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Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size. [ABSTRACT FROM AUTHOR]

We show that the likelihood function for a multinomial vector observed under arbitrary interval censoring constraints on the frequencies or their partial sums is completely log-concave by proving that the constrained sample spaces comprise M-convex subsets of the discrete simplex. [ABSTRACT FROM AUTHOR]

Existing likelihood methods for the additive hazards model with interval censored survival data are limited and often ignore the non-negative constraints on hazards. This paper proposes a maximum penalized likelihood method to fit additive hazards models with interval censoring. Our method firstly models the baseline hazard using a finite number of non-negative basis functions, and then regression coefficients and baseline hazard are estimated simultaneously by maximizing a penalized log-likelihood function, where a penalty function is introduced to regularize the baseline hazard estimate. In the estimation procedure, non-negative constraints are imposed on both the baseline hazard and the hazard of each subject. A primal–dual interior-point algorithm is applied to solve the constrained optimization problem. Asymptotic properties are obtained and a simulation study is conducted for assessment of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This paper discusses regression analysis of interval-censored failure time data with a cured subgroup under a general class of semiparametric transformation cure models. For inference, a novel and stable expectation maximization (EM) algorithm with the use of Poisson variables is developed to overcome the difficulty in maximizing the observed data likelihood function with complex form. The asymptotic properties of the resulting estimators are established and in particular, the estimators of regression parameters are shown to be semiparametrically efficient. The numerical results obtained from a simulation study indicate that the proposed approach works well for practical situations. An application to a set of data on children's mortality is also provided. [ABSTRACT FROM AUTHOR]

Cox regression is one of the most commonly used methods in the analysis of interval-censored failure time data. In many practical studies, the covariate effects on the failure time may not be constant over time. Time-varying coefficients are therefore of great interest due to their flexibility in capturing the temporal covariate effects. To analyze spatially correlated interval-censored time-to-event data with time-varying covariate effects, a Bayesian approach with dynamic Cox regression model is proposed. The coefficient is estimated as a piecewise constant function and the number of jump points estimated from the data. A conditional autoregressive distribution is employed to model the spatial dependency. The posterior summaries are obtained via an efficient reversible jump Markov chain Monte Carlo algorithm. The properties of our method are illustrated by simulation studies as well as an application to smoking cessation data in southeast Minnesota. [ABSTRACT FROM AUTHOR]

The consistency and asymptotic normality of the maximum likelihood estimators (MLEs), based on progressively type-I interval censored (PIC-I) data are proved under appropriate regularity conditions. The information obtained in the PIC-I setup is compared with that of grouped data and also with progressively type-I censored (PC-I) data. [ABSTRACT FROM AUTHOR]

Inference for cause-specific hazards from competing risks data under interval censoring and possible left truncation has been understudied. Aiming at this target, a penalized likelihood approach for a Cox-type proportional cause-specific hazards model is developed, and the associated asymptotic theory is discussed. Monte Carlo simulations show that the approach performs very well for moderate sample sizes. An application to a longitudinal study of dementia illustrates the practical utility of the method. In the application, the age-specific hazards of AD, other dementia and death without dementia are estimated, and risk factors of all competing risks are studied. [ABSTRACT FROM AUTHOR]

The proportional hazards mixture cure model is a popular analysis method for survival data where a subgroup of patients are cured. When the data are interval censored, the estimation of this model is challenging due to its complex data structure. A multiple imputation algorithm is proposed to obtain parameter and variance estimates for both the cure probability and the survival distribution of the uncured patients. The proposed approach can be easily implemented in commonly used statistical softwares, such as R and SAS, and its performance is comparable to fully parametric methods via comprehensive simulation studies. For illustration, the approach is applied to the 2000–2010 Greater Georgia breast cancer data set from the Surveillance, Epidemiology, and End Results Program. [ABSTRACT FROM AUTHOR]

There has been considerable progress in the development of semiparametric transformation models for regression analysis of time-to-event data. However, most of the current work focuses on right-censored data. Significantly less work has been done for interval-censored data, especially when the population contains a nonignorable cured subgroup. A broad and flexible class of semiparametric transformation cure models is proposed for analyzing interval-censored data in the presence of a cure fraction. The proposed modeling approach combines a logistic regression formulation for the probability of cure with a partially linear transformation model for event times of susceptible subjects. The estimation is achieved by using a spline-based sieve maximum likelihood method, which is computationally efficient and leads to estimators with appealing properties such as consistency, asymptotic normality and semiparametric efficiency. Furthermore, a goodness-of-fit test can be constructed for the proposed models based on the sieve likelihood ratio. Simulations and a real data analysis are provided for illustration of the methodology. [ABSTRACT FROM AUTHOR]

