Testing Inference from Logistic Regression Models in Data with Unobserved Heterogeneity at Cluster Levels

Clustering due to unobserved heterogeneity may seriously impact on inference from binary regression models. We examined the performance of the logistic, and the logistic-normal models for data with such clustering. The total variance of unobserved heterogeneity rather than the level of clustering determines the size of bias of the maximum likelihood (ML) estimator, for the logistic model. Incorrect specification of clustering as level 2, using the logistic-normal model, provides biased estimates of the structural and random parameters, while specifying level 1, provides unbiased estimates for the former, and adequately estimates the latter. The proposed procedure appeals to many research areas.     

Inference for Bivariate Survival Data by Copula Models Adjusted for the Boundary Effect

Copula models describe the dependence structure of two random variables separately from their marginal distributions and hence are particularly useful in studying the association for bivariate survival data. Semiparametric inference for bivariate survival data based on copula models has been studied for various types of data, including complete data, right-censored data, and current status data. This article discusses the boundary effect on these inference procedures, a problem that has been neglected in the previous literature. Specifically, asymptotic distribution of the association estimator on the boundary of parameter space is derived for one-dimensional copula models. The boundary properties are applied to test independence and to study the estimation efficiency. Simulation study is conducted for the bivariate right-censored data and current status data.     

Approximate Bayesian Inference for Survival Models

Abstract. Bayesian analysis of time‐to‐event data, usually called survival analysis, has received increasing attention in the last years. In Cox‐type models it allows to use information from the full likelihood instead of from a partial likelihood, so that the baseline hazard function and the model parameters can be jointly estimated. In general, Bayesian methods permit a full and exact posterior inference for any parameter or predictive quantity of interest. On the other side, Bayesian inference often relies on Markov chain Monte Carlo (MCMC) techniques which, from the user point of view, may appear slow at delivering answers. In this article, we show how a new inferential tool named integrated nested Laplace approximations can be adapted and applied to many survival models making Bayesian analysis both fast and accurate without having to rely on MCMC‐based inference.     

Presmoothed Estimation with Left-Truncated and Right-Censored Data

We propose a new method to estimate the cumulative hazard function and the corresponding distribution function of survival times under randomly left-truncated and right-censored observations (LTRC). The new estimators are based on presmoothing ideas, the estimation of the conditional expectation m of the censoring indicator. An almost sure representation for both estimators is established, from which a strong consistency rate and asymptotic normality are derived. It is shown that the presmoothed modification leads to a gain in terms of asymptotic mean squared error. This efficiency with respect to the classical estimators is also shown in a simulation study. Finally, an application to a real data set is provided.     

Dependence Estimation for Marginal Models of Multivariate Survival Data

We have previously(Segal and Neuhaus, 1993) devised methods for obtaining marginal regression coefficients and associated variance estimates for multivariate survival data, using a synthesis of the Poisson regression formulation for univariate censored survival analysis and generalized estimating equations (GEE's). The method is parametric in that a baseline survival distribution is specified. Analogous semiparametric models, with unspecified baseline survival, have also been developed (Wei, Lin and Weissfeld, 1989; Lin, 1994).Common to both these approaches is the provision of robust variances for the regression parameters. However, none of this work has addressed the more difficult area of dependence estimation. While GEE approaches ostensibly provide such estimates, we show that there are problems adopting these with multivariate survival data. Further, we demonstrate that these problems can affect estimation of the regression coefficients themselves. An alternate, ad hoc approach to dependence estimation, based on design effects, is proposed and evaluated via simulation and illustrative examples. This revised version was published online in July 2006 with corrections to the Cover Date.     

Generalized Empirical Likelihood Inference in Generalized Linear Models for Longitudinal Data

In this article, the generalized linear model for longitudinal data is studied. A generalized empirical likelihood method is proposed by combining generalized estimating equations and quadratic inference functions based on the working correlation matrix. It is proved that the proposed generalized empirical likelihood ratios are asymptotically chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. In addition, the maximum empirical likelihood estimates of parameters are obtained, and their asymptotic normalities are proved. Some simulations are undertaken to compare the generalized empirical likelihood and normal approximation-based method in terms of coverage accuracies and average areas/lengths of confidence regions/intervals. An example of a real data is used for illustrating our methods.     

