Fitting semiparametric accelerated failure time models for nested case–control data

A nested case–control (NCC) study is an efficient cohort-sampling design in which a subset of controls are sampled from the risk set at each event time. Since covariate measurements are taken only for the sampled subjects, time and efforts of conducting a full scale cohort study can be saved. In this paper, we consider fitting a semiparametric accelerated failure time model to failure time data from a NCC study. We propose to employ an efficient induced smoothing procedure for rank-based estimating method for regression parameters estimation. For variance estimation, we propose to use an efficient resampling method that utilizes the robust sandwich form. We extend our proposed methods to a generalized NCC study that allows a sampling of cases. Finite sample properties of the proposed estimators are investigated via an extensive stimulation study. An application to a tumor study illustrates the utility of the proposed method in routine data analysis.     

Regression analysis of clustered interval-censored failure time data with linear transformation models in the presence of informative cluster size

This paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided.     

Variable selection for longitudinal data with high-dimensional covariates and dropouts

A new variable selection approach utilizing penalized estimating equations is developed for high-dimensional longitudinal data with dropouts under a missing at random (MAR) mechanism. The proposed method is based on the best linear approximation of efficient scores from the full dataset and does not need to specify a separate model for the missing or imputation process. The coordinate descent algorithm is adopted to implement the proposed method and is computational feasible and stable. The oracle property is established and extensive simulation studies show that the performance of the proposed variable selection method is much better than that of penalized estimating equations dealing with complete data which do not account for the MAR mechanism. In the end, the proposed method is applied to a Lifestyle Education for Activity and Nutrition study and the interaction effect between intervention and time is identified, which is consistent with previous findings.     

Hedging Barrier Options in GARCH Models with Transaction Costs

This study proposes a modified strike‐spread method for hedging barrier options in generalized autoregressive conditional heteroskedasticity (GARCH) models with transaction costs. A simulation study was conducted to investigate the hedging performance of the proposed method in comparison with several well‐known static methods for hedging barrier options. An accurate, easy‐to‐implement and fast scheme for generating the first passage time under the GARCH framework which enhances the accuracy and efficiency of the simulation is also proposed. Simulation results and an empirical study using real data indicate that the proposed approach has a promising performance for hedging barrier options in GARCH models when transaction costs are taken into consideration.     

A copula model for bivariate hybrid censored survival data with application to the MACS study

A copula model for bivariate survival data with hybrid censoring is proposed to study the association between survival time of individuals infected with HIV and persistence time of infection with an additional virus. Survival with HIV is right censored and the persistence time of the additional virus is subject to interval censoring case 1. A pseudo-likelihood method is developed to study the association between the two event times under such hybrid censoring. Asymptotic consistency and normality of the pseudo-likelihood estimator are established based on empirical process theory. Simulation studies indicate good performance of the estimator with moderate sample size. The method is applied to a motivating HIV study which investigates the effect of GB virus type C (GBV-C) co-infection on survival time of HIV infected individuals.     

Morbidity measures in the presence of recurrent composite endpoints

The analysis of recurrent event data in clinical trials presents a number of difficulties. The statistician is faced with issues of event dependency, composite endpoints, unbalanced follow‐up times and informative dropout. It is not unusual, therefore, for statisticians charged with responsibility for providing reliable and valid analyses to need to derive new methods specific to the clinical indication under investigation. One method is proposed that appears to have possible advantages over those that are often used in the analysis of recurrent event data in clinical trials. Based on an approach that counts periods of time with events instead of single event counts, the proposed method makes an adjustment for patient time on study and incorporates heterogeneity by estimating an individual per‐patient risk of experiencing a morbid event. Monte Carlo simulations demonstrate that, with use of a real clinical study data, the proposed method consistently outperforms other measures of morbidity. Copyright © 2003 John Wiley & Sons, Ltd.     

A Comparison of Multiple Outlier Detection Methods for Regression Data

The problem of outliers in statistical data has attracted many researchers for a long time. Consequently, numerous outlier detection methods have been proposed in the statistical literature. However, no consensus has emerged as to which method is uniformly better than the others or which one is recommended for use in practical situations. In this article, we perform an extensive comparative Monte Carlo simulation study to assess the performance of the multiple outlier detection methods that are either recently proposed or frequently cited in the outlier detection literature. Our simulation experiments include a wide variety of realistic and challenging regression scenarios. We give recommendations on which method is superior to others under what conditions.     

