Nonparametric estimation of current status data with dependent censoring

This paper discusses nonparametric estimation of a survival function when one observes only current status data (McKeown and Jewell, Lifetime Data Anal 16:215-230, 2010; Sun, The statistical analysis of interval-censored failure time data, 2006; Sun and Sun, Can J Stat 33:85-96, 2005). In this case, each subject is observed only once and the failure time of interest is observed to be either smaller or larger than the observation or censoring time. If the failure time and the observation time can be assumed to be independent, several methods have been developed for the problem. Here we will focus on the situation where the independent assumption does not hold and propose two simple estimation procedures under the copula model framework. The proposed estimates allow one to perform sensitivity analysis or identify the shape of a survival function among other uses. A simulation study performed indicates that the two methods work well and they are applied to a motivating example from a tumorigenicity study.     

A nonparametric test for current status data with unequal censoring

Nonparametric tests for the comparison of different treatments based on current status data are proposed. For this problem, most methods proposed in the literature require that observation times on all subjects follow the same distribution. In other words, censoring distributions are identical between the treatment groups. In this paper, we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given. The asymptotic distribution of the test proposed is derived. The method proposed is applied to data arising from a tumorigenicity experiment.     

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.     

Efficient estimation for the proportional hazards model with bivariate current status data

We consider efficient estimation of regression and association parameters jointly for bivariate current status data with the marginal proportional hazards model. Current status data occur in many fields including demographical studies and tumorigenicity experiments and several approaches have been proposed for regression analysis of univariate current status data. We discuss bivariate current status data and propose an efficient score estimation approach for the problem. In the approach, the copula model is used for joint survival function with the survival times assumed to follow the proportional hazards model marginally. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. A real life data application is provided for illustration.     

Nonparametric estimation for survival data with censoring indicators missing at random

In this paper, we consider the problem of hazard rate estimation in the presence of covariates, for survival data with censoring indicators missing at random. We propose in the context usually denoted by MAR (missing at random, in opposition to MCAR, missing completely at random, which requires an additional independence assumption), nonparametric adaptive strategies based on model selection methods for estimators admitting finite dimensional developments in functional orthonormal bases. Theoretical risk bounds are provided, they prove that the estimators behave well in term of mean square integrated error (MISE). Simulation experiments illustrate the statistical procedure.     

Inference for a series system with dependent masked data under progressive interval censoring

This paper considers the statistical analysis of masked data in a series system with Burr-XII distributed components. Based on progressively Type-I interval censored sample, the maximum likelihood estimators for the parameters are obtained by using the expectation maximization algorithm, and the associated approximate confidence intervals are also derived. In addition, Gibbs sampling procedure using important sampling is applied for obtaining the Bayesian estimates of the parameters, and Monte Carlo method is employed to construct the credible intervals. Finally, a simulation study is proposed to illustrate the efficiency of the methods under different removal schemes and masking probabilities.     

Wavelet estimation of density for censored data with censoring indicator missing at random

In this paper, we define the nonlinear wavelet estimator of density for the right censoring model with the censoring indicator missing at random (MAR), and develop its asymptotic expression for mean integrated squared error (MISE). Unlike for kernel estimator, the MISE expression of the estimator is not affected by the presence of discontinuities in the curve. Meanwhile, asymptotic normality of the estimator is established. The proposed estimator can reduce to the estimator defined by Li [Non-linear wavelet-based density estimators under random censorship. J Statist Plann Inference. 2003;117(1):35–58] when the censoring indicator MAR does not occur and a bandwidth in non-parametric estimation is close to zero. Also, we define another two nonlinear wavelet estimators of the density. A simulation is done to show the performance of the three proposed estimators.     

Efficient estimation for the proportional hazards model with competing risks and current status data

The proportional hazards model is the most commonly used model in regression analysis of failure time data and has been discussed by many authors under various situations (Kalbfleisch & Prentice, 2002. The Statistical Analysis of Failure Time Data, Wiley, New York). This paper considers the fitting of the model to current status data when there exist competing risks, which often occurs in, for example, medical studies. The maximum likelihood estimates of the unknown parameters are derived and their consistency and convergence rate are established. Also we show that the estimates of regression coefficients are efficient and have asymptotically normal distributions. Simulation studies are conducted to assess the finite sample properties of the estimates and an illustrative example is provided. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

A stochastic approximation algorithm for maximum-likelihood estimation with incomplete data

We propose a new stochastic approximation (SA) algorithm for maximum-likelihood estimation (MLE) in the incomplete-data setting. This algorithm is most useful for problems when the EM algorithm is not possible due to an intractable E-step or M-step. Compared to other algorithm that have been proposed for intractable EM problems, such as the MCEM algorithm of Wei and Tanner (1990), our proposed algorithm appears more generally applicable and efficient. The approach we adopt is inspired by the Robbins-Monro (1951) stochastic approximation procedure, and we show that the proposed algorithm can be used to solve some of the long-standing problems in computing an MLE with incomplete data. We prove that in general O(n) simulation steps are required in computing the MLE with the SA algorithm and O(n log n) simulation steps are required in computing the MLE using the MCEM and/or the MCNR algorithm, where n is the sample size of the observations. Examples include computing the MLE in the nonlinear error-in-variable model and nonlinear regression model with random effects.     

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...     

