Interval-censored Data Research Articles

Nonparametric analysis of doubly truncated and interval-censored data.

In epidemiological studies, it is easier to collect data only from individuals whose failure events are within a calendar time interval, the so-called interval sampling, which leads to doubly truncated data. In many situations, the calendar time of the failure event can only be recorded within time intervals, leading to doubly truncated and interval censored (DTIC) data. Firstly, we point out that although the existing methods for DTIC data work adequately under the sampling scheme (Scheme 1) for doubly truncated data, Scheme 1 is not realistic for DTIC data. Secondly, we consider a commonly used sampling scheme (Scheme 2) , under which the individuals are included in the sample based on diagnosis date. We point out that under Scheme 2, due to violation of assumptions for Scheme 1, the NPMLE of the cumulative distribution function is severely biased if the likelihood function for Scheme 1 is used. To overcome this difficulty, we define a target population, under which a sampling scheme (Scheme 3) can be implemented such that appropriate truncation variables can be defined and the NPMLE of the cumulative distribution function can be obtained using the expectation-maximization algorithm. We also consider estimation of the joint distribution function for successive duration times. Using the imputed first failure times based on the NPMLE from Scheme 3, we then obtain the imputed right censored data of the second failure event. Based on the imputed data, we propose a nonparametric estimator of the joint distribution function using the inverse-probability-weighted approach. Simulation studies demonstrate that the proposed method performs well with moderate sample sizes.

Subgroup Identification and Regression Analysis of Clustered and Heterogeneous Interval-Censored Data

Clustered and heterogeneous interval-censored data occur in many fields such as medical studies. For example, in a migraine study with the Netherlands Twin Registry, the information including time to diagnosis of migraine and gender was collected for 3975 monozygotic and dizygotic twins. Since each study subject is observed only at discrete and periodic follow-up time points, the failure times of interest (i.e., the time when the individual first had a migraine) are known only to belong to certain intervals and hence are interval-censored. Furthermore, these twins come from different genetic backgrounds and may be associated with differential risks for developing migraines. For simultaneous subgroup identification and regression analysis of such data, we propose a latent Cox model where the number of subgroups is not assumed a priori but rather data-driven estimated. The nonparametric maximum likelihood method and an EM algorithm with monotone ascent property are also developed for estimating the model parameters. Simulation studies are conducted to assess the finite sample performance of the proposed estimation procedure. We further illustrate the proposed methodologies by an empirical analysis of migraine data.

Variable Selection for Generalized Linear Models with Interval-Censored Failure Time Data

Variable selection is often needed in many fields and has been discussed by many authors in various situations. This is especially the case under linear models and when one observes complete data. Among others, one common situation where variable selection is required is to identify important risk factors from a large number of covariates. In this paper, we consider the problem when one observes interval-censored failure time data arising from generalized linear models, for which there does not seem to exist an established method. To address this, we propose a penalized least squares method with the use of an unbiased transformation and the oracle property of the method is established along with the asymptotic normality of the resulting estimators of regression parameters. Simulation studies were conducted and demonstrated that the proposed method performed well for practical situations. In addition, the method was applied to a motivating example about children’s mortality data of Nigeria.

Inference for set-based effects in genetic association studies with interval-censored outcomes.

The rapid acceleration of genetic data collection in biomedical settings has recently resulted in the rise of genetic compendiums filled with rich longitudinal disease data. One common feature of these data sets is their plethora of interval-censored outcomes. However, very few tools are available for the analysis of genetic data sets with interval-censored outcomes, and in particular, there is a lack of methodology available for set-based inference. Set-based inference is used to associate a gene, biological pathway, or other genetic construct with outcomes and is one of the most popular strategies in genetics research. This work develops three such tests for interval-censored settings beginning with a variance components test for interval-censored outcomes, the interval-censored sequence kernel association test (ICSKAT). We also provide the interval-censored version of the Burden test, and then we integrate ICSKAT and Burden to construct the interval censored sequence kernel association test-optimal (ICSKATO) combination. These tests unlock set-based analysis of interval-censored data sets with analogs of three highly popular set-based tools commonly applied to continuous and binary outcomes. Simulation studies illustrate the advantages of the developed methods over ad hoc alternatives, including protection of the type I error rate at very low levels and increased power. The proposed approaches are applied to the investigation that motivated this study, an examination of the genes associated with bone mineral density deficiency and fracturerisk.

Association between childhood maltreatment and the clinical course of bipolar disorders: A survival analysis of mood recurrences.

