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.     

Simultaneous estimation for non-crossing multiple quantile regression with right censored data

In this paper, we consider the estimation problem of multiple conditional quantile functions with right censored survival data. To account for censoring in estimating a quantile function, weighted quantile regression (WQR) has been developed by using inverse-censoring-probability weights. However, the estimated quantile functions from the WQR often cross each other and consequently violate the basic properties of quantiles. To avoid quantile crossing, we propose non-crossing weighted multiple quantile regression (NWQR), which estimates multiple conditional quantile functions simultaneously. We further propose the adaptive sup-norm regularized NWQR (ANWQR) to perform simultaneous estimation and variable selection. The large sample properties of the NWQR and ANWQR estimators are established under certain regularity conditions. The proposed methods are evaluated through simulation studies and analysis of a real data set.     

The McDonald Weibull model

For the first time, we propose a five-parameter lifetime model called the McDonald Weibull distribution to extend the Weibull, exponentiated Weibull, beta Weibull and Kumaraswamy Weibull distributions, among several other models. We obtain explicit expressions for the ordinary moments, quantile and generating functions, mean deviations and moments of the order statistics. We use the method of maximum likelihood to fit the new distribution and determine the observed information matrix. We define the log-McDonald Weibull regression model for censored data. The potentiality of the new model is illustrated by means of two real data sets.     

A log-location-scale lifetime distribution with censored data: Regression modeling,residuals, and global influence

In survival analysis applications, the presence of failure rate functions with non monotone shapes is common. Therefore, models that can accommodate such different shapes are needed. In this article, we present a location regression model based on the complementary exponentiated exponential geometric distribution as an alternative to the usual bathtub, increasing, and decreasing failure rates in lifetime data. Assuming censored data, we consider the maximum likelihood inference for analysis, graphical verification for residuals, and test statistics for influential points.     

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.     

The estimation of treatment effect for the censored bivariate data under the univariate censoring

This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given     

A semi-parametric estimation of a survival function from incomplete and doubly censored data

The purpose of this paper is to present a semi-parametric estimation of a survival function when analyzing incomplete and doubly censored data. Under the assumption that the chance of censoring is not related to the individual's survivorship, we propose a consistent estimation of survival. The derived estimator treats the uncensored observations nonparametrically and uses parametric models for both right and left censored data. Some asymptotic properties and simulation studies are also presented in order to analyze the behavior of the proposed estimator.     

Estimating Mean Survival Time: When is it Possible?

For right‐censored survival data, it is well‐known that the mean survival time can be consistently estimated when the support of the censoring time contains the support of the survival time. In practice, however, this condition can be easily violated because the follow‐up of a study is usually within a finite window. In this article, we show that the mean survival time is still estimable from a linear model when the support of some covariate(s) with non‐zero coefficient(s) is unbounded regardless of the length of follow‐up. This implies that the mean survival time can be well estimated when the support of linear predictor is wide in practice. The theoretical finding is further verified for finite samples by simulation studies. Simulations also show that, when both models are correctly specified, the linear model yields reasonable mean square prediction errors and outperforms the Cox model, particularly with heavy censoring and short follow‐up time.     

Empirical likelihood inference for the bivariate survival function under univariate censoring

In this article, we apply the empirical likelihood method to make inference on the bivariate survival function of paired failure times by estimating the survival function of censored time with the Kaplan–Meier estimator. Adjusted empirical likelihood (AEL) confidence intervals for the bivariate survival function are developed. We conduct a simulation study to compare the proposed AEL method with other methods. The simulation study shows the proposed AEL method has better performance than other existing methods. We illustrate the proposed method by analyzing the skin graft data.     

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.     

The exponentiated G geometric family of distributions

We propose a new class of distributions called the exponentiated G geometric family motivated mainly by lifetime issues which can generate several lifetime models discussed in the literature. Some mathematical properties of the new family including asymptotes and shapes, moments, quantile and generating functions, extreme values and order statistics are fully investigated. We propose the log-exponentiated Weibull geometric and log-exponentiated log-logistic geometric regression models to cope with censored data. The model parameters are estimated by maximum likelihood. Three examples with real data expose quite well the new family.     

