Interval-censored Data Research Articles

Instrumental variable estimation of complier causal treatment effect with interval-censored data.

Assessing causal treatment effect on a time-to-event outcome is of key interest in many scientific investigations. Instrumental variable (IV) is a useful tool to mitigate the impact of endogenous treatment selection to attain unbiased estimation of causal treatment effect. Existing development of IV methodology, however, has not attended to outcomes subject to interval censoring, which are ubiquitously present in studies with intermittent follow-up but are challenging to handle in terms of both theory and computation. In this work, we fill in this important gap by studying a general class of causal semiparametric transformation models with interval-censored data. We propose a nonparametric maximum likelihood estimator of the complier causal treatment effect. Moreover, we design a reliable and computationally stable expectation-maximization (EM) algorithm, which has a tractable objective function in the maximization step via the use of Poisson latent variables. The asymptotic properties of the proposed estimators, including the consistency, asymptotic normality, and semiparametric efficiency, are established with empirical process techniques. We conduct extensive simulation studies and an application to a colorectal cancer screening data set, showing satisfactory finite-sample performance of the proposed method as well as its prominent advantages over naivemethods.

Canine anal sac gland carcinoma with regional lymph node metastases treated with sacculectomy and lymphadenectomy: Outcome and possible prognostic factors.

The staging system commonly used in canine anal sac gland carcinoma (ASGC) is a revised Tumour-Node-Metastasis (TNM) system published in 2007. This staging system consists in four stages and, for dogs with nodal metastases, the size of the metastatic lymph node (mLN) defines the N stage. However, we hypothesise that (1) the mLN size has no prognostic significance when the mLN can be excised, (2) a high number of mLNs is associated with poorer prognosis and (3) the measurement of the mLN on imaging is not reproducible. To investigate these hypotheses, medical records and diagnostic images of dogs with ASGC and mLN, treated with sacculectomy and lymphadenectomy, with or without chemotherapy, were reviewed. Interobserver variability for mLN measurement was assessed. Prognostic factors including mLN size and number were investigated. Time to documented progression (TDP) and disease-specific survival (DSS) were evaluated. Progression-free interval (PFI) was analysed with interval-censored data analysis. Fifty-seven dogs were included. The median PFI, TDP and DSS were 110 (95%CI 61.5-185.5), 196 (95%CI 162-283) and 340 days (95%CI 321-471), respectively. For measurement of the largest mLN, interobserver agreement was excellent but limits of agreement reached 39.7%. Neither the size of the largest mLN nor the use of adjuvant chemotherapy were associated with outcome. The number of mLNs was associated with outcome and having more than four mLNs was associated with shorter PFI (p< .001), TDP (p= .004) and DSS (p< .001). While mLN size measurement was not consistently reproducible and did not influence outcome in our cohort, number of mLNs did. Further studies are required for development of a revised staging system.

Semiparametric regression analysis of clustered interval-censored failure time data with a cured subgroup.

This article discusses regression analysis of clustered interval-censored failure time data in the presence of a cured fraction or subgroup. Such data often occur in many areas, including epidemiological studies, medical studies, and social sciences. For the problem, a class of semiparametric transformation nonmixture cure models is presented and for estimation, the maximum likelihood estimation procedure is derived. For the implementation of the proposed method, we develop a novel EM algorithm based on a Poisson variable-based augmentation. An extensive simulation study is conducted and suggests that the proposed approach works well in practical situations. Finally the method is applied to an example that motivated this study.

Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction.

Left-truncated data are often encountered in epidemiological cohort studies, where individuals are recruited according to a certain cross-sectional sampling criterion. Length-biased data, a special case of left-truncated data, assume that the incidence of the initial event follows a homogeneous Poisson process. In this article, we consider an analysis of length-biased and interval-censored data with a nonsusceptible fraction. We first point out the importance of a well-defined target population, which depends on the prior knowledge for the support of the failure times of susceptible individuals. Given the target population, we proceed with a length-biased sampling and draw valid inferences from a length-biased sample. When there is no covariate, we show that it suffices to consider a discrete version of the survival function for the susceptible individuals with jump points at the left endpoints of the censoring intervals when maximizing the full likelihood function, and propose an EM algorithm to obtain the nonparametric maximum likelihood estimates of nonsusceptible rate and the survival function of the susceptible individuals. We also develop a novel graphical method for assessing the stationarity assumption. When covariates are present, we consider the Cox proportional hazards model for the survival time of the susceptible individuals and the logistic regression model for the probability of being susceptible. We construct the full likelihood function and obtain the nonparametric maximum likelihood estimates of the regression parameters by employing the EM algorithm. The large sample properties of the estimates are established. The performance of the method is assessed by simulations. The proposed model and method are applied to data from an early-onset diabetes mellitus study.

