Interval-censored Data Research Articles

Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data

In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).

Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease

In this paper, we discuss regression analysis of censored failure time data when there exist missing covariates and more specifically, we will consider interval-censored data, a general form of censored data, and the nonignorable missing. Although many methods have been proposed in the literature for censored data with missing covariates, they only apply to limited situations and it does not seem to exist an established procedure for the situation discussed here. For the analysis, we employ the semiparametric linear transformation model and develop a two-step estimation procedure. In addition, the asymptotic properties of the resulting estimators are established and a Poisson variable-based EM algorithm is provided for the implementation of the proposed estimation procedure. Finally the proposed approach is applied to an Alzheimer Disease study that motivated this investigation.

Clinical predictors of recurrences in bipolar disorders type 1 and 2: A FACE-BD longitudinal study

ObjectiveTo examine which characteristics predict the time to a first mood recurrence at three years in Bipolar Disorder type I (BD-I) and type II (BD-II). MethodsIndividuals with BD were followed up to 3 years. Turbull's extension of the Kaplan-Meier analysis for interval-censored data was used to estimate the cumulative probability of recurrence over time. Separate models were performed according to BD subtype to determine which baseline factors were predictive of recurrences and were adjusted for age, gender and educational level. ResultsWe included 630 individuals with BD-I and 505 with BD-II. The first recurrence of any polarity occurred earlier in BD-II (p = 0.03). The first depressive recurrence occurred earlier in BD-II (p < 0.0001), whereas the first (hypo)manic recurrence occurred earlier in BD-I (p = 0.0003). In BD-I, the clinical variables that were associated to the time to a first mood recurrence were depressive symptoms, lifetime rapid cycling, global activation and the number of psychotropic medications at baseline. In BD-II, the time to a first recurrence was associated with a younger age at onset of BD and a higher number of lifetime mood episodes. The Areas Under the Curve for both models were moderate. ConclusionPredictors of recurrences showed few specificities to BD-I or BD-II. The ability to predict recurrences in BD based on socio-demographic and clinical variables remained too moderate for a transfer in daily practice. This study highlights the need for further studies that would include other types of predictors, such as molecular, cognitive or neuro-imaging ones, to achieve an accurate level of prediction of recurrences in BD.

Age of initiation of cigarillos, filtered cigars and/or traditional cigars among youth: Findings from the Population Assessment of Tobacco and Health (PATH) study, 2013-2017.

Early age of initiation of tobacco use is associated with sustained tobacco use and lower rates of smoking cessation. Although much is known about age of initiation of cigarette use, much less is known about the age of initiation of cigar product use among youth. Survival analyses of the Population Assessment of Tobacco and Health youth annual datasets (ages 12-17) from 2013 to 2017 were conducted for any cigar product use, cigarillos or filtered cigars, and traditional cigars across four cigar use outcomes, age of initiation of: susceptibility to use, ever use, past 30-day use and "fairly regular" use. An interval censoring survival method was implemented to estimate the probability of each outcome for age of initiation of each cigar product overall. Differences in age of initiation by sex and race/ethnicity were assessed using weighted Cox proportional hazards models for interval-censored data. For each outcome across the three cigar products, striking increases in the probability of initiation begin before 17 years old. For cigarillo or filtered cigars, males had a higher risk of onset of susceptibility to use, initiating ever use, and initiating past 30-day use at earlier ages than females. Compared to Non-Hispanic Whites, Hispanic and Non-Hispanic Other had lower risk of initiating ever use and past 30-day use at earlier ages. Non-Hispanic Black youth had higher risk of initiating past 30-day use and "fairly regular" use than Non-Hispanic White youth at earlier ages. Similar findings are reported for any cigar use and traditional cigar use. Developmentally and culturally appropriate cigar use interventions and communication campaigns should be provided to youth before 17 years of age to prevent the onset and progression of cigar products. Regulatory policies that reduce appeal of all cigar products should be implemented to curb cigar initiation among youth.

Joint analysis of multivariate interval-censored survival data and a time-dependent covariate.

We develop a joint modeling method for multivariate interval-censored survival data and a time-dependent covariate that is intermittently measured with error. The joint model is estimated using nonparametric maximum likelihood estimation, which is carried out via an expectation-maximization algorithm, and the inference for finite-dimensional parameters is performed using bootstrap. We also develop a similar joint modeling method for univariate interval-censored survival data and a time-dependent covariate, which excels the existing methods in terms of model flexibility and interpretation. Simulation studies show that the model fitting and inference approaches perform very well under realistic sample sizes. We apply the method to a longitudinal study of dental caries in African-American children from low-income families in the city of Detroit, Michigan.