In some retrospective observational studies, the subject is asked to recall the age at a particular landmark event. The resulting data may be partially incomplete because of the inability of the subject to recall. This type of incompleteness may be regarded as interval censoring, where the censoring is likely to be informative. The problem of fitting Cox’s relative risk regression model to such data is considered. While a partial likelihood is not available, a method of semi-parametric inference of the regression parameters as well as the baseline distribution is proposed. Monte Carlo simulations show reasonable performance of the regression parameters, compared to Cox estimators of the same parameters computed from the complete version of the data. The proposed method is illustrated through the analysis of data on age at menarche from an anthropometric study of adolescent and young adult females in Kolkata, India. [ABSTRACT FROM AUTHOR]

We consider conditional maximum likelihood estimator (cMLE) for the proportional hazards model with left-truncated and interval-censored data. We show that when the covariates are discrete the cMLE is the MLE, and under some regularity conditions the cMLE for the regression parameter is asymptotically normal and efficient. [ABSTRACT FROM AUTHOR]

One of the most promising applications of the methodology of imprecise probabilities in statistics is the reliable analysis of interval data (or more generally coarsened data). As soon as one refrains from making strong, often unjustified assumptions on the coarsening process, statistical models are naturally only partially identified and set-valued parameter estimators (identification regions) have to be derived. In this paper we consider linear regression analysis under interval data in the dependent variable. While in the traditional case of neglected imprecision different understandings of regression modeling lead to the same parameter estimators, we now have to distinguish between two different types of identification regions, called (Sharp) Marrow Region (SMR) and (Sharp) Collection Region (SCR) here. In addition, we propose the Set-loss Region (SR) as a compromise between SMR and SCR based on a set-domained loss function. We elaborate and discuss some fundamental properties of these regions and then illustrate the methodology in detail by an example, where the influence of different covariates on wine quality, measured by a coarse rating scale, is investigated. We also compare the different identification regions to classical estimates from a naive analysis and from common interval censorship modeling. [ABSTRACT FROM AUTHOR]

Abstract: In many medical studies, individuals are seen periodically, at a set of pre-scheduled clinical visits. In such cases, when the outcome of interest is the occurrence of an event, the corresponding times are only known to fall within an interval, formed by the times of two consecutive visits. Such data are called interval censored. Most methods for the analysis of interval-censored event times are based on a simplified likelihood function which relies on the assumption that the only information provided by the censoring intervals is that they contain the actual event time (i.e. non-informative censoring). In this simulation study, the performance of parametric models for interval-censored data when individuals miss some of the pre-scheduled visits completely at random (MCAR), at random (MAR) or not at random (MNAR) was assessed comparing also with a simpler approach that is often used in practice. A sample of HIV-RNA measurements and baseline covariates of HIV-1 infected individuals from the CASCADE study is used for illustration in an analysis of the time between the initiation of antiretroviral treatment and viral load suppression to undetectable levels. Results suggest that parametric models based on flexible distributions (e.g. generalised Gamma) can fit such data reasonably well and are robust to irregular visit times caused by an MCAR or MAR mechanism. Violating the non-informative censoring assumption though, leads to biased estimators with the direction and the magnitude of the bias depending on the direction and the strength of the association between the probability of missing visits and the actual time-to-event. Finally, simplifying the data in order to use standard survival analysis techniques, can yield misleading results even when the censoring intervals depend only on a baseline covariate. [Copyright &y& Elsevier]

Abstract: The additive hazard regression (AHR) model is known for its convenience in interpretation, as hazard is modeled as a linear function of covariates. One outstanding issue in the application of such a model in the analysis of current status data is that there lacks an efficient and computationally simple approach for parameter estimation. In the current literature, method enjoys the computational ease but it is not semi-parametrically efficient, whereas method is semi-parametrically efficient but difficult to compute. In this paper, we propose a new estimation approach in the context of Lin et al.’s AHR models where the monitor time process follows a proportional hazard model. We show that not only the proposed estimator achieves semi-parametric information bound, but also its implementation can be done easily using existing statistical software. We evaluate this new method via simulation studies. Also, we illustrate the proposed method through an analysis of renal function recovery data. [Copyright &y& Elsevier]

Abstract: Analyzing interval-censored data is difficult due to its complex data structure containing left-, interval-, and right-censored observations. An easy-to-implement Bayesian approach is proposed under the proportional odds (PO) model for analyzing such data. The nondecreasing baseline log odds function is modeled with a linear combination of monotone splines. Two efficient Gibbs samplers are developed based on two different data augmentations using the relationship between the PO model and the logistic distribution. In the first data augmentation, the logistic distribution is achieved by the scaled normal mixture with the scale parameter related to the Kolmogorov–Smirnove distribution. In the second data augmentation, the logistic distribution is approximated by a Student’s t distribution up to a scale constant. The proposed methods are evaluated by simulation studies and illustrated with an application of an HIV data set. [Copyright &y& Elsevier]

