Diagnostic Plots for Assessing the Frailty Distribution in Multivariate Survival Data

In biomedical studies, frailty models arecommonly used in analyzing multivariate survival data, wherethe objective of the study is to estimate both the covariateeffect and the dependence between the multivariate survival times.However, inference based on these models are dependent on thedistributional assumption of frailty. We propose a diagnosticplot for assessing the frailty assumption. The proposed methodis based on the cross-ratio function and the diagnostic plotsuggested by Oakes (1989). We use kernel regression smoothingwith bandwidth choice by cross-validation, to obtain the proposedplot. The resulting plot is capable of differentiating betweenthe gamma and positive stable frailty models when strong associationis present. We illustrate the feasibility of our method usingsimulation studies under known frailty distributions. The approachis applied to data on blindness for each eye of diabetic patientswith adult onset diabetes and a reasonable fit to the gamma frailtymodel is found.     

Logistic与分类树模型变量筛选的比较——基于信用卡邮寄业务响应率分析

基于信用卡邮寄业务响应率分析来讨论Logistic模型和分类树模型在变量选取上的区别,并尝试从几个不同角度去解释两类模型变量筛选差异的原因。笔者认为没有绝对占优势的方法,需要结合具体场景和模型的特点来选择合适的模型。分类树模型在训练集上容易过度拟合,对单个变量的影响很敏感,在进行危险因素分析时结果更能强调危险因素,对孤立点的识别率很高。Logistic模型容易受到解释变量依存关系的影响,加上分类变量的影响容易过多地选入变量或者因子,对孤立点敏感,对噪点不敏感。判别函数的差异是变量筛选差异的关键因素。     

A new local estimation method for single index models for longitudinal data

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They are very useful for longitudinal data analysis. In this paper, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonparametric parts will be established. Monte Carlo simulation studies show excellent finite sample performance. Furthermore, we illustrate our methods with a real data example.     

Marginal Regression of Multivariate Event Times Based on Linear Transformation Models

Multivariate event time data are common in medical studies and have received much attention recently. In such data, each study subject may potentially experience several types of events or recurrences of the same type of event, or event times may be clustered. Marginal distributions are specified for the multivariate event times in multiple events and clustered events data, and for the gap times in recurrent events data, using the semiparametric linear transformation models while leaving the dependence structures for related events unspecified. We propose several estimating equations for simultaneous estimation of the regression parameters and the transformation function. It is shown that the resulting regression estimators are asymptotically normal, with variance–covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. Simulation studies show that the proposed approach is appropriate for practical use. An application to the well-known bladder cancer tumor recurrences data is also given to illustrate the methodology.     

The effects of model mis-specifications in linear measurement error models

In the literature, there are many results on the consequences of mis-specified models for linear models with error in the response only, see, e.g., Seber(1977). There are also discussions of estimation for the model writh errors both in the response and in the predictor variables (called measurement error models; see, e.g., Fuller(1987)). In this paper, we consider the problem of model mis-specification for measurement error models. Only a few special cases have been tackled in the past (Edland, 1996; Carroll and Ruppert, 1996 and Lakshminarayanan Amp; Gunst, 1984); we deal with the situation here in some generality. Results have been obtained as follows: (a) When a model is under-fitted, the estimate of the variance of the measurement error will be asymptotically biased, as will the regression coefficients, and the asymptotic biases in the estimates of the regression coefficients will always exist for under-fitted models. Even orthogonality of the variables in the model will not make the biases vanish. (b)For over-fitting, the estimates of the variances of measurement errors and of the regression coefficients are asymptotically unbiased. However, the variance of the estimated regression coefficients will increase. Over-fitting will cause larger changes in the variances of the estimated parameters in measurement error models than in no measurement error models.     

Events per variable for risk differences and relative risks using pseudo-observations

A method based on pseudo-observations has been proposed for direct regression modeling of functionals of interest with right-censored data, including the survival function, the restricted mean and the cumulative incidence function in competing risks. The models, once the pseudo-observations have been computed, can be fitted using standard generalized estimating equation software. Regression models can however yield problematic results if the number of covariates is large in relation to the number of events observed. Guidelines of events per variable are often used in practice. These rules of thumb for the number of events per variable have primarily been established based on simulation studies for the logistic regression model and Cox regression model. In this paper we conduct a simulation study to examine the small sample behavior of the pseudo-observation method to estimate risk differences and relative risks for right-censored data. We investigate how coverage probabilities and relative bias of the pseudo-observation estimator interact with sample size, number of variables and average number of events per variable.     