Maximum approximate Bernstein likelihood estimation in proportional hazard model for interval-censored data.

Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data result in smooth estimates of the survival functions which enjoys an almost n1/2 -rate of convergence faster than the n1/3 -rate for the existing estimates. The proposed method was shown by a simulation to have better finite sample performance than its main competitors. Some examples including real data are used to illustrate the usage of the proposed method.

Analysis of clustered interval-censored data using a class of semiparametric partly linear frailty transformation models.

A flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval-censored data, which arise naturally in complex diseases and dental research. This class of models features two nonparametric components, resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate. The dependence among failure times within a cluster is induced by a shared, unobserved frailty term. A sieve maximum likelihood estimation method based on piecewise linear functions is proposed. The proposed estimators of the regression, dependence, and transformation parameters are shown to be strongly consistent and asymptotically normal, whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence. An extensive simulation study is conducted to study the finite-sample performance of the proposed estimators. We provide an application to a dental study forillustration.

A Bayesian model for spatial partly interval-censored data

Partly interval-censored data often occur in cancer clinical trials and have been analyzed as right-censored data. Patients’ geographic information sometimes is also available and can be useful in testing treatment effects and predicting survivorship. We propose a Bayesian semiparametric method for analyzing partly interval-censored data with areal spatial information under the proportional hazards model. A simulation study is conducted to compare the performance of the proposed method with the main method currently available in the literature and the traditional Cox proportional hazards model for right-censored data. The method is illustrated through a leukemia survival data set and a dental health data set. The proposed method will be especially useful for analyzing progression-free survival in multi-regional cancer clinical trials.

Simultaneous variable selection and estimation for joint models of longitudinal and failure time data with interval censoring.

This paper discusses variable selection in the context of joint analysis of longitudinal data and failure time data. A large literature has been developed for either variable selection or the joint analysis but there exists only limited literature for variable selection in the context of the joint analysis when failure time data are right censored. Corresponding to this, we will consider the situation where instead of right-censored data, one observes interval-censored failure time data, a more general and commonly occurring form of failure time data. For the problem, a class of penalized likelihood-based procedures will be developed for simultaneous variable selection and estimation of relevant covariate effects for both longitudinal and failure time variables of interest. In particular, a Monte Carlo EM (MCEM) algorithm is presented for the implementation of the proposed approach. The proposed method allows for the number of covariates to be diverging with the sample size and is shown to have the oracle property. An extensive simulation study is conducted to assess the finite sample performance of the proposed approach and indicates that it works well in practical situations. An application is alsoprovided.

Variable selection for generalized odds rate mixture cure models with interval-censored failure time data

Variable selection for failure time data with a cured fraction has been discussed by many authors but most of existing methods apply only to right-censored failure time data. In this paper, we consider variable selection when one faces interval-censored failure time data arising from a general class of generalized odds rate mixture cure models, and we propose a penalized variable selection method by maximizing a derived penalized likelihood function. In the method, the sieve approach is employed to approximate the unknown function, and it is implemented using a novel penalized expectation–maximization (EM) algorithm. Also the asymptotic properties of the proposed estimators of regression parameters, including the oracle property, are obtained. Furthermore, a simulation study is conducted to assess the finite sample performance of the proposed method, and the results indicate that it works well in practice. Finally, the approach is applied to a set of real data on childhood mortality taken from the Nigeria Demographic and Health Survey.

Estimation of the force of infection and infectious period of skin sores in remote Australian communities using interval-censored data.

Prevalence of impetigo (skin sores) remains high in remote Australian Aboriginal communities, Fiji, and other areas of socio-economic disadvantage. Skin sore infections, driven primarily in these settings by Group A Streptococcus (GAS) contribute substantially to the disease burden in these areas. Despite this, estimates for the force of infection, infectious period and basic reproductive ratio-all necessary for the construction of dynamic transmission models-have not been obtained. By utilising three datasets each containing longitudinal infection information on individuals, we estimate each of these epidemiologically important parameters. With an eye to future study design, we also quantify the optimal sampling intervals for obtaining information about these parameters. We verify the estimation method through a simulation estimation study, and test each dataset to ensure suitability to the estimation method. We find that the force of infection differs by population prevalence, and the infectious period is estimated to be between 12 and 20 days. We also find that optimal sampling interval depends on setting, with an optimal sampling interval between 9 and 11 days in a high prevalence setting, and 21 and 27 days for a lower prevalence setting. These estimates unlock future model-based investigations on the transmission dynamics of skin sores.

EM algorithm for the additive risk mixture cure model with interval-censored data.