Simultaneous variable selection in regression analysis of multivariate interval-censored data.

Multivariate interval-censored data arise when each subject under study can potentially experience multiple events and the onset time of each event is not observed exactly but is known to lie in a certain time interval formed by adjacent examination times with changed statuses of the event. This type of incomplete and complex data structure poses a substantial challenge in practical data analysis. In addition, many potential risk factors exist in numerous studies. Thus, conducting variable selection for event-specific covariates simultaneously becomes useful in identifying important variables and assessing their effects on the events of interest. In this paper, we develop a variable selection technique for multivariate interval-censored data under a general class of semiparametric transformation frailty models. The minimum information criterion (MIC) method is embedded in the optimization step of the proposed expectation-maximization (EM) algorithm to obtain the parameter estimator. The proposed EM algorithm greatly reduces the computational burden in maximizing the observed likelihood function, and the MIC naturally avoids selecting the optimal tuning parameter as needed in many other popular penalties, making the proposed algorithm promising and reliable. The proposed method is evaluated through extensive simulation studies and illustrated by an analysis of patient data from the Aerobics Center LongitudinalStudy.

Multi-marker genetic association and interaction tests with interval-censored survival outcomes.

The development of set-based genetic-survival association tests has been focusing on right-censored survival outcomes. However, interval-censored failure time data arise widely from health science studies, especially those on the development of chronic diseases. In this paper, we proposed a suite of set-based genetic association and interaction tests for interval-censored survival outcomes under a unified weighted-V-statistic framework. Besides dealing with interval censoring, the new tests can account for genetic effect heterogeneity and accommodate left truncation of survival outcomes. Simulation studies showed that the new tests perform well in terms of size and power under various scenarios and that the new interaction test is more powerful than the standard likelihood ratio test for testing gene-gene/gene-environment interactions. The practical utility of the developed tests was illustrated by a genome-wide association study of age to early childhood caries.

Exposure assessment for Cox proportional hazards cure models with interval-censored survival data.

Mixture cure models have been developed as an effective tool to analyze failure time data with a cure fraction. Used in conjunction with the logistic regression model, this model allows covariate-adjusted inference of an exposure effect on the cured probability and the hazard of failure for the uncured subjects. However, the covariate-adjusted inference for the overall exposure effect is not directly provided. In this paper, we describe a Cox proportional hazards cure model to analyze interval-censored survival data in the presence of a cured fraction and then apply a post-estimation approach by using model-predicted estimates difference to assess the overall exposure effect on the restricted mean survival time scale. For baseline hazard/survival function estimation, simple parametric models as fractional polynomials or restricted cubic splines are utilized to approximate the baseline logarithm cumulative hazard function, or, alternatively, the full likelihood is specified through a piecewise linear approximation for the cumulative baseline hazard function. Simulation studies were conducted to demonstrate the unbiasedness of both estimation methods for the overall exposure effect estimates over various baseline hazard distribution shapes. The methods are applied to analyze the interval-censored relapse time data from a smoking cessation study.

A comparative study of two-sample tests for interval-censored data

Interval-censored data are ubiquitous in clinical studies where actual time-to-event is difficult to measure. A number of nonparametric tests have been proposed to conduct a two-sample test using interval-censored data, and these tests can be used for assessing and comparing treatment effects over the control group. Alternatively, as commonly perceived, parametric tests can also be used assuming data are generated from a parametric family of distributions. To provide some guidance on choosing an appropriate method, in this paper, the performance of parametric tests and a series of nonparametric tests are compared through extensive simulation studies that cover a wide range of scenarios with varying sample sizes, varying censoring mechanisms and varying alternative hypotheses. For the purpose of illustration, we also apply these procedures to analyse three real datasets.