Pseudo-observations for competing risks with covariate dependent censoring

Regression analysis for competing risks data can be based on generalized estimating equations. For the case with right censored data, pseudo-values were proposed to solve the estimating equations. In this article we investigate robustness of the pseudo-values against violation of the assumption that the probability of not being lost to follow-up (un-censored) is independent of the covariates. Modified pseudo-values are proposed which rely on a correctly specified regression model for the censoring times. Bias and efficiency of these methods are compared in a simulation study. Further illustration of the differences is obtained in an application to bone marrow transplantation data and a corresponding sensitivity analysis.     

Non parametric hazard estimation with dependent censoring using penalized likelihood and an assumed copula

This article introduces a novel non parametric penalized likelihood hazard estimation when the censoring time is dependent on the failure time for each subject under observation. More specifically, we model this dependence using a copula, and the method of maximum penalized likelihood (MPL) is adopted to estimate the hazard function. We do not consider covariates in this article. The non negatively constrained MPL hazard estimation is obtained using a multiplicative iterative algorithm. The consistency results and the asymptotic properties of the proposed hazard estimator are derived. The simulation studies show that our MPL estimator under dependent censoring with an assumed copula model provides a better accuracy than the MPL estimator under independent censoring if the sign of dependence is correctly specified in the copula function. The proposed method is applied to a real dataset, with a sensitivity analysis performed over various values of correlation between failure and censoring times.     

A general censoring scheme for circular data

A generalized censoring scheme in the survival analysis context was introduced by the authors in Jammalamadaka and Mangalam [S. Rao Jammalamadaka, V. Mangalam, Nonparametric estimation for middle censored data, J. Nonparametr. Stat. 15 (2003) 253–265]. In this article we discuss how such a censoring scheme applies to circular data and in particular when the original data is assumed to come from a parametric model such as the von Mises. Maximum likelihood estimation of the parameters as well as their large-sample properties are considered under this censoring scheme. We also consider nonparametric estimation of the circular probability distribution under such a general censoring scheme and use Monte Carlo methods to investigate its effects on the estimation of the mean direction and concentration.     

Adjusting win statistics for dependent censoring

For composite outcomes whose components can be prioritized on clinical importance, the win ratio, the net benefit and the win odds apply that order in comparing patients pairwise to produce wins and subsequently win proportions. Because these three statistics are derived using the same win proportions and they test the same hypothesis of equal win probabilities in the two treatment groups, we refer to them as win statistics. These methods, particularly the win ratio and the net benefit, have received increasing attention in methodological research and in design and analysis of clinical trials. For time-to-event outcomes, however, censoring may introduce bias. Previous work has shown that inverse-probability-of-censoring weighting (IPCW) can correct the win ratio for bias from independent censoring. The present article uses the IPCW approach to adjust win statistics for dependent censoring that can be predicted by baseline covariates and/or time-dependent covariates (producing the CovIPCW-adjusted win statistics). Theoretically and with examples and simulations, we show that the CovIPCW-adjusted win statistics are unbiased estimators of treatment effect in the presence of dependent censoring.     

Hazard function estimation from homogeneous right censored data with missing censoring indicators

The kernel smoothed Nelson–Aalen estimator has been well investigated, but is unsuitable when some of the censoring indicators are missing. A representation introduced by Dikta, however, facilitates hazard estimation when there are missing censoring indicators. In this article, we investigate (i) a kernel smoothed semiparametric hazard estimator and (ii) a kernel smoothed “pre-smoothed” Nelson–Aalen estimator. We derive the asymptotic normality of the proposed estimators and compare their asymptotic variances.     

A class of semiparametric cure models with current status data

Current status data occur in many biomedical studies where we only know whether the event of interest occurs before or after a particular time point. In practice, some subjects may never experience the event of interest, i.e., a certain fraction of the population is cured or is not susceptible to the event of interest. We consider a class of semiparametric transformation cure models for current status data with a survival fraction. This class includes both the proportional hazards and the proportional odds cure models as two special cases. We develop efficient likelihood-based estimation and inference procedures. We show that the maximum likelihood estimators for the regression coefficients are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in finite samples. For illustration, we provide an application of the models to a study on the calcification of the hydrogel intraocular lenses.

     

Regression analysis of longitudinal data with outcome‐dependent sampling and informative censoring

We consider a regression analysis of longitudinal data in the presence of outcome‐dependent observation times and informative censoring. Existing approaches commonly require a correct specification of the joint distribution of longitudinal measurements, the observation time process, and informative censoring time under the joint modeling framework and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semiparametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified, and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite‐sample performance of the proposed method and apply it to a study of weight loss data that motivated our investigation.     

Accelerated life tests for log-normal series system with dependent masked data under Type-I progressive hybrid censoring

This article considers the constant stress accelerated life test for series system products, where independent log-normal distributed lifetimes are assumed for the components. Based on Type-I progressive hybrid censored and masked data, the expectation-maximization algorithm is applied to obtain the estimation for the unknown parameters, and the parametric bootstrap method is used for the standard deviation estimation. In addition, Bayesian approach combining latent variable with Gibbs sampling is developed. Further, the reliability functions of the system and components are estimated at use stress level. The proposed method is illustrated through a numerical example under different masking probabilities and censoring schemes.     

Adaptive estimation of the conditional cumulative distribution function from current status data

Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T  : δ=_I{Y≤T}$\delta ={\mathbb{I}}_{\{Y\le T\}}$ with I$\mathbb{I}$ the indicator function. This paper presents a procedure to estimate the conditional cumulative distribution function F of Y given X   from an independent identically distributed sample of (X,T,δ)$(X,T,\delta )$.