Childhood maltreatment, also referred as childhood trauma, increases the severity of bipolar disorders (BD). Childhood maltreatment has been associated with more frequent mood recurrences, however, mostly in retrospective studies. Since scarce, further prospective studies are required to identify whether childhood maltreatment may be associated with the time to recurrence in BD. Individuals with BD (N=2008) were assessed clinically and for childhood maltreatment at baseline, and followed up for two years. The cumulative probability of mood recurrence over time was estimated with the Turnbull's extension of the Kaplan-Meier analysis for interval-censored data, including childhood maltreatment as a whole, and then maltreatment subtypes as predictors. Analyses were adjusted for potential confounding factors. The median duration of follow-up was 22.3months (IQR:12.0-24.8). Univariable analyses showed associations between childhood maltreatment, in particular all types of abuses (emotional, physical, and sexual) or emotional neglect, and a shorter time to recurrence (all p<0.001). When including potential confounders into the multivariable models, the time to mood recurrence was associated with multiple/severe childhood maltreatment (i.e., total score above the 75th percentile) (HR=1.32 95%CI (1.11-1.57), p=0.002), and more specifically with moderate/severe physical abuse (HR=1.44 95%CI(1.21-1.73), p<0.0001). Living alone, lifetime anxiety disorders, lifetime number of mood episodes, baseline depressive and (hypo)manic symptoms, and baseline use of atypical antipsychotics were also associated with the time to recurrence. In addition to typical predictors of mood recurrences, an exposure to multiple/severe forms of childhood maltreatment, and more specifically to moderate to severe physical abuse, may increase the risk for a mood recurrence in BD. This leads to the recommendations of more scrutiny and denser follow-up of the individuals having been exposed to such early-life stressors.

An efficient penalized estimation approach for semiparametric linear transformation models with interval-censored data.

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semiparametric models, the unknown monotone function is approximated via a monotone B-spline. A penalization technique is used to provide computationally efficient estimation of all parameters. To accomplish model fitting and inference, an easy to implement nested iterative expectation-maximization (EM) algorithm is developed for estimation, and a simple variance-covariance estimation approach is proposed which makes large-sample inference for the regression parameters possible. Theoretically, we show that the estimator of the unknown monotone increasing function achieves the optimal rate of convergence, and the estimators of the regression parameters are asymptotically normal and efficient under the appropriate selection of the order of the smoothing parameter and the knots of the spline space. The proposed penalized procedure is assessed through extensive numerical experiments and implemented in R package PenIC. The proposed methodology is further illustrated via a signal tandmobiel study.

Assessing Performance of the Generalized Exponential Model in the Presence of the Interval Censored Data with Covariate

This study aims to extend the generalized exponential model (GEM) to include covariates in the presence of interval-censored data. The maximum likelihood estimator (MLE) was obtained for the parameter of the model formulated. Afterward, a thorough simulation study was carried out to evaluate the estimator's performance based on the values of bias, standard error (SE), and root mean square error (RMSE). The result indicated that the (SE) and (RMSE) decrease with the increase in sample sizes and decrease in censoring proportions. Finally, the performance of the Wald confidence interval estimation technique for the GE model with interval-censored data covariate was assessed by a coverage probability study at several censoring proportions and different sample sizes.

Analysis of composite endpoints with component-wise censoring in the presence of differential visit schedules.

Composite endpoints are very common in clinical research, such as recurrence-free survival in oncology research, defined as the earliest of either death or disease recurrence. Because of the way data are collected in such studies, component-wise censoring is common, where, for example, recurrence is an interval-censored event and death is a right-censored event. However, a common way to analyze such component-wise censored composite endpoints is to treat them as right-censored, with the date at which the non-fatal event was detected serving as the date the event occurred. This approach is known to introduce upward bias when the Kaplan-Meier estimator is applied, but has more complex impact on semi-parametric regression approaches. In this article we compare the performance of the Cox model estimators for right-censored data and the Cox model estimators for interval-censored data in the context of component-wise censored data where the visit process differs across levels of a covariate of interest, a common scenario in observational data. We additionally examine estimators of the cause-specific hazard when applied to the individual components of such component-wise censored composite endpoints. We found that when visit schedules differed according to levels of a covariate of interest, the Cox model estimators for right-censored data and the estimators for cause-specific hazards were increasingly biased as the frequency of visits decreased. The Cox model estimator for interval-censored data with censoring at the last disease-free date is recommended for use in the presence of differential visit schedules.

Bayesian nonparametric analysis of restricted mean survival time.

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right- and interval-censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right- and interval-censored data.

