M-estimation of the accelerated failure time model under a convex discrepancy function

Based on the Kaplan–Meier weight functions, we introduce a class of M-estimators of regression parameters for the accelerated failure time (AFT) model with right censored data. The proposed M-estimator is root-n consistent and asymptotically normal under appropriate assumptions. For robustness analysis, we also derive the corresponding influence functions. Appropriate criteria are developed for tests of hypotheses concerning regression parameters. The results are applied to several particular cases. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies.     

Semiparametric estimation method for accelerated failure time model with dependent censoring

Independent censoring is commonly assumed in survival analysis. However, it may be questionable when censoring is related to event time. We model the event and censoring time marginally through accelerated failure time models, and model their association by a known copula. An iteration algorithm is proposed to estimate the regression parameters. Simulation results show the improvement of the proposed method compared to the naive method under independent censoring. Sensitivity analysis gives the evidences that the proposed method can obtain reasonable estimates even when the forms of copula are misspecified. We illustrate its application by analyzing prostate cancer data.     

On gehan's wilcoxon and the accelerated failure time model

A proof is provided to show that Gehan's 1965 generalization of the two sample Wilcoxon test lies outside the class of efficient score procedures for right censored data (Prentice 1978).     

Semiparametric Bayesian accelerated failure time model with interval-censored data

Many existing approaches to analysing interval-censored data lack flexibility or efficiency. In this paper, we propose an efficient, easy to implement approach on accelerated failure time model with a logarithm transformation of the failure time and flexible specifications on the error distribution. We use exact inference for the Dirichlet process without approximation in imputation. Our algorithm can be implemented with simple Gibbs sampling which produces exact posterior distributions on the features of interest. Simulation and real data analysis demonstrate the advantage of our method compared to some other methods.     

Bayesian parametric accelerated failure time spatial model and its application to prostate cancer

Prostate cancer (PrCA) is the most common cancer diagnosed in American men and the second leading cause of death from malignancies. There are large geographical variation and racial disparities existing in the survival rate of PrCA. Much work on the spatial survival model is based on the proportional hazards (PH) model, but few focused on the accelerated failure time (AFT) model. In this paper, we investigate the PrCA data of Louisiana from the Surveillance, Epidemiology, and End Results program and the violation of the PH assumption suggests that the spatial survival model based on the AFT model is more appropriate for this data set. To account for the possible extra-variation, we consider spatially referenced independent or dependent spatial structures. The deviance information criterion is used to select a best-fitting model within the Bayesian frame work. The results from our study indicate that age, race, stage, and geographical distribution are significant in evaluating PrCA survival.     

Asymptotic expansions and the reliability of tests in accelerated failure time models

This paper gives matrix formilae for the O(n^-1 ) cerrecti0n applicable to asymptotically efficient conditional moment tests. These formulae only require expectations of functions involving, at most, second order derivatives of the log-likelihood; unlike those previously providcd by Ferrari and Corddro(1994). The correction is used to assess the reliability of first order asymptotic theory for arbitrary residual-based diagnostics in a class of accelerated failure time models: this correction is always parameter free, depending only on the number of included covariates in the regression design. For all but one of the tests considered, first order theory is found to be extremely unreliable, even in quite large samples, although this may not be widely appreciated by applied workers.     

On confidence intervals for the mean past lifetime function under random censorship

The mean past lifetime (MPL) function (also known as the expected inactivity time function) is of interest in many fields such as reliability theory and survival analysis, actuarial studies and forensic science. For estimation of the MPL function some procedures have been proposed in the literature. In this paper, we give a central limit theorem result for the estimator of MPL function based on a right-censored random sample from an unknown distribution. The limiting distribution is used to construct normal approximation-based confidence interval for MPL. Furthermore, we use the empirical likelihood ratio procedure to obtain confidence interval for the MPL function. These two intervals are compared with each other through simulation study in terms of coverage probability. Finally, a couple of numerical example illustrating the theory is also given.     

Imputation methods for doubly censored HIV data

In medical research, it is common to have doubly censored survival data: origin time and event time are both subject to censoring. In this paper, we review simple and probability-based methods that are used to impute interval censored origin time and compare the performance of these methods through extensive simulations in the one-sample problem, two-sample problem and Cox regression model problem. The use of a bootstrap procedure for inference is demonstrated.     

Statistical diagnosis for non-parametric regression models with random right censorship based on the empirical likelihood method

In this paper, we consider statistical diagnostic for non-parametric regression models with right-censored data based on empirical likelihood. First, the primary model is transformed to the non-parametric regression model. Then, based on empirical likelihood methodology, we define some diagnostic statistics. At last, some simulation studies show that our proposed procedure can work fairly well.     

Approximate MLE for the scale parameter of the generalized exponential distribution under random censoring

In this paper, we consider the maximum likelihood estimator (MLE) of the scale parameter of the generalized exponential (GE) distribution based on a random censoring model. We assume the censoring distribution also follows a GE distribution. Since the estimator does not provide an explicit solution, we propose a simple method of deriving an explicit estimator by approximating the likelihood function. In order to compare the performance of the estimators, Monte Carlo simulation is conducted. The results show that the MLE and the approximate MLE are almost identical in terms of bias and variance.     

