Additive hazards models for gap time data with multiple causes

Recurrent event data with multiple causes are often observed in biomedical studies. The additive hazards model describes a different aspect of the association between covariates and the failure time than does the proportional hazards model. In this paper, we introduce additive hazards models for the analysis of gap time data of recurrent events with multiple causes. We estimate the regression parameter vector and cumulative baseline cause specific hazard rate function using counting process approach. Asymptotic properties of the estimators are studied. The proposed model is applied to the kidney dialysis data given in Lawless (2003). A simulation study is carried out to assess the performance of the estimates.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

The Additive-multiplicative Hazards Mo del for Multiple Typ e of Recurrent Gap Times

Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards...     

Partially varying coefficient single-index additive hazard models

The partially linear additive hazards model has been proposed to study the interaction between some covariates and an exposure variable. In this paper, we extend it to the partially varying coefficient single-index additive hazard model where the high dimension covariates are collapsed to a single index, due to practical needs. Two sets of estimating equations were proposed to estimate the varying coefficient functions in the linear components: the link function for the single index and the single-index parameter vector separately. It was shown that the proposed local and global estimators are asymptotically normal. Simulation studies were conducted to examine the finite-sample performance of our method to compare the relative performance of our method with existing ones. A real data analysis was used to illustrate the proposed methods.     

The Additive Hazards Model for Multiple Type Recurrent Gap Times

In many biomedical and engineering studies, recurrent event data and gap times between successive events are common and often more than one type of recurrent events is of interest. It is well known that the proportional hazards model may not be appropriate for fitting survival times in some settings. In the paper, we consider an additive hazards model for multiple type recurrent gap times data to assess the effect of covariates. For inferences about regression coefficients and baseline cumulative hazard functions, an estimating equation approach is developed. Furthermore, we establish asymptotic properties of the proposed estimators.     

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The additive model is a more flexible nonparametric statistical model which allows a data-analytic transform of the covariates.When the number of covariates is big and grows exponentially with the sample size the urgent issue is to reduce dimensionality from high to a moderate scale. In this paper, we propose and investigate marginal empirical likelihood screening methods in ultra-high dimensional additive models. The proposed nonparametric screening method selects variables by ranking a measure of the marginal empirical likelihood ratio evaluated at zero to differentiate contributions of each covariate given to a response variable. We show that, under some mild technical conditions, the proposed marginal empirical likelihood screening methods have a sure screening property and the extent to which the dimensionality can be reduced is also explicitly quantified. We also propose a data-driven thresholding and an iterative marginal empirical likelihood methods to enhance the finite sample performance for fitting sparse additive models. Simulation results and real data analysis demonstrate the proposed methods work competitively and performs better than competitive methods in error of a heteroscedastic case.     

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.     

多元失效时间数据的一般边际半参数危险率模型研究

在生物医学研究中,多元失效时间数据非常常见.该文提出用一般边际半参数危险率回归模型来分析多元失效时间数据.此模型包括了三种常用边际模型:边际比例风险模型、边际加速失效时间模型和边际加速危险模型作为子模型.对于模型中的回归系数,可以通过估计方程的方法来估计它,同时也给出了基准累积危险率函数的估计.得到的估计可以证明是相合的和渐近正态的.     

Additive–multiplicative hazards model with current status data

The additive–multiplicative hazards (AMH) regression model specifies an additive and multiplicative form on the hazard function for the counting process associated with a multidimensional covariate process, which contains the Cox proportional hazards model and the additive hazards model as its special cases. In this paper, we study the AMH model with current status data, where the cumulative hazard hazard function is assumed to be nonparametric and is estimated using B-splines with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood estimation is proposed to estimate regression parameters. The proposed estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The B-splines estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and a real data example is presented for illustration.     

A class of additive-accelerated means regression models for recurrent event data

In this article, we propose a class of additive-accelerated means regression models for analyzing recurrent event data. The class includes the proportional means model, the additive rates model, the accelerated failure time model, the accelerated rates model and the additive-accelerated rate model as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the model parameters, estimating equation approaches are derived and asymptotic properties of the proposed estimators are established. In addition, a technique is provided for model checking. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is illustrated.     

Covariate selection for semiparametric hazard function regression models

We study a flexible class of nonproportional hazard function regression models in which the influence of the covariates splits into the sum of a parametric part and a time-dependent nonparametric part. We develop a method of covariate selection for the parametric part by adjusting for the implicit fitting of the nonparametric part. Asymptotic consistency of the proposed covariate selection method is established, leading to asymptotically normal estimators of both parametric and nonparametric parts of the model in the presence of covariate selection. The approach is applied to a real data set and a simulation study is presented.     

The proportional hazards model for multiple type recurrent gap times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies, and often more than one type of recurrent events is of interest. In this paper, we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covariates on the censored event processes of interest. An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions. We examine asymptotic properties of the proposed estimators. Finite sample properties of these estimators are demonstrated by simulations.     

纵向数据部分线性测量误差模型的二次推断函数估计

基于纵向数据部分线性测量误差模型, 研究了模型中兴趣参数部分回归系数的估计问题. 首先采用B样条方法逼近模型中的非参数函数, 然后提出修正的二次推断函数(QIF)方法对模型中参数部分的回归系数进行估计, 所提方法可以提高估计的效率. 在一定的正则条件下, 证明了所得到的估计量具有相合性和渐近正态性. 最后, 通过模拟研究和实例分析验证了所提出估计方法的有限大样本性质.     