A survival tree for interval-censored failure time data

&lt;abstract&gt;&lt;p&gt;Interval-censored failure time data as a general type of survival data often arises in medicine and other applied fields. Survival tree is a flexible predictive method for survival data because no specific assumptions are required.&lt;/p&gt; &lt;p&gt;Generalized Log-Rank Test have good power with parameters for interval-censored failure time data. We construct a special test statistic of Generalized Log-Rank Tests, and propose a new survival tree with hyper-parameter by combining the test statistic with Conditional Inference Framework for interval-censored failure time data. The effect of tuning hyper-parameter are discussed and hyper-parameter tuning allows the tree method to be more general and flexible. Thus the tree method either improve upon or remain competitive with existing tree method for interval-censored failure time data-ICtree, which is a special case of ours. An extensive simulation is executed to assess the predictive performance of our tree methods. Finally, the tree methods are applied to a tooth emergence data.&lt;/p&gt;&lt;/abstract&gt;

A spline-based nonparametric analysis for interval-censored bivariate survival data.

In this manuscript we propose a spline-based sieve nonparametric maximum likelihood estimation method for joint distribution function with bivariate interval-censored data. We study the asymptotic behavior of the proposed estimator by proving the consistency and deriving the rate of convergence. Based on the sieve estimate of the joint distribution, we also develop an efficient nonparametric test for making inference about the dependence between two interval-censored event times and establish its asymptotic normality. We conduct simulation studies to examine the finite sample performance of the proposed methodology. Finally we apply the method to assess the association between two subtypes of mild cognitive impairment (MCI): amnestic MCI and non-amnestic MCI, for Huntington disease (HD) using data from a 12-year observational cohort study on premanifest HD individuals, PREDICT-HD.

Variable selection for time-varying effects based on interval-censored failure time data

Variable selection for time-varying effects based on interval-censored failure time data

Randomized two-stage optimal design for interval-censored data

ABSTRACT Interval-censored data occur in a study where the exact event time of each participant is not observed but it is known to be within a certain time interval. Multiple tests were proposed for such data, including the logrank test by Sun, the proportional hazard test by Finkelstein, and the Wilcoxon-type test by Peto and Peto. We propose sample size calculations based on these tests for a parallel one-stage or two-stage design. When the proportional hazard assumption is met, the proportional hazard test and the logrank test need smaller sample sizes than the Wilcoxon-type test, and the sample size savings are substantial. But this trend is reversed when the proportional hazard assumption does not hold, and the sample size savings using the Wilcoxon-type test are sizable. An example from a lung cancer clinical trial is used to illustrate the application of the proposed sample size calculations.

Regression analysis of multivariate interval-censored failure time data with informative censoring.

Regression analysis of multivariate interval-censored failure time data has been discussed by many authors1-6. For most of the existing methods, however, one limitation is that they only apply to the situation where the censoring is non-informative or the failure time of interest is independent of the censoring mechanism. It is apparent that this may not be true sometimes and as pointed out by some authors, the analysis that does not take the dependent censoring into account could lead to biased or misleading results7,8. In this study, we consider regression analysis of multivariate interval-censored data arising from the additive hazards model and propose an estimating equation-based approach that allows for the informative censoring. The method can be easily implemented and the asymptotic properties of the proposed estimator of regression parameters are established. Also we perform a simulation study for the evaluation of the proposed method and it suggests that the method works well for practical situations. Finally, the proposed approach is applied to a set of real data.

Timing of ENDS Uptake by Sexual Orientation among Adolescents and Young Adults in Urban Texas.

IntroductionEarly-onset of Electronic Nicotine Delivering Systems (ENDS) use puts users at higher risk of developing a regular ENDS use pattern and/or transitioning to combusted tobacco products. Previous studies on ENDS use among adolescents have not considered sexual orientation as a fluid trait that can change over time. Our objective was to evaluate whether ENDS initiation differed by sexual orientation in a longitudinal, population-based cohort of adolescents transitioning into young adulthood in Texas.MethodsSample (n = 1712) was drawn from the Texas Adolescent Tobacco and Marketing Surveillance System (waves 5–11) and stratified into three groups, representing sexual orientation: (1) respondents who reported being heterosexuals at each wave (straight), (2) those who consistently self-identified as lesbian, gay or bisexual individuals (LGB), and (3) subjects who reported sexual orientation mobility across waves (mobile). Nonparametric models for interval-censored data were used to estimate the cumulative distribution of age at ENDS initiation by sexual orientation group. Cox models for interval-censored data were used to evaluate whether ENDS initiation varied by sexual orientation group after adjusting for sex assigned at birth, race/ethnicity, cohort, and socioeconomic status.ResultsCompared to Straight adolescents, the risk of earlier-onset of ENDS use was higher among mobile individuals (HR = 1.43, 95% CI: 1.12 to 1.83) and LGB individuals (HR = 1.49, 95% CI: 1.13 to 1.98), respectively, after adjusting for sociodemographic risk factors. Differences between Straight adolescents and LGB/mobile individuals became more pronounced with increasing age.ConclusionAnalyzing sexual mobility overtime is necessary for understanding the risk associated with youth ENDS initiation and subsequent use.ImplicationsFuture research should use more accurate sexual orientation assessments to explore further the relationship between sexual orientation mobility and early-onset Electronic Nicotine Delivering Systems (ENDS) use. Understanding the implications of sexual orientation mobility on ENDS initiation will be critical for developing inclusive public health programs aimed at preventing or delaying ENDS use and for providing practical recommendations at state and local levels.

