On estimation and diagnostics analysis in log-generalized gamma regression model for interval-censored data

The interval-censored survival data appear very frequently, where the event of interest is not observed exactly but it is only known to occur within some time interval. In this paper, we propose a location-scale regression model based on the log-generalized gamma distribution for modelling interval-censored data. We shall be concerned only with parametric forms. The proposed model for interval-censored data represents a parametric family of models that has, as special submodels, other regression models which are broadly used in lifetime data analysis. Assuming interval-censored data, we consider a frequentist analysis, a Jackknife estimator and a non-parametric bootstrap for the model parameters. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some techniques to perform global influence.     

Nonparametric Test for Doubly Interval-Censored Failure Time Data

This paper considers comparison of discrete failure time distributions when the survival time of interest measures elapsed time between two related events and observations on the occurrences of both events could be interval-censored. This kind of data is often referred to as doubly interval-censored failure time data. If the occurrence of the first event defining the survival time can be exactly observed, the data are usually referred to as interval-censored data. For the comparison problem based on interval-censored failure time data, Sun (1996) proposed a nonparametric test procedure. In this paper we generalize the procedure given in Sun (1996) to doubly interval-censored data case and the generalized test is evaluated by simulations.     

A transformation approach for the analysis of interval-censored failure time data

This paper discusses the analysis of interval-censored failure time data, which has recently attracted a great amount of attention (Li and Pu, Lifetime Data Anal 9:57–70, 2003; Sun, The statistical analysis of interval-censored data, 2006; Tian and Cai, Biometrika 93(2):329–342, 2006; Zhang et al., Can J Stat 33:61–70, 2005). Interval-censored data mean that the survival time of interest is observed only to belong to an interval and they occur in many fields including clinical trials, demographical studies, medical follow-up studies, public health studies and tumorgenicity experiments. A major difficulty with the analysis of interval-censored data is that one has to deal with a censoring mechanism that involves two related variables. For the inference, we present a transformation approach that transforms general interval-censored data into current status data, for which one only needs to deal with one censoring variable and the inference is thus much easy. We apply this general idea to regression analysis of interval-censored data using the additive hazards model and numerical studies indicate that the method performs well for practical situations. An illustrative example is provided.     

Bayesian statistical inference of the loglogistic model with interval-censored lifetime data

Interval-censored data arise when a failure time say, T cannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods.     

Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model

In recent years the analysis of interval-censored failure time data has attracted a great deal of attention and such data arise in many fields including demographical studies, economic and financial studies, epidemiological studies, social sciences, and tumorigenicity experiments. This is especially the case in medical studies such as clinical trials. In this article, we discuss regression analysis of one type of such data, Case I interval-censored data, in the presence of left-truncation. For the problem, the additive hazards model is employed and the maximum likelihood method is applied for estimations of unknown parameters. In particular, we adopt the sieve estimation approach that approximates the baseline cumulative hazard function by linear functions. The resulting estimates of regression parameters are shown to be consistent and efficient and have an asymptotic normal distribution. An illustrative example is provided.     

Maximum likelihood estimation for the proportional odds model with mixed interval-censored failure time data

This article discusses regression analysis of mixed interval-censored failure time data. Such data frequently occur across a variety of settings, including clinical trials, epidemiologic investigations, and many other biomedical studies with a follow-up component. For example, mixed failure times are commonly found in the two largest studies of long-term survivorship after childhood cancer, the datasets that motivated this work. However, most existing methods for failure time data consider only right-censored or only interval-censored failure times, not the more general case where times may be mixed. Additionally, among regression models developed for mixed interval-censored failure times, the proportional hazards formulation is generally assumed. It is well-known that the proportional hazards model may be inappropriate in certain situations, and alternatives are needed to analyze mixed failure time data in such cases. To fill this need, we develop a maximum likelihood estimation procedure for the proportional odds regression model with mixed interval-censored data. We show that the resulting estimators are consistent and asymptotically Gaussian. An extensive simulation study is performed to assess the finite-sample properties of the method, and this investigation indicates that the proposed method works well for many practical situations. We then apply our approach to examine the impact of age at cranial radiation therapy on risk of growth hormone deficiency in long-term survivors of childhood cancer.     

The analysis of mixed interval-censored and complete data

The article focuses mainly on a conditional imputation algorithm of quantile-filling to analyze a new kind of censored data, mixed interval-censored and complete data related to interval-censored sample. With the algorithm, the imputed failure times, which are the conditional quantiles, are obtained within the censoring intervals in which some exact failure times are. The algorithm is viable and feasible for the parameter estimation with general distributions, for instance, a case of Weibull distribution that has a moment estimation of closed form by log-transformation. Furthermore, interval-censored sample is a special case of the new censored sample, and the conditional imputation algorithm can also be used to deal with the failure data of interval censored. By comparing the interval-censored data and the new censored data, using the imputation algorithm, in the view of the bias of estimation, we find that the performance of new censored data is better than that of interval censored.     

Frequentist and Bayesian approaches for interval-censored data

Interval censoring appears when the event of interest is only known to have occurred within a random time interval. Estimation and hypothesis testing procedures for interval-censored data are surveyed. We distinguish between frequentist and Bayesian approaches. Computational aspects for every proposed method are described and solutions with S-Plus, whenever are feasible, are mentioned. Three real data sets are analyzed.     

Regression analysis of clustered interval-censored failure time data with linear transformation models in the presence of informative cluster size

This paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided.     

