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Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social, or genomic studies. However, the existing methodology for structural equation modeling is not concerned with interval-censored data, a type of coarse survival data arising typically from periodic examinations for the occurrence of asymptomatic disease. The present study aims to fill this gap and provide a flexible semiparametric structural equation modeling framework. A general class of factor-augmented transformation models is proposed to model the interval-censored outcome of interest in the presence of latent risk factors. An expectation–maximization algorithm is subtly designed to conduct the nonparametric maximum likelihood estimation. Furthermore, the asymptotic properties of the proposed estimators are established by leveraging the empirical process theory. The numerical results obtained from extensive simulations and an application to the Alzheimer's disease data set demonstrate the proposed method's empirical performance and practical utility. [ABSTRACT FROM AUTHOR]

Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval‐censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow‐up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval‐censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and B$$ B $$‐splines, respectively. We develop an easy‐to‐implement expectation‐maximization algorithm coupled with three‐stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness. [ABSTRACT FROM AUTHOR]

The case–cohort design is widely used as a way of reducing costs when the disease incidence is low and covariates are expensive to measure. In this paper, we consider regression analysis of interval‐censored failure time data arising from the case–cohort design under a class of semiparametric transformation models. Although some methods have been proposed for the situation, they only make use of the information on the subjects in the subcohort and thus can be less efficient. To address this, we propose a class of linear inverse probability weighted estimators that make use of the information on all subjects. Furthermore, a method is provided to determine the optimal weights, and the proposed estimator is shown to be consistent and asymptotically normal. A simulation study is performed and indicates that the proposed method works well for practical situations, and it is illustrated by using the data arising from an Alzheimer's disease study. [ABSTRACT FROM AUTHOR]

Interval‐censored data arise when a failure process is under intermittent observation and failure status is only known at assessment times. We consider the development of predictive algorithms when training samples involve interval censoring. Using censoring unbiased transformations and pseudo‐observations, we define observed data loss functions, which are unbiased estimates of the corresponding complete data loss functions. We show that regression trees based on these loss functions can recover the tree structure and yield good predictive accuracy. An application is given to a study involving individuals with psoriatic arthritis where the aim is to identify genetic markers useful for the prediction of axial disease within 10 years of a baseline assessment. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data arise frequently in periodical follow-up studies including clinical trials and epidemiological surveys. In addition, some covariates may be subject to measurement errors due to the instrumental contamination, biological variation or other reasons. For the analysis of interval-censored data with mis-measured covariates, the existing methods either assume a parametric model or rely on the availability of replicated surrogate measurements for the error-prone covariate, which both have obvious limitations. To overcome these shortcomings, the authors propose a simulation-extrapolation estimation procedure under a general class of transformation models. The resulting estimators are shown to be consistent and asymptotically normal. The numerical results obtained from a simulation study indicate that the proposed method performs reasonably well in practice. In particular, the proposed method can reduce the estimation bias given by the naive method that does not take measurement errors into account. Finally, the proposed method is applied to a real data set on hypobaric decompression sickness. [ABSTRACT FROM AUTHOR]

In multi-site studies, sharing individual-level information across multiple data-contributing sites usually poses a significant risk to data security. Thus, due to privacy constraints, analytical tools without using individual-level data have drawn considerable attention to researchers in recent years. In this work, we consider regression analysis of current status data arising from multi-site cross-sectional studies and develop two distributed estimation methods tailored to the unstratified and stratified additive hazards models, respectively. In particular, instead of utilizing the individual-level data, the proposed methods only require transferring the summary statistics from each site to the analysis center, which achieves the aim of privacy protection. We establish the asymptotic properties of the proposed estimators, including the consistency and asymptotic normality. Specifically, the distributed estimators derived are shown to be asymptotically equivalent to those based on the pooled individual-level data. Simulation studies and an application to a multi-site gonorrhea infection data set demonstrate the proposed methods’ satisfactory performance and practical utility. [ABSTRACT FROM AUTHOR]

Abstract Breast cancer is the most common cancer in women. Previous studies have investigated estimating and predicting the proportional hazard rates and survival in breast cancer. This study deals with predicting accelerated hazards (AH) rate based on age categories in breast cancer patients using deep learning methods. The AH has a time-dependent structure whose rate changes according to time and variable effects. We have collected data related to 1225 female patients with breast cancer at the Mandarin University of Medical Sciences. The patients' demographic and clinical characteristics including family history, age, history of tobacco use, hysterectomy, first menstruation age, gravida, number of breastfeeding, disease grade, marital status, and survival status have been recorded. Initially, we dealt with predicting three age groups of patients: ≤ 40, 41–60, and ≥ 61 years. Then, the prediction of accelerated risk value based on age categories for each breast cancer patient through deep learning and the importance of variables using LightGBM is discussed. Improving clinical management and treatment of breast cancer requires advanced methods such as time-dependent AH calculation. When the behavioral effect is assumed as a time scale change between hazard functions, the AH model is more appropriate for randomized clinical trials. The study results demonstrate the proper performance of the proposed model for predicting AH by age categories based on breast cancer patients' demographic and clinical characteristics.

