Nonparametric inference for panel count data with competing risks

In survival and reliability studies, panel count data arise when we investigate a recurrent event process and each study subject is observed only at discrete time points. If recurrent events of several types are possible, we obtain panel count data with competing risks. Such data arise frequently from transversal studies on recurrent events in demography, epidemiology and reliability experiments where the individuals cannot be observed continuously. In the present paper, we propose an isotonic regression estimator for the cause specific mean function of the underlying recurrent event process of a competing risks panel count data. Further, a nonparametric test is proposed to compare the cause specific mean functions of the panel count competing risks data. Asymptotic properties of the proposed estimator and test statistic are studied. A simulation study is conducted to assess the finite sample behaviour of the proposed estimator and test statistic. Finally, the procedures developed are applied to a real data arising from skin cancer chemo prevention trial.     

Variable Selection for Panel Count Data via Non-Concave Penalized Estimating Function

Abstract.  Variable selection is an important issue in all regression analyses, and in this paper we discuss this in the context of regression analysis of panel count data. Panel count data often occur in long-term studies that concern occurrence rate of a recurrent event, and their analysis has recently attracted a great deal of attention. However, there does not seem to exist any established approach for variable selection with respect to panel count data. For the problem, we adopt the idea behind the non-concave penalized likelihood approach and develop a non-concave penalized estimating function approach. The proposed methodology selects variables and estimates regression coefficients simultaneously, and an algorithm is presented for this process. We show that the proposed procedure performs as well as the oracle procedure in that it yields the estimates as if the correct submodel were known. Simulation studies are conducted for assessing the performance of the proposed approach and suggest that it works well for practical situations. An illustrative example from a cancer study is provided.     

A nonparametric time-varying coefficient model for panel count data

In this research, we describe a nonparametric time-varying coefficient model for the analysis of panel count data. We extend the traditional panel count data models by incorporating B-splines estimates of time-varying coefficients. We show that the proposed model can be implemented using a nonparametric maximum pseudo-likelihood method. We further examine the theoretical properties of the estimators of model parameters. The operational characteristics of the proposed method are evaluated through a simulation study. For illustration, we analyse data from a study of childhood wheezing, and describe the time-varying effect of an inflammatory marker on the risk of wheezing.     

Semiparametric analysis of panel count data with correlated observation and follow-up times

This paper discusses regression analysis of panel count data that often arise in longitudinal studies concerning occurrence rates of certain recurrent events. Panel count data mean that each study subject is observed only at discrete time points rather than under continuous observation. Furthermore, both observation and follow-up times can vary from subject to subject and may be correlated with the recurrent events. For inference, we propose some shared frailty models and estimating equations are developed for estimation of regression parameters. The proposed estimates are consistent and have asymptotically a normal distribution. The finite sample properties of the proposed estimates are investigated through simulation and an illustrative example from a cancer study is provided.     

Saddlepoint <Emphasis Type="Italic">p</Emphasis>-values and confidence intervals for a class of two sample permutation tests for current status and panel count data

The current status and panel count data frequently arise from cancer and tumorigenicity studies when events currently occur. A common and widely used class of two sample tests, for current status and panel count data, is the permutation class. We manipulate the double saddlepoint method to calculate the exact mid-p-values of the underlying permutation distributions of this class of tests. Permutation simulations are replaced by analytical saddlepoint computations which provide extremely accurate mid-p-values that are exact for most practical purposes and almost always more accurate than normal approximations. The method is illustrated using two real tumorigenicity panel count data. To compare the saddlepoint approximation with the normal asymptotic approximation, a simulation study is conducted. The speed and accuracy of the saddlepoint method facilitate the calculation of the confidence interval for the treatment effect. The inversion of the mid-p-values to calculate the confidence interval for the mean rate of development of the recurrent event is discussed.     