Covariate selection for accelerated failure time data

Selection of appropriate predictors for right censored time to event data is very often encountered by the practitioners. We consider the ?₁ penalized regression or “least absolute shrinkage and selection operator” as a tool for predictor selection in association with accelerated failure time model. The choice of the penalizing parameter λ is crucial to identify the correct set of covariates. In this paper, we propose an information theory-based method to choose λ under log-normal distribution. Furthermore, an efficient algorithm is discussed in the same context. The performance of the proposed λ and the algorithm is illustrated through simulation studies and a real data analysis. The convergence of the algorithm is also discussed.     

Censored regression with the multistate accelerated sojourn times model

Many disease processes are characterized by two or more successive health states, and it is often of interest and importance to assess state-specific covariate effects. However, with incomplete follow-up data such inference has not been satisfactorily addressed in the literature. We model the logarithm-transformed sojourn time in each state as linearly related to the covariates; however, neither the distributional form of the error term nor the dependence structure of the states needs to be specified. We propose a regression procedure to accommodate incomplete follow-up data. Asymptotic theory is presented, along with some tools for goodness-of-fit diagnostics. Simulation studies show that the proposal is reliable for practical use. We illustrate it by application to a cancer clinical trial.     

On the use of extreme value tail modeling for generalized pairwise comparisons with censored outcomes

In randomized clinical trials, methods of pairwise comparisons such as the ‘Net Benefit’ or the ‘win ratio’ have recently gained much attention when interests lies in assessing the effect of a treatment as compared to a standard of care. Among other advantages, these methods are usually praised for delivering a treatment measure that can easily handle multiple outcomes of different nature, while keeping a meaningful interpretation for patients and clinicians. For time-to-event outcomes, a recent suggestion emerged in the literature for estimating these treatment measures by providing a natural handling of censored outcomes. However, this estimation procedure may lead to biased estimates when tails of survival functions cannot be reliably estimated using Kaplan–Meier estimators. The problem then extrapolates to the other outcomes incorporated in the pairwise comparison construction. In this work, we suggest to extend the procedure by the consideration of a hybrid survival function estimator that relies on an extreme value tail model through the Generalized Pareto distribution. We provide an estimator of treatment effect measures that notably improves on bias and remains easily apprehended for practical implementation. This is illustrated in an extensive simulation study as well as in an actual trial of a new cancer immunotherapy.     

Estimation of a change point in the hazard rate of Lindley model under right censoring

In this article, we consider a single change point model for a sudden change in the hazard rate of Lindley distribution to model right-censored survival data. We derive the quantile function to generate random numbers from the proposed distribution by using the Lambert function. The maximum likelihood estimation method is used to estimate parameters of the change point model. A simulation study is also carried out to analyze the performance of the estimators. To validate our findings, a dataset on bone marrow transplant for patients of acute lymphoblastic leukemia is analyzed using the proposed model and is compared with the existing exponential single change point model.     

A linear transformation model for multivariate interval‐censored failure time data

This paper discusses multivariate interval‐censored failure time data observed when several correlated survival times of interest exist and only interval censoring is available for each survival time. Such data occur in many fields, for instance, studies of the development of physical symptoms or diseases in several organ systems. A marginal inference approach was used to create a linear transformation model and applied to bivariate interval‐censored data arising from a diabetic retinopathy study and an AIDS study. The results of simulation studies that were conducted to evaluate the performance of the presented approach suggest that it performs well. The Canadian Journal of Statistics 41: 275–290; 2013 © 2013 Statistical Society of Canada     

Empirical likelihood method for the multivariate accelerated failure time models

In applications, multivariate failure time data appears when each study subject may potentially experience several types of failures or recurrences of a certain phenomenon, or failure times may be clustered. Three types of marginal accelerated failure time models dealing with multiple events data, recurrent events data and clustered events data are considered. We propose a unified empirical likelihood inferential procedure for the three types of models based on rank estimation method. The resulting log-empirical likelihood ratios are shown to possess chi-squared limiting distributions. The properties can be applied to do tests and construct confidence regions without the need to solve the rank estimating equations nor to estimate the limiting variance-covariance matrices. The related computation is easy to implement. The proposed method is illustrated by extensive simulation studies and a real example.     

Interval estimation for the generalized inverted exponential distribution under progressive first failure censoring

In this paper, we consider the inferential procedures for the generalized inverted exponential distribution under progressive first failure censoring. The exact confidence interval for the scale parameter is derived. The generalized confidence intervals (GCIs) for the shape parameter and some commonly used reliability metrics such as the quantile and the reliability function are explored. Then the proposed procedure is extended to the prediction interval for the future measurement. The GCIs for the reliability of the stress-strength model are discussed under both equal scale and unequal scale scenarios. Extensive simulations are used to demonstrate the performance of the proposed GCIs and prediction interval. Finally, an example is used to illustrate the proposed methods.