Hierarchical Dependency Models for Multivariate Survival Data with Censoring

A familyof partial likelihood logistic models is proposed for clusteredsurvival data that are reported in discrete time and that maybe censored. The possible dependence of individual survival timeswithin clusters is modeled, while distinct clusters are assumedto be independent. Two types of clusters are considered. First,all clusters have the same size and are identically distributed.Second, the clusters may vary in size. In both cases our asymptoticresults apply to a large number of small independent clusters.     

Bayesian Transformation Models for Multivariate Survival Data

In this paper, we propose a general class of Gamma frailty transformation models for multivariate survival data. The transformation class includes the commonly used proportional hazards and proportional odds models. The proposed class also includes a family of cure rate models. Under an improper prior for the parameters, we establish propriety of the posterior distribution. A novel Gibbs sampling algorithm is developed for sampling from the observed data posterior distribution. A simulation study is conducted to examine the properties of the proposed methodology. An application to a data set from a cord blood transplantation study is also reported.     

缺失偏态数据下联合位置与尺度模型的统计推断

为了研究缺失偏态数据下的联合位置与尺度模型,基于分布自身的特点,提出了一种适合缺失偏态数据下联合建模的插补方法———修正随机回归插补方法,该方法对缺失数据下模型偏度参数的调整十分显著。通过随机模拟和实例研究,并与回归插补和随机回归插补方法进行比较,结果表明,所提出的修正随机回归插补方法是有用和有效的。     

Methods of Statistical Inference for Median Regression Models with Doubly Censored Data

Recently, least absolute deviations (LAD) estimator for median regression models with doubly censored data was proposed and the asymptotic normality of the estimator was established. However, it is invalid to make inference on the regression parameter vectors, because the asymptotic covariance matrices are difficult to estimate reliably since they involve conditional densities of error terms. In this article, three methods, which are based on bootstrap, random weighting, and empirical likelihood, respectively, and do not require density estimation, are proposed for making inference for the doubly censored median regression models. Simulations are also done to assess the performance of the proposed methods.     

局部平稳部分线性面板数据模型的统计推断

部分线性模型是一类非常重要的半参数回归模型,由于它既含有参数部分又含有非参数部分,与常规的线性模型相比具有更强的适应性和解释能力。文章研究带有局部平稳协变量的固定效应部分线性面板数据模型的统计推断。首先提出一个两阶段估计方法得到模型中未知参数和非参数函数的估计,并证明估计量的渐近性质,然后运用不变原理构造出非参数函数的一致置信带,最后通过数值模拟研究和实例分析验证了该方法的有效性。     

Statistical Inference for Single‐index Panel Data Models

We study estimation and hypothesis testing in single‐index panel data models with individual effects. Through regressing the individual effects on the covariates linearly, we convert the estimation problem in single‐index panel data models to that in partially linear single‐index models. The conversion is valid regardless of the individual effects being random or fixed. We propose an estimating equation approach, which has a desirable double robustness property. We show that our method is applicable in single‐index panel data models with heterogeneous link functions. We further design a chi‐squared test to evaluate whether the individual effects are random or fixed. We conduct simulations to demonstrate the finite sample performance of the method and conduct a data analysis to illustrate its usefulness.     

Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions

In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non‐parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper.     

A Quantile Survival Model for Censored Data

In this paper we propose a quantile survival model to analyze censored data. This approach provides a very effective way to construct a proper model for the survival time conditional on some covariates. Once a quantile survival model for the censored data is established, the survival density, survival or hazard functions of the survival time can be obtained easily. For illustration purposes, we focus on a model that is based on the generalized lambda distribution (GLD). The GLD and many other quantile function models are defined only through their quantile functions, no closed‐form expressions are available for other equivalent functions. We also develop a Bayesian Markov Chain Monte Carlo (MCMC) method for parameter estimation. Extensive simulation studies have been conducted. Both simulation study and application results show that the proposed quantile survival models can be very useful in practice.     

Parameter Orthogonality in Mixed Regression Models for Survival Data

The implications of parameter orthogonality for the robustness of survival regression models are considered. The question of which of the proportional hazards or the accelerated life families of models would be more appropriate for analysis is usually ignored, and the proportional hazards family is applied, particularly in medicine, for convenience. Accelerated life models have conventionally been used in reliability applications. We propose a one-parameter family mixture survival model which includes both the accelerated life and the proportional hazards models. By orthogonalizing relative to the mixture parameter, we can show that, for small effects of the covariates, the regression parameters under the alternative families agree to within a constant. This recovers a known misspecification result. We use notions of parameter orthogonality to explore robustness to other types of misspecification including misspecified base-line hazards. The results hold in the presence of censoring. We also study the important question of when proportionality matters.     