基于病例队列数据的比例风险模型的诊断

病例队列设计是一种在生存分析中广泛应用的可以降低成本又能提高效率的抽样方法.对于病例队列数据,已经有很多统计方法基于比例风险模型来估计协变量对生存时间的影响.然而,很少有工作基于病例队列数据来检验模型的假设是否成立.在这篇文章中,我们基于渐近的零均的值随机过程提出了一类检验统计量,这类检验统计量可以基于病例队列数据来检验比例风险模型的假设是否成立.我们通过重抽样的方法来逼近上述检验统计量的渐近分布,通过数值模拟来研究所提方法在有限样本下的表现,最后将所提出的方法应用于一个国家肾母细胞瘤研究的真实数据集上.     

A simple construction of optimal estimation in multivariate marginal Cox regression

The multivariate extension of the Cox model proposed by Wei,Lin and Weissfeld in 1989 has been widely used for analyzing multivariate survival data.Under the model assumption,failure times from an individual are assumed to marginally follow their respective proportional hazards regression relation,leaving the joint distribution completely unspecified.This paper presents a simple approach to efficiency improvement through segmentation of stochastic integrals in the marginal estimating equations and incorporation of the limiting covariance structure.It is shown that when partition of the time interval is done at a suitable rate,the resulting estimator is consistent and asymptotically normal.Through the reproducing kernel Hilbert space arising from the covariance function of the limiting Gaussian process,it is also shown that the proposed estimator is asymptotically optimal within a reasonable class of estimators under marginal specification.Simulations are conducted to assess the finite-sample performance of the proposed method.     

Semiparametric estimation based on parametric modeling of the cause-specific hazard ratios in competing risks

This paper is intended as an investigation of estimating cause-specific cumulative hazard and cumulative incidence functions in a competing risks model. The proportional model in which ratios of the cause-specific hazards to the overall hazard are assumed to be constant (independent of time) is a well-known semiparametric model. We are here concerned with relaxation of the proportionality assumption. The set C of all causes are decomposed into two disjoint subsets of causes as C=C₁∪C₂. The relative risk of cause A in the sub-causes C₁ can be represented as a function defined by ratio of the cause-specific hazard of cause A to the sum of cause-specific hazards in the sub-causes C₁. We call this function the risk pattern function of cause A in C₁, and consider a semiparametric model in which risk pattern functions in C₁ are not constant (independent of time) but those functional forms, except for finite-dimensional parameters, are known. Based on this model, semiparametric estimators are obtained, and estimated variances of them are derived by delta methods. We investigate asymptotic properties of the semiparametric estimators and compare them with the nonparametric estimators. The semiparametric procedure is illustrated with the radiation-exposed mice data set, which represents lifetimes and causes of death of mice exposed to radiation in two different environments.     

A class of weighted estimators for additive hazards model in case-cohort studies

Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose＇a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.     

Empirical likelihood inference for linear transformation models

Empirical likelihood inference is developed for censored survival data under the linear transformation models, which generalize Cox's [Regression models and life tables (with Discussion), J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] proportional hazards model. We show that the limiting distribution of the empirical likelihood ratio is a weighted sum of standard chi-squared distribution. Empirical likelihood ratio tests for the regression parameters with and without covariate adjustments are also derived. Simulation studies suggest that the empirical likelihood ratio tests are more accurate (under the null hypothesis) and powerful (under the alternative hypothesis) than the normal approximation based tests of Chen et al. [Semiparametric of transformation models with censored data, Biometrika 89 (2002) 659-668] when the model is different from the proportional hazards model and the proportion of censoring is high.     

Model checking in errors-in-variables regression

This paper discusses a class of minimum distance tests for fitting a parametric regression model to a class of regression functions in the errors-in-variables model. These tests are based on certain minimized distances between a nonparametric regression function estimator and a deconvolution kernel estimator of the conditional expectation of the parametric model being fitted. The paper establishes the asymptotic normality of the proposed test statistics under the null hypothesis and that of the corresponding minimum distance estimators. We also prove the consistency of the proposed tests against a fixed alternative and obtain the asymptotic distributions for general local alternatives. Simulation studies show that the testing procedures are quite satisfactory in the preservation of the finite sample level and in terms of a power comparison.     

Multivariate Failure Times Regression with a Continuous Auxiliary Covariate

How to take advantage of the available auxiliary covariate information when the primary covariate of interest is not measured is a frequently encountered question in biomedical study. In this paper, we consider the multivariate failure times regression analysis in which the primary covariate is assessed only in a validation set, but a continuous auxiliary covariate for it is available for all subjects in the study cohort. Under the frame of marginal hazard model, we propose to estimate the induced relative risk function in the non-validation set through kernel smoothing method and then obtain an estimated pseudo-partial likelihood function. The proposed estimator which maximizes the estimated pseudo-partial likelihood is shown to be consistent and asymptotically normal. We also give an estimator of the marginal cumulative baseline hazard function. Simulation studies are conducted to evaluate the finite sample performance of our proposed estimator. The proposed method is illustrated by analyzing a heart disease data from the Study of Left Ventricular Dysfunction (SOLVD).