Nonparametric Comparison for Multivariate Panel Count Data

Multivariate panel count data often occur when there exist several related recurrent events or response variables defined by occurrences of related events. For univariate panel count data, several nonparametric treatment comparison procedures have been developed. However, it does not seem to exist a nonparametric procedure for multivariate cases. Based on differences between estimated mean functions, this article proposes a class of nonparametric test procedures for multivariate panel count data. The asymptotic distribution of the new test statistics is established and a simulation study is conducted. Moreover, the new procedures are applied to a skin cancer problem that motivated this study.     

Analysis of Panel Count Data with Dependent Observation Times

In this article, a semiparametric approach is proposed for the regression analysis of panel count data. Panel count data commonly arise in clinical trials and demographical studies where the response variable is the number of multiple recurrences of the event of interest and observation times are not fixed, varying from subject to subject. It is assumed that two processes exist in this data: the first is for a recurrent event and the second is for observation time. Many studies have been done to estimate mean function and regression parameters under the independency between recurrent event process and observation time process. In this article, the same statistical inference is studied, but the situation where these two processes may be related is also considered. The mixed Poisson process is applied for the recurrent event processes, and a frailty intensity function for the observation time is also used, respectively. Simulation studies are conducted to study the performance of the suggested methods. The bladder tumor data are applied to compare previous studie' results.     

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.     

Variable selection and estimation for multivariate panel count data via the seamless‐${\it L}_{{\rm 0}}$ penalty

This paper considers regression analysis of multivariate panel count data with the focus on variable selection and estimation of significant covariate effects. For the problem, we adopt the penalized estimating equation approach with a focus on the use of the seamless‐$L_0$ penalty. The proposed approach selects variables and estimates regression coefficients simultaneously and the asymptotic properties of the resulting estimates are established. The procedure can be easily carried out with the Newton–Raphson algorithm and is evaluated by simulation studies. Also it is applied to a motivating data set arising from a skin cancer study. The Canadian Journal of Statistics 41: 368–385; 2013 © 2013 Statistical Society of Canada     

Semiparametric analysis of multivariate panel count data with nonlinear interactions

Lifetime Data Analysis - Multivariate panel count data frequently arise in follow up studies involving several related types of recurrent events. For univariate panel count data, several varying...     

基于改进的自适应传播模型的农业风险区划分析

农业险定价中的核心问题是农业风险区划问题,为了体现农业区划中个体指标的动态发展特征,根据近邻传播改进自适应近邻传播聚类方法对数据进行优化,基于轮廓系数、归属度和吸引度得到最佳聚类中心和几何聚类中心,并将聚类转化为新数据集的聚类问题;选取代表性的棉花为例进行实证分析,通过计算生产、销售、收入、财政等指标进行棉花风险区划实例分析,计算最优棉花风险区划,结果表明对于具有动态特征的数据,本模型具有很好的有效性、实用性和解释性。     

Testing for constancy in varying coefficient models

We consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example, time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data.     

Additive transformation models for clustered failure time data

We propose a class of additive transformation risk models for clustered failure time data. Our models are motivated by the usual additive risk model for independent failure times incorporating a frailty with mean one and constant variability which is a natural generalization of the additive risk model from univariate failure time to multivariate failure time. An estimating equation approach based on the marginal hazards function is proposed. Under the assumption that cluster sizes are completely random, we show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also provide goodness-of-fit test statistics for choosing the transformation. Simulation studies and real data analysis are conducted to examine the finite-sample performance of our estimators.     

Random Effects Modeling and the Zero-Inflated Poisson Distribution

Overdispersion due to a large proportion of zero observations in data sets is a common occurrence in many applications of many fields of research; we consider such scenarios in count panel (longitudinal) data. A well-known and widely implemented technique for handling such data is that of random effects modeling, which addresses the serial correlation inherent in panel data, as well as overdispersion. To deal with the excess zeros, a zero-inflated Poisson distribution has come to be canonical, which relaxes the equal mean-variance specification of a traditional Poisson model and allows for the larger variance characteristic of overdispersed data. A natural proposal then to approach count panel data with overdispersion due to excess zeros is to combine these two methodologies, deriving a likelihood from the resulting conditional probability. In performing simulation studies, we find that this approach in fact poses problems of identifiability. In this article, we construct and explain in full detail why a model obtained from the marriage of two classical and well-established techniques is unidentifiable and provide results of simulation studies demonstrating this effect. A discussion on alternative methodologies to resolve the problem is provided in the conclusion.     