Variable Selection for Partially Linear Models with Randomly Censored Data

This article proposes a variable selection procedure for partially linear models with right-censored data via penalized least squares. We apply the SCAD penalty to select significant variables and estimate unknown parameters simultaneously. The sampling properties for the proposed procedure are investigated. The rate of convergence and the asymptotic normality of the proposed estimators are established. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property. In addition, an iterative algorithm is proposed to find the solution of the penalized least squares. Simulation studies are conducted to examine the finite sample performance of the proposed method.     

Multivariate Parametric Spatiotemporal Models for County Level Breast Cancer Survival Data

In clustered survival settings where the clusters correspond to geographic regions, biostatisticians are increasingly turning to models with spatially distributed random effects. These models begin with spatially oriented frailty terms, but may also include further region-level terms in the parametrization of the baseline hazards or various covariate effects (as in a spatially-varying coefficients model). In this paper, we propose a multivariate conditionally autoregressive (MCAR) model as a mixing distribution for these random effects, as a way of capturing correlation across both the regions and the elements of the random effect vector for any particular region. We then extend this model to permit analysis of temporal cohort effects, where we use the term temporal cohort to mean a group of subjects all of whom were diagnosed with the disease of interest (and thus, entered the study) during the same time period (say, calendar year). We show how our spatiotemporal model may be efficiently fit in a hierarchical Bayesian framework implemented using Markov chain Monte Carlo (MCMC) computational techniques. We illustrate our approach in the context of county-level breast cancer data from 22 annual cohorts of women living in the state of Iowa, as recorded by the Surveillance, Epidemiology, and End Results (SEER) database. Hierarchical model comparison using the Deviance Information Criterion (DIC), as well as maps of the fitted county-level effects, reveal the benefit of our approach.     

Survival Weibull regression model for mismeasured outcomes

In some survival studies, the exact time of the event of interest is unknown, but the event is known to have occurred during a particular period of time (interval-censored data). If the diagnostic tool used to detect the event of interest is not perfectly sensitive and specific, outcomes may be mismeasured; a healthy subject may be diagnosed as sick and a sick one may be diagnosed as healthy. In such cases, traditional survival analysis methods produce biased estimates for the time-to-failure distribution parameters (Paggiaro and Torelli 2004 Paggiaro, A., and N. Torelli. 2004. The effect of classification errors in survival data analysis. Statistical Methods and Applications 13:213–25.[Crossref] , [Google Scholar]). In this context, we developed a parametric model that incorporates sensitivity and specificity into a grouped survival data analysis (a case of interval-censored data in which all subjects are tested at the same predetermined time points). Inferential aspects and properties of the methodology, such as the likelihood function and identifiability, are discussed in this article. Assuming known and non differential misclassification, Monte Carlo simulations showed that the proposed model performed well in the case of mismeasured outcomes; the estimates of the relative bias of the model were lower than those provided by the naive method that assumes perfect sensitivity and specificity. The proposed methodology is illustrated by a study related to mango tree lifetimes.     

Bayesian Survival Analysis of Head and Neck Cancer Data Using Lognormal Model

The paper considers a lognormal model for the survival times and obtains a Bayes solution by means of Gibbs sampler algorithm when the priors for the parameters are vague. The formulation given in the paper is mainly focused for censored data problems though it is equally well applicable for complete data scenarios as well. For the purpose of numerical illustration, we considered two real data sets on head and neck cancer patients when they have been treated using either radiotherapy or chemotherapy followed by radiotherapy. The paper not only compares the survival functions for the two therapies assuming a lognormal model but also provides a model compatibility study based on predictive simulation results so that the choice of lognormal model can be justified for the two data sets. The ease of our analysis as compared to an earlier approach is certainly an advantage.     

半参数纵向模型的惩罚二次推断函数估计

针对纵向数据半参数模型E(y|x,t)=XTβ+f(t),采用惩罚二次推断函数方法同时估计模型中的回归参数β和未知光滑函数f(t)。首先利用截断幂函数基对未知光滑函数进行基函数展开近似,然后利用惩罚样条的思想构造关于回归参数和基函数系数的惩罚二次推断函数,最小化惩罚二次推断函数便可得到回归参数和基函数系数的惩罚二次推断函数估计。理论结果显示,估计结果具有相合性和渐近正态性,通过数值方法也得到了较好的模拟结果。