Application and Comparison of Methods for Analysing Correlated Interval-censored Data from Sexual Partnerships

In epidemiological studies where subjects are seen periodically on follow-up visits, interval-censored data occur naturally. The exact time the change of state (such as HIV seroconversion) occurs is not known exactly, only that it occurred sometime within a specific time interval. This paper considers estimation of parameters when HIV infection times are intervalcensored and correlated. It is assumed that each sexual partnership has a specific unobservable random effect that induces association between infection times. Parameters are estimated using the expectation-maximization algorithm and the Gibbs sampler. The results from the two methods are compared. Both methods yield fixed effects and baseline hazard estimates that are comparable. However, standard errors and frailty variance estimates are underestimated in the expectation-maximization algorithm compared to those from the Gibbs sampler. The Gibbs sampler is considered a plausible alternative to the expectation-maximization algorithm.

A unified approach to variable selection for Cox's proportional hazards model with interval-censored failure time data.

Cox's proportional hazards model is the most commonly used model for regression analysis of failure time data and some methods have been developed for its variable selection under different situations. In this paper, we consider a general type of failure time data, case K interval-censored data, that include all of other types discussed as special cases, and propose a unified penalized variable selection procedure. In addition to its generality, another significant feature of the proposed approach is that unlike all of the existing variable selection methods for failure time data, the proposed approach allows dependent censoring, which can occur quite often and could lead to biased or misleading conclusions if not taken into account. For the implementation, a coordinate descent algorithm is developed and the oracle property of the proposed method is established. The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Alzheimer's Disease Neuroimaging Initiative study that motivated this study.

New methods for the additive hazards model with the informatively interval-censored failure time data.

The additive hazards model is one of the most commonly used models for regression analysis of failure time data and many inference procedures have been developed for it under various situations. In particular, Wang etal. (2018a, Computational Statistics and Data Analysis, 125, 1-9) discussed the situation where one observes informatively interval-censored data and proposed a likelihood estimation approach. However , it involves estimation of the unknown baseline cumulative hazard function and thus may be time-consuming . Corresponding to this, we propose two new procedures, an estimating equation-based one and an empirical likelihood-based one, and both do not need estimation of the cumulative hazard function and can be easily implemented. The asymptotic properties of the proposed methods are established and an extensive simulation study suggests that they work well in practical situations. An application is alsoprovided.

Modeling lifetime of parallel components system with covariate, right and interval censored data

This research aims to model the lifetime of parallel components system with covariates, right, and interval censored data. The lifetimes of the components are assumed to follow the exponential distribution, with constant failure rates. A simulation study is conducted to assess the performance of the maximum likelihood estimates, without and with midpoint imputation method at various sample sizes, censoring proportions, and number of components in the system. The combination which produces the best parameter estimates is then identified by comparing the bias, standard error and root mean square error of these estimates. The simulation results indicate that the midpoint imputation method produces more efficient and accurate parameter estimates with smaller bias, standard error and root mean square error. Also, in general, better estimates are obtained at low censoring levels, large sample sizes, and a high number of parallel components in the system. The proposed model is then fitted to a modified real data of diabetic retinopathy patients. Following that, the non-parametric log-rank test and Wald hypothesis test are carried out to check the significance of the covariate, age in the model. The results show that the model fits the data rather well and the age of patients has no significant effect on the survival time of the patients’ eyes.

A semiparametric mixture model approach for regression analysis of partly interval-censored data with a cured subgroup.

Failure time data with a cured subgroup are frequently confronted in various scientific fields and many methods have been proposed for their analysis under right or interval censoring. However, a cure model approach does not seem to exist in the analysis of partly interval-censored data, which consist of both exactly observed and interval-censored observations on the failure time of interest. In this article, we propose a two-component mixture cure model approach for analyzing such type of data. We employ a logistic model to describe the cured probability and a proportional hazards model to model the latent failure time distribution for uncured subjects. We consider maximum likelihood estimation and develop a new expectation-maximization algorithm for its implementation. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed method is examined through simulation studies. An application to a set of real data on childhood mortality in Nigeria is provided.