一种基于函数型数据的综合评价方法研究

 在经济管理与决策中, 经常遇到大量的函数型数据。当指标为函数型数据时，提出了一种基于函数型数据的综合评价方法，而综合评价的核心是评价指标在不同时刻的权重系数的确定。针对由函数型数据表支持的综合评价问题的特殊性，提出了一种新的确定权重系数的“全局”拉开档次法，利用Matlab编程，使得该方法具有可操作性，并给出一个实际例子。最后将该方法与传统方法进行比较，得出本文所提方法的优势。     

Joint analysis of interval-censored failure time data and panel count data

Interval-censored failure time data and panel count data are two types of incomplete data that commonly occur in event history studies and many methods have been developed for their analysis separately (Sun in The statistical analysis of interval-censored failure time data. Springer, New York, 2006; Sun and Zhao in The statistical analysis of panel count data. Springer, New York, 2013). Sometimes one may be interested in or need to conduct their joint analysis such as in the clinical trials with composite endpoints, for which it does not seem to exist an established approach in the literature. In this paper, a sieve maximum likelihood approach is developed for the joint analysis and in the proposed method, Bernstein polynomials are used to approximate unknown functions. The asymptotic properties of the resulting estimators are established and in particular, the proposed estimators of regression parameters are shown to be semiparametrically efficient. In addition, an extensive simulation study was conducted and the proposed method is applied to a set of real data arising from a skin cancer study.     

Jackknife Empirical Likelihood for the Accelerated Failure Time Model with Censored Data

Kendall and Gehan estimating functions are commonly used to estimate the regression parameter in accelerated failure time model with censored observations in survival analysis. In this paper, we apply the jackknife empirical likelihood method to overcome the computation difficulty about interval estimation. A Wilks’ theorem of jackknife empirical likelihood for U-statistic type estimating equations is established, which is used to construct the confidence intervals for the regression parameter. We carry out an extensive simulation study to compare the Wald-type procedure, the empirical likelihood method, and the jackknife empirical likelihood method. The proposed jackknife empirical likelihood method has a better performance than the existing methods. We also use a real data set to compare the proposed methods.     

Comparison of Times Series with Unequal Length in the Frequency Domain

In statistical data analysis it is often important to compare, classify, and cluster different time series. For these purposes various methods have been proposed in the literature, but they usually assume time series with the same sample size. In this article, we propose a spectral domain method for handling time series of unequal length. The method make the spectral estimates comparable by producing statistics at the same frequency. The procedure is compared with other methods proposed in the literature by a Monte Carlo simulation study. As an illustrative example, the proposed spectral method is applied to cluster industrial production series of some developed countries.     

Nonparametric Quantile Estimation with Correlated Failure Time Data

In biomedical studies, correlated failure time data arise often. Although point and confidence interval estimation for quantiles with independent censored failure time data have been extensively studied, estimation for quantiles with correlated failure time data has not been developed. In this article, we propose a nonparametric estimation method for quantiles with correlated failure time data. We derive the asymptotic properties of the quantile estimator and propose confidence interval estimators based on the bootstrap and kernel smoothing methods. Simulation studies are carried out to investigate the finite sample properties of the proposed estimators. Finally, we illustrate the proposed method with a data set from a study of patients with otitis media.     

An improved estimator to analyse missing data

Missing data due to nonresponse, though undesirable, is a reality of any survey. In this paper we consider a situation in which, at a given time, observations are missing for one of the several auxiliary characteristics; thus the ‘missing’ phenomenon occurs for the characteristics separately but not simultaneously. A new method, making use of all the available observations, is proposed. A simulation study based on three real populations was performed to test the proposed technique.     

Small area estimation under a multivariate linear model for repeated measures data

In this article, small area estimation under a multivariate linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units, and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points, and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.     

An omnibus CUSUM chart for monitoring time to event data

A non-parametric method is proposed for monitoring time-to-event data. A cumulative sum chart is constructed that is able to detect an unknown out-of-control state. This method exploits the absolute differences between the Kaplan–Meier estimator and the in-control distribution over specific time intervals. The efficiency of the algorithm is studied via a simulation and a real data study. The new method is also tested via the simulation study against existing methods.     

