration,the proposed approach is applied to a tumorigenicity experiment.

Joint Analysis of Recurrent Event Data with a Dependent Terminal Event

Recurrent event data frequently occur in many longitudinal studies, and the observation on recurrent events could be stopped by a terminal event such as death. This paper considers joint modeling and analysis of recurrent event and terminal event data through a common subject-specific frailty, in which the proportional intensity model is used for modeling the recurrent event process and the additive hazards model is used for modeling the terminal event time. Estimating equation approaches are developed for parameter estimation and asymptotic properties of the resulting estimators are established. In addition, some procedures are presented for model checking. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a heart failure study is provided.