Interval-censored failure time data arise in a number of fields and many authors have recently paid more attention to their analysis. However, regression analysis of interval-censored data under the additive risk model can be challenging in maximizing the complex likelihood, especially when there exists a non-ignorable cure fraction in the population. For the problem, we develop a sieve maximum likelihood estimation approach based on Bernstein polynomials. To relieve the computational burden, an expectation-maximization algorithm by exploiting a Poisson data augmentation is proposed. Under some mild conditions, the asymptotic properties of the proposed estimator are established. The finite sample performance of the proposed method is evaluated by extensive simulations, and is further illustrated through a real data set from the smoking cessation study.

Estimation of conditional power for cluster-randomized trials with interval-censored endpoints.

Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: dependencies may exist between observations from the same cluster, and event occurrence may be assessed only at intermittent study visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. In this article, we propose a flexible framework for conditional power estimation when outcomes are correlated and interval-censored. Under the assumption that the survival times follow a shared frailty model, we first characterize the correspondence between the marginal and cluster-conditional survival functions, and then use this relationship to semiparametrically estimate the cluster-specific survival distributions from the available interim data. We incorporate assumptions about changes to the event process over the remainder of the trial-as well as estimates of the dependency among observations in the same cluster-to extend these survival curves through the end of the study. Based on these projected survival functions, we generate correlated interval-censored observations, and then calculate the conditional power as the proportion of times (across multiple full-data generation steps) that the null hypothesis of no treatment effect is rejected. We evaluate the performance of the proposed method through extensive simulation studies, and illustrate its use on a large cluster-randomized HIV preventiontrial.

Penalised maximum likelihood estimation in multi-state models for interval-censored data

Continuous-time multi-state Markov models can be used to describe transitions over time across health states. Given longitudinal interval-censored data on transitions between states, statistical inference on changing health is possible by specifying models for transition hazards. Parametric time-dependent hazards can be restrictive, and nonparametric hazard specifications using splines are presented as an alternative. The smoothing of the splines is controlled by using penalised maximum likelihood estimation. With multiple time-dependent hazards in a multi-state model, there are multiple penalty parameters and selecting the optimal amount of smoothing is a challenge. A grid search to estimate the penalty parameters is computational intensive especially when combined with methods to deal with interval-censored transition times. A new and efficient method is proposed to estimate multi-state models with splines where the estimation of the penalty parameters is automatic. A simulation study is undertaken to validate the method and to illustrate the effect of interval censoring. The feasibility of the method is illustrated with two applications.

On hazard-based penalized likelihood estimation of accelerated failure time model with partly interval censoring

In survival analysis, the semiparametric accelerated failure time model is an important alternative to the widely used Cox proportional hazard model. The existing methods for accelerated failure time models include least-squares, log rank-based estimating equations and approximations to the nonparametric error distribution. In this paper, we propose another fitting method for the accelerated failure time model, formulated from the hazard function of the exponential error term. Our method can handle partly interval-censored data which contains event time, as well as left, right and interval censoring time. We adopt the maximum penalized likelihood method to estimate all the parameters in the model, including the nonparametric component. The penalty function is used to regularize the nonparametric component of the accelerated failure time model. Asymptotic properties of the penalized likelihood estimate are developed. A simulation study is conducted to investigate the performance of the proposed method and an application of this method to an AIDS study is presented as an example.

Nonparametric screening and feature selection for ultrahigh-dimensional Case II interval-censored failure time data.

For the analysis of ultrahigh-dimensional data, the first step is often to perform screening and feature selection to effectively reduce the dimensionality while retaining all the active or relevant variables with high probability. For this, many methods have been developed under various frameworks but most of them only apply to complete data. In this paper, we consider an incomplete data situation, case II interval-censored failure time data, for which there seems to be no screening procedure. Basing on the idea of cumulative residual, a model-free or nonparametric method is developed and shown to have the sure independent screening property. In particular, the approach is shown to tend to rank the active variables above the inactive ones in terms of their association with the failure time of interest. A simulation study is conducted to demonstrate the usefulness of the proposed method and, in particular, indicates that it works well with general survival models and is capable of capturing the nonlinear covariates with interactions. Also the approach is applied to a childhood cancer survivor study that motivated thisinvestigation.