Bayesian transformation models with partly interval‐censored data

In many scientific fields, partly interval-censored data, which consist of exactly observed and interval-censored observations on the failure time of interest, appear frequently. However, methodological developments in the analysis of partly interval-censored data are relatively limited and have mainly focused on additive or proportional hazards models. The general linear transformation model provides a highly flexible modeling framework that includes several familiar survival models as special cases. Despite such nice features, the inference procedure for this class of models has not been developed for partly interval-censored data. We propose a fully Bayesian approach coped with efficient Markov chain Monte Carlo methods to fill this gap. A four-stage data augmentation procedure is introduced to tackle the challenges presented by the complex model and data structure. The proposed method is easy to implement and computationally attractive. The empirical performance of the proposed method is evaluated through two simulation studies, and the model is then applied to a dental health study.

A new approach to regression analysis of linear transformation model with interval-censored data

Interval-censored failure time data often occur in medical follow-up studies among other areas. Regression analysis of linear transformation models with interval-censored data has been investigated by several authors under different contexts, but most of the existing methods assume that the covariates are discrete because these methods rely on the estimation of conditional survival distribution function. Without this assumption, this paper constructs a new generalized estimating equation using the propensity score. The proposed inference procedure does not need to estimate the conditional survival distribution any more and then can be used not only in the discrete but also in the continuous covariate situation. The asymptotic properties of the resulting estimates are given, and an extensive simulation study is performed. Finally, the application to two real datasets is also provided. Key words: Estimating equation; Interval-censored data; Propensity score; Linear transformation model.

A functional proportional hazard cure rate model for interval-censored data.

Existing survival models involving functional covariates typically rely on the Cox proportional hazards structure and the assumption of right censorship. Motivated by the aim of predicting the time of conversion to Alzheimer's disease from sparse biomarker trajectories in patients with mild cognitive impairment, we propose a functional mixture cure rate model with both functional and scalar covariates for interval censoring and sparsely sampled functional data. To estimate the nonparametric coefficient function that depicts the effect of the shape of the trajectories on the survival outcome and cure probability, we utilize the functional principal component analysis to extract the functional features from the sparsely and irregularly sampled trajectories. To obtain parameter estimates from the mixture cure rate model with interval censoring, we apply the expectation-maximization algorithm based on Poisson data augmentation. The estimation accuracy of our method is assessed via a simulation study and we apply our model on Alzheimer's disease Neuroimaging Initiative data set.

Generalized exponential distribution with interval-censored data and time dependent covariate

This study will improve the performance of the Generalized Exponential Distribution (GED) by incorporating time-dependent covariates (TD) in the presence of interval-censored data. Interval-censored data usually arises in clinical and epidemiological studies where lifetime is only known to fall within an interval. Moreover, this study concentrates on the parameters estimation for this distribution. This study will compare the maximum likelihood estimation (MLE) for two distinct models, namely time-dependent covariates model and time-independent covariates model in terms of their bias, standard error (SE) and root mean square error (RMSE) at various attendance probability (AP) and sample sizes. The results indicate that bias, SE and RMSE values of the parameter estimates increase with the increase in attendance probability and decrease with the increase in sample size.

Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction

Censored data are considered to be of the interval type where the upper and lower bounds of an event’s failure time cannot be directly observed but only determined between interval inspection times. The analyses of interval-censored data have attracted attention because they are common in the fields of reliability and medicine. A proportion of patients enrolled in clinical trials can sometimes be cured. In some instances, their symptoms mostly disappear without any recurrence of the disease. In this study, the proportion of such patients who are cured is estimated. Furthermore, the Bayesian approach under the gamma prior and maximum likelihood estimation (MLE) is used to estimate the cure fraction depending on the bounded cumulative hazard (BCH) model based on interval-censored data with an exponential distribution. The Bayesian approach uses three loss functions: squared error, linear exponential, and general entropy. These functions are compared with the MLE and used between estimators. Moreover, they are obtained using the mean squared error, which locates the best option to estimate the parameter of an exponential distribution. The results show that the BCH model and lambda parameter of the exponential distribution based on the interval-censored data can be best estimated using the Bayesian gamma prior with a positive loss function of the linear exponential.