Cellular automata and Riccati equation models for diffusion of innovations

Innovation diffusion represents a central topic both for researchers and for managers and policy makers. Traditionally, it has been examined using the successful Bass models (BM, GBM), based on an aggregate differential approach, which assures flexibility and reliable forecasts. More recently, the rising interest towards adoptions at the individual level has suggested the use of agent based models, like Cellular Automata models (CA), that are generally implemented through computer simulations. In this paper we present a link between a particular kind of CA and a separable non autonomous Riccati equation, whose general structure includes the Bass models as a special case. Through this link we propose an alternative to direct computer simulations, based on real data, and a new aggregate model, which simultaneously considers birth and death processes within the diffusion. The main results, referred to the closed form solution, the identification and the statistical analysis of our new model, may be both of theoretical and empirical interest. In particular, we examine two applied case studies, illustrating some forecasting improvements obtained.     

Mixtures of regression models with incomplete and noisy data

The estimation of the mixtures of regression models is usually based on the normal assumption of components and maximum likelihood estimation of the normal components is sensitive to noise, outliers, or high-leverage points. Missing values are inevitable in many situations and parameter estimates could be biased if the missing values are not handled properly. In this article, we propose the mixtures of regression models for contaminated incomplete heterogeneous data. The proposed models provide robust estimates of regression coefficients varying across latent subgroups even under the presence of missing values. The methodology is illustrated through simulation studies and a real data analysis.     

General partially linear varying-coefficient transformation models for ranking data

In this paper,we propose a class of general partially linear varying-coefficient transformation models for ranking data. In the models, the functional coefficients are viewed as nuisance parameters and approximated by B-spline smoothing approximation technique. The B-spline coefficients and regression parameters are estimated by rank-based maximum marginal likelihood method. The three-stage Monte Carlo Markov Chain stochastic approximation algorithm based on ranking data is used to compute estimates and the corresponding variances for all the B-spline coefficients and regression parameters. Through three simulation studies and a Hong Kong horse racing data application, the proposed procedure is illustrated to be accurate, stable and practical.     

Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions

The purpose of this paper is to develop diagnostics analysis for nonlinear regression models (NLMs) under scale mixtures of skew-normal (SMSN) distributions introduced by Garay et al. [Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115–124]. This novel class of models provides a useful generalization of the symmetrical NLM [Vanegas LH, Cysneiros FJA. Assessment of diagnostic procedures in symmetrical nonlinear regression models. Comput. Statist. Data Anal. 2010;54:1002–1016] since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as the skew-t, skew-slash, skew-contaminated normal distributions, among others. Motivated by the results given in Garay et al. [Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115–124], we presented a score test for testing the homogeneity of the scale parameter and its properties are investigated through Monte Carlo simulations studies. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. The newly developed procedures are illustrated considering a real data set.     

Models for longitudinal data with censored changepoints

Summary.  In longitudinal studies of biological markers, different individuals may have different underlying patterns of response. In some applications, a subset of individuals experiences latent events, causing an instantaneous change in the level or slope of the marker trajectory. The paper presents a general mixture of hierarchical longitudinal models for serial biomarkers. Interest centres both on the time of the event and on levels of the biomarker before and after the event. In observational studies where marker series are incomplete, the latent event can be modelled by a survival distribution. Risk factors for the occurrence of the event can be investigated by including covariates in the survival distribution. A combination of Gibbs, Metropolis–Hastings and reversible jump Markov chain Monte Carlo sampling is used to fit the models to serial measurements of forced expiratory volume from lung transplant recipients.     

Bayesian quantile regression for skew-normal linear mixed models

Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples.     

Longitudinal poisson regression with disturbed random intercept

Consider repeated event-count data from a sequence of exposures, during each of which a subject can experience some number of events, which is reported at ‘visits’ following each exposure. Within-subject heterogeneity not accounted for by visit-varying covariates is called ‘visit-level’ heterogeneity. Using generalized linear mixed models with log link for longitudinal Poisson regression, I model visit-level heterogeneity by cumulatively adding ‘disturbances’ to the random intercept of each subject over visits to create a ‘disturbed-random-intercept$rsquo; model. I also create a ‘disturbed-random-slope’ model, where the slope is over visits, and both intercept and slope are random but only the slope is disturbed. Simulation studies compare fixed-effect estimation for these models in data with 15 visits, large visit-level heterogeneity, and large multiplicative overdispersion. These studies show statistically significant superiority of the disturbed-random-intercept model. Examples with epidemiological data compare results of this model with those from other published models.     