Regression modelling of interval censored data based on the adaptive ridge procedure

A new method for the analysis of time to ankylosis complication on a dataset of replanted teeth is proposed. In this context of left-censored, interval-censored and right-censored data, a Cox model with piecewise constant baseline hazard is introduced. Estimation is carried out with the expectation maximisation (EM) algorithm by treating the true event times as unobserved variables. This estimation procedure is shown to produce a block diagonal Hessian matrix of the baseline parameters. Taking advantage of this interesting feature in the EM algorithm, a L 0 penalised likelihood method is implemented in order to automatically determine the number and locations of the cuts of the baseline hazard. This procedure allows to detect specific areas of time where patients are at greater risks for ankylosis. The method can be directly extended to the inclusion of exact observations and to a cure fraction. Theoretical results are obtained which allow to derive statistical inference of the model parameters from asymptotic likelihood theory. Through simulation studies, the penalisation technique is shown to provide a good fit of the baseline hazard and precise estimations of the resulting regression parameters.

Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model.

With the spread of the novel coronavirus disease 2019 (COVID-19) around the world, the estimation of the incubation period of COVID-19 has become a hot issue. Based on the doubly interval-censored data model, we assume that the incubation period follows lognormal and Gamma distribution, and estimate the parameters of the incubation period of COVID-19 by adopting the maximum likelihood estimation, expectation maximization algorithm and a newly proposed algorithm (expectation mostly conditional maximization algorithm, referred as ECIMM). The main innovation of this paper lies in two aspects: Firstly, we regard the sample data of the incubation period as the doubly interval-censored data without unnecessary data simplification to improve the accuracy and credibility of the results; secondly, our new ECIMM algorithm enjoys better convergence and universality compared with others. With the framework of this paper, we conclude that 14-day quarantine period can largely interrupt the transmission of COVID-19, however, people who need specially monitoring should be isolated for about 20 days for the sake of safety. The results provide some suggestions for the prevention and control of COVID-19. The newly proposed ECIMM algorithm can also be used to deal with the doubly interval-censored data model appearing in various fields.

Time to licensure for driving among U.S. teens: Survival analysis of interval-censored survey data

Objective Novice drivers who delay in driving licensure may miss safety benefits of Graduate Driver Licensing (GDL) programs, potentially putting themselves at higher crash-risk. Time to licensure relates their access to independent transportation to potential future economic- and educational-related opportunities. The objective of this study was to explore time to licensure associations with teens’ race/ethnicity and GDL restrictions. Methods Secondary analysis using all seven annual assessments of the NEXT Generation Health Study, a nationally representative longitudinal study starting with 10th grade (N = 2785; 2009–2010 school year). Data were collected in U.S. public/private schools, colleges, workplaces, and other settings. The outcome variable was interval-censored time to licensure (event = obtained driving licensure). Independent variables included race/ethnicity and state-specific GDL restrictions. Covariates included family affluence, parent education, nativity, sex, and urbanicity. Proportional hazards (PH) models were conducted for interval-censored survival analysis based on stepwise backward elimination for fitting multivariate models with consideration of complex survey features. In the PH models, a hazard ratio (HR) estimates a greater (>1) or lesser (<1) likelihood of licensure at all timepoints. Results Median time to licensure after reaching legal driving age for Latinos, African Americans, and Non-Latino Whites was 3.47, 2.90, and 0.41 years, respectively. Multivariate PH models showed that Latinos were 46% less likely (HR = 0.54, 95%CI: 0.35–0.72) and African Americans were 56% less likely (HR = 0.44, 95%CI: 0.32–0.56) to have obtained licensure at any time compared to Non-Latino Whites. Only learner minimum age GDL restriction was associated with time to licensure. Living in a state with a required learner driving minimum age of ≥16 years (HR = 0.57, 95%CI: 0.16–0.98) also corresponded with 43% lower likelihood of licensure at legal eligibility compared to living in other states with a required learner driving minimum age of <16 years. Conclusion Latinos and African American teens obtained their license approximately three years after eligibility on average, and much later than Non-Latino Whites. Time to licensure likelihood was associated with race/ethnicity and required minimum age of learner permit, indicating important implications for teens of different racial/ethnic groups in relation to licensure, access to independent transportation, and exposure to GDL programs.

Semiparametric regression analysis of partly interval-censored failure time data with application to an AIDS clinical trial.

Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an EM algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.

Seizures after decompressive hemicraniectomy for large middle cerebral artery territory infarcts: Incidence, associated factors, and impact on long-term outcomes.