New flexible models generated by gamma random variables for lifetime modeling

In this paper we introduce a new three-parameter exponential-type distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have constant, decreasing, increasing, upside-down bathtub and bathtub-shaped hazard rate functions. It also generalizes some well-known distributions. We discuss maximum likelihood estimation of the model parameters for complete sample and for censored sample. Additionally, we formulate a new cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time to this event follows the proposed distribution. Maximum likelihood estimation of the model parameters of the new cure rate survival model is discussed for complete sample and censored sample. Two applications to real data are provided to illustrate the flexibility of the new model in practice.     

Quantile regression methods for left-truncated and right-censored data

Left-truncated and right-censored (LTRC) data are encountered frequently due to a prevalent cohort sampling in follow-up studies. Because of the skewness of the distribution of survival time, quantile regression is a useful alternative to the Cox's proportional hazards model and the accelerated failure time model for survival analysis. In this paper, we apply the quantile regression model to LTRC data and develops an unbiased estimating equation for regression coefficients. The proposed estimation methods use the inverse probabilities of truncation and censoring weighting technique. The resulting estimator is uniformly consistent and asymptotically normal. The finite-sample performance of the proposed estimation methods is also evaluated using extensive simulation studies. Finally, analysis of real data is presented to illustrate our proposed estimation methods.     

Estimation Of A Survival Function With Doubly Censored Data And Dirichlet Process Prior Knowledge On The Observable Variable

This article presents a nonparametric Bayesian procedure for estimating a survival curve in a proportional hazard model when some of the data are censored on the left and some are censored on the right. The method works under the assumption that there is a Dirichlet process prior knowledge on the observable variable. Strong consistency of the estimator is proved and an example is given. To finish some simulation is presented to analyze the estimator.     

A General Quantile Function Model for Economic and Financial Time Series

This article proposed a general quantile function model that covers both one- and multiple-dimensional models and that takes several existing models in the literature as its special cases. This article also developed a new uniform Bayesian framework for quantile function modelling and illustrated the developed approach through different quantile function models. Many distributions are defined explicitly only via their quanitle functions as the corresponding distribution or density functions do not have an explicit mathematical expression. Such distributions are rarely used in economic and financial modelling in practice. The developed methodology makes it more convenient to use these distributions in analyzing economic and financial data. Empirical applications to economic and financial time series and comparisons with other types of models and methods show that the developed method can be very useful in practice.     

Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits

We propose a semiparametric estimator for single‐index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non‐parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy‐tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set.     

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.     

Joint modeling of censored longitudinal and event time data

Censoring of a longitudinal outcome often occurs when data are collected in a biomedical study and where the interest is in the survival and or longitudinal experiences of a study population. In the setting considered herein, we encountered upper and lower censored data as the result of restrictions imposed on measurements from a kinetic model producing “biologically implausible” kidney clearances. The goal of this paper is to outline the use of a joint model to determine the association between a censored longitudinal outcome and a time to event endpoint. This paper extends Guo and Carlin's [6] paper to accommodate censored longitudinal data, in a commercially available software platform, by linking a mixed effects Tobit model to a suitable parametric survival distribution. Our simulation results showed that our joint Tobit model outperforms a joint model made up of the more naïve or “fill-in” method for the longitudinal component. In this case, the upper and/or lower limits of censoring are replaced by the limit of detection. We illustrated the use of this approach with example data from the hemodialysis (HEMO) study [3] and examined the association between doubly censored kidney clearance values and survival.     

Bayesian Semiparametric Modelling in Quantile Regression

Abstract. We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non‐parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non‐parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.     

Robust confidence intervals for log-location-scale models with right censored data

In this paper, we combine empirical likelihood and estimating functions for censored data to obtain robust confidence regions for the parameters and more generally for functions of the parameters of distributions used in lifetime data analysis. The proposed method works with type I, type II or randomly censored data. It is illustrated by considering inference for log-location-scale models. In particular, we focus on the log-normal and the Weibull models and we tackle the problem of constructing robust confidence regions (or intervals) for the parameters of the model, as well as for quantiles and values of the survival function. The usefulness of the method is demonstrated through a Monte Carlo study and by examples on two lifetime data sets.