Sensitivity analyses for partially observed recurrent event data

Recurrent events involve the occurrences of the same type of event repeatedly over time and are commonly encountered in longitudinal studies. Examples include seizures in epileptic studies or occurrence of cancer tumors. In such studies, interest lies in the number of events that occur over a fixed period of time. One considerable challenge in analyzing such data arises when a large proportion of patients discontinues before the end of the study, for example, because of adverse events, leading to partially observed data. In this situation, data are often modeled using a negative binomial distribution with time‐in‐study as offset. Such an analysis assumes that data are missing at random (MAR). As we cannot test the adequacy of MAR, sensitivity analyses that assess the robustness of conclusions across a range of different assumptions need to be performed. Sophisticated sensitivity analyses for continuous data are being frequently performed. However, this is less the case for recurrent event or count data. We will present a flexible approach to perform clinically interpretable sensitivity analyses for recurrent event data. Our approach fits into the framework of reference‐based imputations, where information from reference arms can be borrowed to impute post‐discontinuation data. Different assumptions about the future behavior of dropouts dependent on reasons for dropout and received treatment can be made. The imputation model is based on a flexible model that allows for time‐varying baseline intensities. We assess the performance in a simulation study and provide an illustration with a clinical trial in patients who suffer from bladder cancer. Copyright © 2015 John Wiley & Sons, Ltd.     

Multivariate measurement error models based on Student-t distribution under censored responses

Measurement error models constitute a wide class of models that include linear and nonlinear regression models. They are very useful to model many real-life phenomena, particularly in the medical and biological areas. The great advantage of these models is that, in some sense, they can be represented as mixed effects models, allowing us to implement well-known techniques, like the EM-algorithm for the parameter estimation. In this paper, we consider a class of multivariate measurement error models where the observed response and/or covariate are not fully observed, i.e., the observations are subject to certain threshold values below or above which the measurements are not quantifiable. Consequently, these observations are considered censored. We assume a Student-t distribution for the unobserved true values of the mismeasured covariate and the error term of the model, providing a robust alternative for parameter estimation. Our approach relies on a likelihood-based inference using an EM-type algorithm. The proposed method is illustrated through some simulation studies and the analysis of an AIDS clinical trial dataset.     

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。     

Multilevel models for longitudinal data

Summary.  Repeated measures and repeated events data have a hierarchical structure which can be analysed by using multilevel models. A growth curve model is an example of a multilevel random-coefficients model, whereas a discrete time event history model for recurrent events can be fitted as a multilevel logistic regression model. The paper describes extensions to the basic growth curve model to handle auto-correlated residuals, multiple-indicator latent variables and correlated growth processes, and event history models for correlated event processes. The multilevel approach to the analysis of repeated measures data is contrasted with structural equation modelling. The methods are illustrated in analyses of children's growth, changes in social and political attitudes, and the interrelationship between partnership transitions and childbearing.     

Asymptotic properties of the estimators of the semi-parametric spatial regression model

Spatial data and non parametric methods arise frequently in studies of different areas and it is a common practice to analyze such data with semi-parametric spatial autoregressive (SPSAR) models. We propose the estimations of SPSAR models based on maximum likelihood estimation (MLE) and kernel estimation. The estimation of spatial regression coefficient ρ was done by optimizing the concentrated log-likelihood function with respect to ρ. Furthermore, under appropriate conditions, we derive the limiting distributions of our estimators for both the parametric and non parametric components in the model.     

空间回归模型选择的反思

空间计量经济学存在两种最基本的模型:空间滞后模型和空间误差模型,这里旨在重新思考和探讨这两种空间回归模型的选择,结论为:Moran’s I指数可以用来判断回归模型后的残差是否存在空间依赖性;在实证分析中,采用拉格朗日乘子检验判断两种模型优劣是最常见的做法。然而,该检验仅仅是基于统计推断而忽略了理论基础,因此,可能导致选择错误的模型;在实证分析中,空间误差模型经常被选择性遗忘,而该模型的适用性较空间滞后模型更为广泛;实证分析大多缺乏空间回归模型设定的探讨,Anselin提出三个统计量,并且,如果模型设定正确,应该遵从Wald统计量>Log likelihood统计量>LM统计量的排列顺序。     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.