Testing for overdispersion in a censored Poisson regression model

In this article, we investigate the efficiency of score tests for testing a censored Poisson regression model against censored negative binomial regression alternatives. Based on the results of a simulation study, score tests using the normal approximation, underestimate the nominal significance level. To remedy this problem, bootstrap methods are proposed. We find that bootstrap methods keep the significance level close to the nominal one and have greater power uniformly than does the normal approximation for testing the hypothesis.     

The heteroscedastic odd log-logistic generalized gamma regression model for censored data

We propose a four-parameter extended generalized gamma model, which includes as special cases some important distributions and it is very useful for modeling lifetime data. A advantage is that it can represent the error distribution for a new heteroscedastic log-odd log-logistic generalized gamma regression model. The proposed heteroscedastic regression model can be used more effectively in the analysis of survival data since it includes as special models several widely-known regression models. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. Overall, the new regression model is very useful to the analysis of real data.     

A new regression model for bimodal data and applications in agriculture

We define the odd log-logistic exponential Gaussian regression with two systematic components, which extends the heteroscedastic Gaussian regression and it is suitable for bimodal data quite common in the agriculture area. We estimate the parameters by the method of maximum likelihood. Some simulations indicate that the maximum-likelihood estimators are accurate. The model assumptions are checked through case deletion and quantile residuals. The usefulness of the new regression model is illustrated by means of three real data sets in different areas of agriculture, where the data present bimodality.     

Partially linear censored quantile regression

Censored regression quantile (CRQ) methods provide a powerful and flexible approach to the analysis of censored survival data when standard linear models are felt to be appropriate. In many cases however, greater flexibility is desired to go beyond the usual multiple regression paradigm. One area of common interest is that of partially linear models: one (or more) of the explanatory covariates are assumed to act on the response through a non-linear function. Here the CRQ approach of Portnoy (J Am Stat Assoc 98:1001–1012, 2003) is extended to this partially linear setting. Basic consistency results are presented. A simulation experiment and unemployment example justify the value of the partially linear approach over methods based on the Cox proportional hazards model and on methods not permitting nonlinearity.     

A semiparametric regression cure model for doubly censored data

This paper discusses regression analysis of doubly censored failure time data when there may exist a cured subgroup. By doubly censored data, we mean that the failure time of interest denotes the elapsed time between two related events and the observations on both event times can suffer censoring (Sun in The statistical analysis of interval-censored failure time data. Springer, New York, 2006). One typical example of such data is given by an acquired immune deficiency syndrome cohort study. Although many methods have been developed for their analysis (De Gruttola and Lagakos in Biometrics 45:1–12, 1989; Sun et al. in Biometrics 55:909–914, 1999; 60:637–643, 2004; Pan in Biometrics 57:1245–1250, 2001), it does not seem to exist an established method for the situation with a cured subgroup. This paper discusses this later problem and presents a sieve approximation maximum likelihood approach. In addition, the asymptotic properties of the resulting estimators are established and an extensive simulation study indicates that the method seems to work well for practical situations. An application is also provided.     

A large-scale monte carlo study of the buckley-james estimator with censored data

Estimation in the presence of censoring is an important problem. In the linear model, the Buckley-James method proceeds iteratively by estimating the censored values than re-estimating the regression coeffi- cients. A large-scale Monte Carlo simulation technique has been developed to test the performance of the Buckley-James (denoted B-J) estimator. One hundred and seventy two randomly generated data sets, each with three thousand replications, based on four failure distributions, four censoring patterns, three sample sizes and four censoring rates have been investigated, and the results are presented. It is found that, except for Type I1 censoring, the B-J estimator is essentially unbiased, even when the data sets with small sample sizes are subjected to a high censoring rate. The variance formula suggested by Buckley and James (1979) is shown to be sensitive to the failure distribution. If the censoring rate is kept constant along the covariate line, the sample variance of the estimator appears to be insensitive to the censoring pattern with a selected failure distribution. Oscillation of the convergence values associated with the B-J estimator is illustrated and thoroughly discussed.     