A method for estimating lorenz curves

This paper proposes a new method for estimating the parameters of Lorenz Curves (LC’s) and fitting LC’s to observed data. The method is very general. It is applicable to any family of LC’s as long as it is given in closed form which is often the case in practice. The method can also be applied to either the LC or to its associated distribution. The estimators are easy to compute as they are obtained one at a time by solving only one equation in one unknown and in many cases the solutions are given in closed-forms. An additional advantage, that is not shared with the currently used method of estimation, is that the method is invariant as to the specification of which variable is written as a function of the other in the LC form. The method is applied to the most commonly suggested LC’s families. An example of real-life data is used to illustrate the methodology. A simulation study is performed to study the properties of the proposed estimators and to compare them with existing ones. The results seem to indicate that the proposed estimators have good properties and they often perform much better than the existing ones.     

Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates

This paper is motivated from a neurophysiological study of muscle fatigue, in which biomedical researchers are interested in understanding the time-dependent relationships of handgrip force and electromyography measures. A varying coefficient model is appealing here to investigate the dynamic pattern in the longitudinal data. The response variable in the study is continuous but bounded on the standard unit interval (0, 1) over time, while the longitudinal covariates are contaminated with measurement errors. We propose a generalization of varying coefficient models for the longitudinal proportional data with errors-in-covariates. We describe two estimation methods with penalized splines, which are formalized under a Bayesian inferential perspective. The first method is an adaptation of the popular regression calibration approach. The second method is based on a joint likelihood under the hierarchical Bayesian model. A simulation study is conducted to evaluate the efficacy of the proposed methods under different scenarios. The analysis of the neurophysiological data is presented to demonstrate the use of the methods.     

大规模数据下基于充分降维的Leverage重要性抽样方法

随着信息技术的飞速发展，大规模数据在短时间内搜集并储存下来，为分析决策提供了巨大的信息量，也给统计建模带来了一定难度。对于样本容量大、变量个数少的数据，Leverage重要性抽样是一个简便可行的方法。本文发现，该方法中度量样本重要性的Leverage分数与因变量无关，而且在维度较大的情形下对样本没有区分程度，使得估计结果较差。为了同时考虑因变量和维度的影响，本文提出了基于充分降维的Leverage重要性抽样方法。该方法以不损失信息为前提，在充分降维的空间内重新计算Leverage分数，使得抽样更具有代表性。模拟数据分析显示，在样本容量较大的复杂数据中，相比于原始的Leverage重要性抽样方法，本文提出的方法可以降低估计的均方误差。三个实际数据也证实了该方法的可行性和有效性。     

An algorithm for the multivariate group lasso with covariance estimation

We study a group lasso estimator for the multivariate linear regression model that accounts for correlated error terms. A block coordinate descent algorithm is used to compute this estimator. We perform a simulation study with categorical data and multivariate time series data, typical settings with a natural grouping among the predictor variables. Our simulation studies show the good performance of the proposed group lasso estimator compared to alternative estimators. We illustrate the method on a time series data set of gene expressions.     

Composite Estimating Equation Method for the Accelerated Failure Time Model with Length‐biased Sampling Data

Length‐biased sampling data are often encountered in the studies of economics, industrial reliability, epidemiology, genetics and cancer screening. The complication of this type of data is due to the fact that the observed lifetimes suffer from left truncation and right censoring, where the left truncation variable has a uniform distribution. In the Cox proportional hazards model, Huang & Qin (Journal of the American Statistical Association, 107, 2012, p. 107) proposed a composite partial likelihood method which not only has the simplicity of the popular partial likelihood estimator, but also can be easily performed by the standard statistical software. The accelerated failure time model has become a useful alternative to the Cox proportional hazards model. In this paper, by using the composite partial likelihood technique, we study this model with length‐biased sampling data. The proposed method has a very simple form and is robust when the assumption that the censoring time is independent of the covariate is violated. To ease the difficulty of calculations when solving the non‐smooth estimating equation, we use a kernel smoothed estimation method (Heller; Journal of the American Statistical Association, 102, 2007, p. 552). Large sample results and a re‐sampling method for the variance estimation are discussed. Some simulation studies are conducted to compare the performance of the proposed method with other existing methods. A real data set is used for illustration.