Cox regression for mixed case interval-censored data with covariate errors

Covariate measurement error problems have been extensively studied in the context of right-censored data but less so for interval-censored data. Motivated by the AIDS Clinical Trial Group 175 study, where the occurrence time of AIDS was examined only at intermittent clinic visits and the baseline covariate CD4 count was measured with error, we describe a semiparametric maximum likelihood method for analyzing mixed case interval-censored data with mismeasured covariates under the proportional hazards model. We show that the estimator of the regression coefficient is asymptotically normal and efficient and provide a very stable and efficient algorithm for computing the estimators. We evaluate the method through simulation studies and illustrate it with AIDS data.     

Study of an imputation algorithm for the analysis of interval-censored data

In this article, an iterative single-point imputation (SPI) algorithm, called quantile-filling algorithm for the analysis of interval-censored data, is studied. This approach combines the simplicity of the SPI and the iterative thoughts of multiple imputation. The virtual complete data are imputed by conditional quantiles on the intervals. The algorithm convergence is based on the convergence of the moment estimation from the virtual complete data. Simulation studies have been carried out and the results are shown for interval-censored data generated from the Weibull distribution. For the Weibull distribution, complete procedures of the algorithm are shown in closed forms. Furthermore, the algorithm is applicable to the parameter inference with other distributions. From simulation studies, it has been found that the algorithm is feasible and stable. The estimation accuracy is also satisfactory.     

Regression analysis of recurrent events data with incomplete observation gaps

For analyzing recurrent event data, either total time scale or gap time scale is adopted according to research interest. In particular, gap time scale is known to be more appropriate for modeling a renewal process. In this paper, we adopt gap time scale to analyze recurrent event data with repeated observation gaps which cannot be observed completely because of unknown termination times of observation gaps. In order to estimate termination times, interval-censored mechanism is applied. Simulation studies are done to compare the suggested methods with the unadjusted method ignoring incomplete observation gaps. As a real example, conviction data set with suspensions is analyzed with suggested methods.     

Generalized Log-Rank Tests for Interval-Censored Failure Time Data

Abstract.  Several non-parametric test procedures have been proposed for incomplete survival data: interval-censored failure time data. However, most of them have unknown asymptotic properties with heuristically derived and/or complicated variance estimation. This article presents a class of generalized log-rank tests for this type of survival data and establishes their asymptotics. The methods are evaluated using simulation studies and illustrated by a set of real data from a cancer study.     

A semiparametric regression cure model for interval-censored and left-truncated data

Medical advancements have made it possible for patients to be cured of certain types of diseases. In follow-up studies, the disease event time can be subject to left truncation and interval censoring. In this article, we propose a semiparametric nonmixture cure model for the regression analysis of left-truncated and interval-censored (LTIC) data. We develop semiparametric maximum likelihood estimation for the nonmixture cure model with LTIC data. A simulation study is conducted to investigate the performance of the proposed estimators.     

On Consistency of the Self-Consistent Estimator of Survival Functions with Interval-Censored Data

The self-consistent estimator is commonly used for estimating a survival function with interval-censored data. Recent studies on interval censoring have focused on case 2 interval censoring, which does not involve exact observations, and double censoring, which involves only exact, right-censored or left-censored observations. In this paper, we consider an interval censoring scheme that involves exact, left-censored, right-censored and strictly interval-censored observations. Under this censoring scheme, we prove that the self-consistent estimator is strongly consistent under certain regularity conditions.     

Non-parametric estimation with doubly censored data

Data from longitudinal studies in which an initiating event and a subsequent event occur in sequence are called 'doubly censored' data if the time of both events is interval-censored. This paper is concerned with using doubly censored data to estimate the distribution function of the so-called 'duration time', i.e. the elapsed time between the originating event and the subsequent event. The paper proposes a generalization of the Gomez and Lagakos two-step method for the case where both the time to the initiating event and the duration time are continuous. This approach is applied to estimate the AIDS-latency time from a haemophiliacs cohort.     

Median regression model with left truncated and interval-censored data

We consider the problem of fitting a heteroscedastic median regression model from left-truncated and interval-censored data. It is demonstrated that the adapted Efron’s self-consistency equation of McKeague, Subramanian, and Sun (2001) can be extended to analyze left-truncated and interval-censored data. The asymptotic property of the proposed estimator is established. We evaluate the finite sample performance of the proposed estimators through simulation studies.     

A Bezier curve method in interval-censored data

In this paper we propose a Bezier curve method to estimate the survival function and the median survival time in interval-censored data. We compare the proposed estimator with other existing methods such as the parametric method, the single point imputation method, and the nonparametric maximum likelihood estimator through extensive numerical studies, and it is shown that the proposed estimator performs better than others in the sense of mean squared error and mean integrated squared error. An illustrative example based on a real data set is given.     

A three-state disease model with interval-censored data: Estimation and applications to AIDS and cancer

In presence of interval-censored data, we propose a general three-state disease model with covariates. Such data can arise, for example, in epidemiologic studies of infectious disease where both the times of infection and disease onset are not directly observed, or in cancer studies where the time of disease metastasis is known up to a specified interval. The proposed model allows the distributions of the transition times between states to depend on covariates and the time in the previous state. An estimation procedure for the underlying distributions and the model coefficients is suggested with the EM algorithm. The EMS algorithm (Smoothed EM algorithm) is also considered to obtain smooth estimates of the distributions. The proposed method is illustrated with data from an AIDS study and a study of patients with malignant melanoma.     

Renovating inverval-censored responses

In this note we provide a general framework for describing interval-censored samples including estimation of the magnitude and rank positions of data that have been interval-censored so as to counteract the effect of censoring. This process of sample adjustment, or renovation, allows samples to be compared graphically, using diagrams (such as boxplots) which are based on ranks. The renovation process is based on Buckley-James regression estimators for linear regression with censored data.