Abstract: The Cox model with frailties has been popular for regression analysis of clustered event time data under right censoring. However, due to the lack of reliable computation algorithms, the frailty Cox model has been rarely applied to clustered current status data, where the clustered event times are subject to a special type of interval censoring such that we only observe for each event time whether it exceeds an examination (censoring) time or not. Motivated by the cataract dataset from a cross-sectional study, where bivariate current status data were observed for the occurrence of cataracts in the right and left eyes of each study subject, we develop a very efficient and stable computation algorithm for nonparametric maximum likelihood estimation of gamma-frailty Cox models with clustered current status data. The algorithm proposed is based on a set of self-consistency equations and the contraction principle. A convenient profile-likelihood approach is proposed for variance estimation. Simulation and real data analysis exhibit the nice performance of our proposal. [ABSTRACT FROM AUTHOR]

Abstract: Correlated or clustered failure time data often occur in medical studies, among other fields (), and sometimes such data arise together with interval censoring (). Furthermore, the failure time of interest may be related to the cluster size. For example, discussed such an example arising from a lymphatic filariasis study. A simple and common approach to the analysis of these data is to simplify or convert interval-censored data to right-censored data due to the lack of proper inference procedures for direct analysis of these data. In this paper, two procedures are presented for regression analysis of clustered failure time data that allow both interval censoring and informative cluster size. Simulation studies are conducted to evaluate the presented approaches and they are applied to a motivating example. [Copyright &y& Elsevier]

Abstract: We describe a Box and Cox power-transformation to confined and censored nonnormal responses in regression. We consider the most general situation where responses include four types of observations, i.e., right, left, interval-censored and exactly specified ones. To evaluate the performance of the estimates from the proposed approach, we perform the simulation study with several simple regression models. Also, one real example is given to illustrate some aspects of the approach. Finally, we discuss an application of the approach to discrete and ordered categorical responses. [Copyright &y& Elsevier]

Abstract: Mixed model-based estimation of additive or geoadditive regression models has become popular throughout recent years. It provides a unified and modular framework that facilitates joint estimation of nonparametric covariate effects and the corresponding smoothing parameters. Therefore, extensions of mixed model-based inference to a Cox-type regression model for the hazard rate are considered, allowing for a combination of general censoring schemes for the survival times and a flexible, geoadditive predictor. In particular, the proposed methodology allows for arbitrary combinations of right, left, and interval censoring as well as left truncation. The geoadditive predictor comprises time-varying effects, nonparametric effects of continuous covariates, spatial effects, and potentially a number of extensions such as cluster-specific frailties or interaction surfaces. In addition, all covariates are allowed to be piecewise constant time-varying. Nonlinear and time-varying effects as well as the baseline hazard rate are modeled by penalized splines. Spatial effects can be included based on either Markov random fields or stationary Gaussian random fields. Estimation is based on a reparametrization of the model as a variance component mixed model. The variance parameters, corresponding to inverse smoothing parameters, can then be determined using an approximate marginal likelihood approach. An analysis on childhood mortality in Nigeria serves as an application, where the interval censoring framework additionally allows to deal with the problem of heaped survival times. The effect of ignoring the impact of interval-censored observations is investigated in a simulation study. [Copyright &y& Elsevier]

Double censoring often occurs in biomedical research, such as HIV/AIDS clinical trials, when an outcome of interest is subject to both left censoring and right censoring. It can also be seen as a mixture of exact and current status data and has long been investigated by several authors for theoretical and practical purposes. In this article, we propose the Buckley-James method for an accelerated failure time model under double random censoring. For the semiparametric inference, where the error distribution of the censored linear model is left unspecified, we develop an efficient EM-based self-consistency procedure to estimate the regression parameter and the unknown residual distribution function. Asymptotic properties, including the uniform consistency and weak convergence, are established for the proposed estimators. Simulation studies demonstrate that the proposed procedure works well under various censoring schemes and outperforms the inverse-probability weighting method in terms of accuracy and efficiency. The method is applied to the HIV/AIDS study. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data often occur in many areas and their analysis has recently attracted a great deal of attention. On the other hand, most of the existing literature for them can only deal with time-independent covariates. Sometimes one may face time dependent covariates and furthermore the covariates could also suffer measurement errors. For the situation, one approach is to conduct a joint analysis for which many methods have been developed in the literature under various framework. One drawback of these methods is that they usually assume that there are no more measurements on the covariates after the failure time and it is apparent that this may not be true. In this paper, a new joint analysis approach is proposed that can take into account the extra observations. In particular, for estimation, a MCEM algorithm is developed that is much more stable and converges much faster than the existing algorithms. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted and suggests that it works well for practical situations. Also the method is applied to an AIDS study that motivated this investigation. [ABSTRACT FROM AUTHOR]