Decompressive hemicraniectomy (DH) reduces mortality of large middle cerebral artery (MCA) territory infarcts. Survivors are at high risk of poststroke seizures (PSSs). This study aims to describe the incidence of PSSs, to identify associated factors, and to assess their impact on long-term outcomes. We included consecutive patients who underwent DH for large MCA infarcts from May 2005 to December 2019 at Lille University Hospital. Patients were followed up at 3months, 1 year, and 3years. We analysed (i) the incidence and associated factors of early onset PSSs (EPSSs) with logistic regression models; (ii) the incidence and associated factors of late onset PSSs (LPSSs) in survivors at 7days with a univariate Cox proportional hazard regression model for interval-censored data; and (iii) the impact of PSSs (EPSSs and LPSSs) on mortality with univariate and multivariate Cox proportional hazard regression models and modified Rankin Scale at 1 and 3years, with univariate and adjusted multivariate ordinal logistic regression analyses. Of 248 patients (150 men, 60.5%; mean age = 50.4 ± 9.6years), 106 (42.7%) presented PSSs (six inaugural seizures, 22 EPSSs, 78 LPSSs) during follow-up. The PSS cumulative incidence was 12.3% at 7days, 24.9% at 3months, 49.8% at 1years, and 54.8% at 3years. No predictor was significantly associated with either EPSSs or LPSSs. PSSs did not significantly impact mortality and long-term functional outcome. The incidence of PSSs after DH is high, reaching more than 50% 3years after stroke, but PSSs did not influence long-term mortality or functional outcome.

Estimating COVID-19 recovery time in a cohort of Italian healthcare workers who underwent surveillance swab testing

ObjectivesThe COVID-19 pandemic is putting a huge strain on the provision and continuity of care. The length of sickness absence of the healthcare workers as a result of SARS-CoV-2 infection plays a pivotal role in hospital staff management. Therefore, the aim of this study was to explore the timing of COVID-19 recovery and viral clearance, and its predictive factors, in a large sample of healthcare workers. Study designThis is a retrospective cohort study. MethodsThe analysis was conducted on data collected during the hospital health surveillance programme for healthcare staff at the University Hospital of Verona; healthcare workers were tested for SARS-CoV-2 through RT-PCR with oronasopharyngeal swab samples. The health surveillance programme targeted healthcare workers who either had close contact with SARS-CoV-2–infected patients or were tested as part of the screening-based strategy implemented according to national and regional requirements. Recovery time was estimated from the first positive swab to two consecutive negative swabs, collected 24 h apart, using survival analysis for both right-censored and interval-censored data. Cox proportional hazard was used for multivariate analysis. ResultsDuring the health surveillance programme, 6455 healthcare workers were tested for SARS-CoV-2 and 248 (3.8%, 95% confidence interval [CI]: 3.4–4.3) reported positive results; among those who tested positive, 49% were asymptomatic, with a median age of 39.8 years, which is significantly younger than symptomatic healthcare workers (48.2 years, P < 0.001). Screening tests as part of the health surveillance programme identified 31 (12.5%) of the positive cases. Median recovery time was 24 days (95% CI: 23–26) and 21.5 days (95% CI: 15.5–30.5) in right- and interval-censoring analysis, respectively, with no association with age, sex or presence of symptoms. Overall, 63% of participants required >20 days to test negative on two consecutive swabs. Hospitalised healthcare workers (4.8%) were older and had a significantly longer recovery time compared with non-hospitalised healthcare workers in both analyses (33.5 vs 24 days, P = 0.005). ConclusionsRecovery from COVID-19 and viral clearance may take a long time, especially in individuals who are hospitalised. To detect asymptomatic cases, screening programmes for healthcare workers is recommended.

Semiparametric regression with the U-shaped baseline hazard function in the additive hazards model under general censoring mechanisms

When employing natural shape constraint knowledge obtained from prior studies in survival data analysis, both restrictions of parametric models and difficulties of nonparametric approaches, including the selection of bandwidth and tuning parameter, can be avoided. We use this technique to derive a nonparametric estimator of the U-shaped baseline hazard function in the semiparametric additive hazards regression model for partly general interval-censored data. An iterative algorithm is developed for computing estimators of the baseline hazard function and regression coefficients simultaneously. Numerical studies using simulation and real dataset are conducted to compare the performance of the proposed approach incorporating shape information with that of the B-spline and I-spline methods without using shape restriction. They show that the proposed method increases the efficiency of estimator for the baseline hazard function in terms of the mean Hellinger distance and performs better, or at least leads to competitive results for estimating regression coefficients.