Modeling the Distribution of Price Sensitivity and Implications for Optimal Retail Pricing

This article focuses on the distribution of price sensitivity across consumers. We employ a random-coefficient logit model in which brand-specific intercepts and price-slope coefficients are allowed to vary across households. The model is estimated with panel data for two product categories. The implications of the estimated model are deduced through an optimal retail pricing analysis that combines the panel data with chain-level cost figures. We test parametric distributional assumptions using semiparametric density estimates based on series expansions.     

面板数据加权聚类分析方法研究

在面板数据聚类分析方法的研究中,基于面板数据兼具截面维度和时间维度的特征,对欧氏距离函数进行了改进,在聚类过程中考虑指标权重与时间权重,提出了适用于面板数据聚类分析的"加权距离函数"以及相应的Ward.D聚类方法。首先定义了考虑指标绝对值、邻近时点增长率以及波动变异程度的欧氏距离函数;然后,将指标权重与时间权重通过线性模型集结成综合加权距离,最终实现面板数据的加权聚类过程。实证分析结果显示,考虑指标权重与时间权重的面板数据加权聚类分析方法具有更好的分辨能力,能提高样本聚类的准确性。     

Semiparametric transformation models for multivariate panel count data with dependent observation process

This article discusses regression analysis of multivariate panel count data in which the observation process may contain relevant information about or be related to the underlying recurrent event processes of interest. Such data occur if a recurrent event study involves several related types of recurrent events and the observation scheme or process may be subject-specific. For the problem, a class of semiparametric transformation models is presented, which provides a great flexibility for modelling the effects of covariates on the recurrent event processes. For estimation of regression parameters, an estimating equation-based inference procedure is developed and the asymptotic properties of the resulting estimates are established. Also the proposed approach is evaluated by simulation studies and applied to the data arising from a skin cancer chemoprevention trial.     

An additive–multiplicative mean model for panel count data with dependent observation and dropout processes

This paper discusses regression analysis of panel count data with dependent observation and dropout processes. For the problem, a general mean model is presented that can allow both additive and multiplicative effects of covariates on the underlying point process. In addition, the proportional rates model and the accelerated failure time model are employed to describe possible covariate effects on the observation process and the dropout or follow‐up process, respectively. For estimation of regression parameters, some estimating equation‐based procedures are developed and the asymptotic properties of the proposed estimators are established. In addition, a resampling approach is proposed for estimating a covariance matrix of the proposed estimator and a model checking procedure is also provided. Results from an extensive simulation study indicate that the proposed methodology works well for practical situations, and it is applied to a motivating set of real data.     

Robust estimation for panel count data with informative observation times and censoring times

Lifetime Data Analysis - We consider the semiparametric regression of panel count data occurring in longitudinal follow-up studies that concern occurrence rate of certain recurrent events. The...     

Variable selection in heterogeneous panel data models with cross-sectional dependence

This paper studies the Bridge estimator for a high-dimensional panel data model with heterogeneous varying coefficients, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We establish oracle efficiency and the asymptotic distribution of the Bridge estimator, when the number of covariates increases to infinity with the sample size in both dimensions. A BIC-type criterion is also provided for tuning parameter selection. We further generalise the marginal Bridge estimator for our model to asymptotically correctly identify the covariates with zero coefficients even when the number of covariates is greater than the sample size under a partial orthogonality condition. The finite sample performance of the proposed estimator is demonstrated by simulated data examples, and an empirical application with the US stock dataset is also provided.