A flexible semiparametric transformation model for survival data

I suggest an extension of the semiparametric transformation model that specifies a time-varying regression structure for the transformation, and thus allows time-varying structure in the data. Special cases include a stratified version of the usual semiparametric transformation model. The model can be thought of as specifying a first order Taylor expansion of a completely flexible baseline. Large sample properties are derived and estimators of the asymptotic variances of the regression coefficients are given. The method is illustrated by a worked example and a small simulation study. A goodness of fit procedure for testing if the regression effects lead to a satisfactory fit is also suggested.     

Variable selection for semiparametric errors-in-variables regression model with longitudinal data

In this paper, we focus on the variable selection for the semiparametric regression model with longitudinal data when some covariates are measured with errors. A new bias-corrected variable selection procedure is proposed based on the combination of the quadratic inference functions and shrinkage estimations. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure with an application.     

A regression method for censored inverse-Gaussian data

Multiple regression methods are considered for progressively right-censored inverse-Gaussian data. Maximum-likelihood estimators are derived using the EM algorithm, and their asymptotic distributional properties are presented. The methodology is demonstrated using two case illustrations, one of which involves the defective feature of the inverse-Gaussian distribution. The relationship of the methodology to regression methods for complete inverse-Gaussian samples and to other regression methods for censored survival data is discussed.     

A log-linear regression model for the odd Weibull distribution with censored data

We introduce the log-odd Weibull regression model based on the odd Weibull distribution (Cooray, 2006). We derive some mathematical properties of the log-transformed distribution. The new regression model represents a parametric family of models that includes as sub-models some widely known regression models that can be applied to censored survival data. We employ a frequentist analysis and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to assess global influence. Further, for different parameter settings, sample sizes and censoring percentages, some simulations are performed. In addition, the empirical distribution of some modified residuals are given and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to check the model assumptions. The extended regression model is very useful for the analysis of real data.     

A non-iterative Bayesian sampling algorithm for censored Student-t linear regression models

ABSTRACT

In this paper, we consider an effective Bayesian inference for censored Student-t linear regression model, which is a robust alternative to the usual censored Normal linear regression model. Based on the mixture representation of the Student-t distribution, we propose a non-iterative Bayesian sampling procedure to obtain independently and identically distributed samples approximately from the observed posterior distributions, which is different from the iterative Markov Chain Monte Carlo algorithm. We conduct model selection and influential analysis using the posterior samples to choose the best fitted model and to detect latent outliers. We illustrate the performance of the procedure through simulation studies, and finally, we apply the procedure to two real data sets, one is the insulation life data with right censoring and the other is the wage rates data with left censoring, and we get some interesting results.     

Variable screening for ultrahigh dimensional censored quantile regression

Quantile regression is a flexible approach to assessing covariate effects on failure time, which has attracted considerable interest in survival analysis. When the dimension of covariates is much larger than the sample size, feature screening and variable selection become extremely important and indispensable. In this article, we introduce a new feature screening method for ultrahigh dimensional censored quantile regression. The proposed method can work for a general class of survival models, allow for heterogeneity of data and enjoy desirable properties including the sure screening property and the ranking consistency property. Moreover, an iterative version of screening algorithm has also been proposed to accommodate more complex situations. Monte Carlo simulation studies are designed to evaluate the finite sample performance under different model settings. We also illustrate the proposed methods through an empirical analysis.     

A power transformation regression model for censored failure time data

A power transformation regression model is considered for exponentially distributed time to failure data with right censoring. Procedures for estimation of parameters by maximum likelihood and assessment of goodness of model fit are described and illustrated.     

Nonparametric regression estimates with censored data based on block thresholding method

Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study.     

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827–842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.     

Estimation of the linear EV model with censored data

In this paper, a censored linear errors-in-variables model is investigated. The asymptotic normality of the unknown parameter's estimator is obtained. Two empirical log-likelihood ratio statistics for the unknown parameter in the model are suggested. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameter of interest. Finite sample performance of the proposed method is illustrated in a simulation study.