Neutrophil Gelatinase-Associated Lipocalin Measured on Clinical Laboratory Platforms for the Prediction of Acute Kidney Injury and the Associated Need for Dialysis Therapy: A Systematic Review and Meta-analysis

The usefulness of measures of neutrophil gelatinase-associated lipocalin (NGAL) in urine or plasma obtained on clinical laboratory platforms for predicting acute kidney injury (AKI) and AKI requiring dialysis (AKI-D) has not been fully evaluated. We sought to quantitatively summarize published data to evaluate the value of urinary and plasma NGAL for kidney risk prediction. Literature-based meta-analysis and individual-study-data meta-analysis of diagnostic studies following PRISMA-IPD guidelines. Studies of adults investigating AKI, severe AKI, and AKI-D in the setting of cardiac surgery, intensive care, or emergency department care using either urinary or plasma NGAL measured on clinical laboratory platforms. PubMed, Web of Science, Cochrane Library, Scopus, and congress abstracts ever published through February 2020 reporting diagnostic test studies of NGAL measured on clinical laboratory platforms to predict AKI. Individual-study-data meta-analysis was accomplished by giving authors data specifications tailored to their studies and requesting standardized patient-level data analysis. Individual-study-data meta-analysis used a bivariate time-to-event model for interval-censored data from which discriminative ability (AUC) was characterized. NGAL cutoff concentrations at 95% sensitivity, 95% specificity, and optimal sensitivity and specificity were also estimated. Models incorporated as confounders the clinical setting and use versus nonuse of urine output as a criterion for AKI. A literature-based meta-analysis was also performed for all published studies including those for which the authors were unable to provide individual-study data analyses. We included 52 observational studies involving 13,040 patients. We analyzed 30 data sets for the individual-study-data meta-analysis. For AKI, severe AKI, and AKI-D, numbers of events were 837, 304, and 103 for analyses of urinary NGAL, respectively; these values were 705, 271, and 178 for analyses of plasma NGAL. Discriminative performance was similar in both meta-analyses. Individual-study-data meta-analysis AUCs for urinary NGAL were 0.75 (95% CI, 0.73-0.76) and 0.80 (95% CI, 0.79-0.81) for severe AKI and AKI-D, respectively; for plasma NGAL, the corresponding AUCs were 0.80 (95% CI, 0.79-0.81) and 0.86 (95% CI, 0.84-0.86). Cutoff concentrations at 95% specificity for urinary NGAL were>580ng/mL with 27% sensitivity for severe AKI and>589ng/mL with 24% sensitivity for AKI-D. Corresponding cutoffs for plasma NGAL were>364ng/mL with 44% sensitivity and>546ng/mL with 26% sensitivity, respectively. Practice variability in initiation of dialysis. Imperfect harmonization of data across studies. Urinary and plasma NGAL concentrations may identify patients at high risk for AKI in clinical research and practice. The cutoff concentrations reported in this study require prospective evaluation.

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.

Estimating the distribution of COVID-19 incubation period by interval-censored data estimation method

Objectives: The COVID-19 has been the public health issues of global concern, but the incubation period was still under discussion. This study aimed to estimate the incubation period distribution of COVID-19. Methods: The exposure and onset information of COVID-19 cases were collected from the official information platform of provincial or municipal health commissions. The distribution of COVID-19 incubation period was estimated based on the Log- normal, Gamma and Weibull distribution by interval-censored data estimation method. Results: A total of 109 confirmed cases were collected, with an average age of 39.825 years. The median COVID-19 incubation period based on Log-normal, Gamma, and Weibull distribution were 4.958 (P(25)-P(75): 3.472-7.318) days, 5.083 (P(25)-P(75): 3.511-7.314) days, and 5.695 (P(25)-P(75): 3.675-7.674) days, respectively. Gamma distribution had the largest log-likelihood result. Conclusions: The distribution of COVID-19 incubation period followed the Gamma distribution, and the interval-censored data estimation method can be used to estimate the incubation period distribution.

A gamma-frailty model for interval-censored data with dependent examination times: a computationally efficient approach

Interval-censored survival data arise naturally in many fields such as medical follow-up studies, in which the event or failure is not observed exactly but only known to occur within a time interval. Most existing approaches for analyzing interval-censored failure time data assume that the examination times and the failure time are independent or conditionally independent given covariates. While this assumption offers considerable simplification, it is not plausible in some situations, e.g., the visiting rate can be positively or negatively correlated with the risk of failure due to unobservable health status even after adjusting for observable covariates. In this article, we consider dependent interval-censored data, where there exists dependence between the failure time and the entire visiting process. A shared frailty is used to characterize the dependence of hazard function of failure time and intensity function of visiting process. Moreover, the joint model could describe the possible none, positive or negative association between failure time and visiting process. We propose the semiparametric maximum likelihood estimators and develop an EM algorithm based on a Poisson data augmentation. The performance of the proposed method is examined through extensive simulation studies and an application to a bladder cancer dataset is presented.