Breast cancer is the most common cancer in women. Previous studies have investigated estimating and predicting the proportional hazard rates and survival in breast cancer. This study deals with predicting accelerated hazards (AH) rate based on age categories in breast cancer patients using deep learning methods. The AH has a time-dependent structure whose rate changes according to time and variable effects. We have collected data related to 1225 female patients with breast cancer at the Mandarin University of Medical Sciences. The patients' demographic and clinical characteristics including family history, age, history of tobacco use, hysterectomy, first menstruation age, gravida, number of breastfeeding, disease grade, marital status, and survival status have been recorded. Initially, we dealt with predicting three age groups of patients: ≤ 40, 41–60, and ≥ 61 years. Then, the prediction of accelerated risk value based on age categories for each breast cancer patient through deep learning and the importance of variables using LightGBM is discussed. Improving clinical management and treatment of breast cancer requires advanced methods such as time-dependent AH calculation. When the behavioral effect is assumed as a time scale change between hazard functions, the AH model is more appropriate for randomized clinical trials. The study results demonstrate the proper performance of the proposed model for predicting AH by age categories based on breast cancer patients' demographic and clinical characteristics. [ABSTRACT FROM AUTHOR]

Field data provide important information on product reliability. Interval sampling is widely used for collection of field data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated (DT) data if the exact failure time is known. In many situations, the exact failure date is known only to fall within an interval, leading to doubly truncated and interval censored (DTIC) data. This article considers analysis of DTIC data under parametric failure time models. We consider a conditional likelihood approach and propose interval estimation for parameters and the cumulative distribution functions. Simulation studies show that the proposed method performs well for finite sample size. [ABSTRACT FROM AUTHOR]

Suppose X is a frequency vector that follows a central multiple hypergeometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We call the event where X satisfies a prespecified set of symmetrical—but otherwise arbitrary—interval constraints in each component a symmetric core event. We show that the probability of any symmetric core event—in other words, the multivariate peakedness in the sense of Birnbaum (1948) and Tong (1988)—is symmetric unimodal as a function of the sample size. Two proofs are given. The shorter one relies on a convolution property of ultra-log-concave sequences, which implies that the sequence of peakedness values is log-concave (even for asymmetric rectangular events). The longer, though more elementary, proof does not rely on notions of log-concavity. To illustrate the use of symmetric core events, we analyze a simple yet interesting wager in a sequential card game. Finally, we indicate that the unimodality result for symmetric core events is pivotal in proving a certain variance reduction inequality involving multinomial frequencies subject to arbitrary interval censoring. [ABSTRACT FROM AUTHOR]

Interval-censored data frequently arise in various biomedical areas involving periodical follow-ups where the failure or event time of interest cannot be observed exactly but is only known to fall into a time interval. This article considers a semiparametric probit regression model, a valuable alternative to other commonly used semiparametric models in survival analysis, to investigate potential risk factors for the interval-censored failure time of interest. We develop an expectation-maximization (EM) algorithm to conduct the pseudo maximum likelihood estimation (MLE) using the working independence strategy for general or mixed-case interval-censored data. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal with the empirical process techniques. In addition, we propose a novel penalized EM algorithm for simultaneously achieving variable selection and parameter estimation in the case of high-dimensional covariates. The proposed variable selection method can be readily implemented with some existing software and considerably reduces the estimation error of the proposed pseudo-MLE approach. Simulation studies demonstrate the satisfactory performance of the proposed methods. An application to a set of interval-censored data on prostate cancer further confirms the utility of the methodology. for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractWith the rapid development of data acquisition and storage space, massive datasets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To accommodate such big volume in the analysis, a variety of methods have been proposed in the circumstances of complete or right censored survival data. However, existing development of big data methodology has not attended to interval-censored outcomes, which are ubiquitous in cross-sectional or periodical follow-up studies. In this work, we propose an easily implemented divide-and-combine approach for analyzing massive interval-censored survival data under the additive hazards model. We establish the asymptotic properties of the proposed estimator, including the consistency and asymptotic normality. In addition, the divide-and-combine estimator is shown to be asymptotically equivalent to the full-data-based estimator obtained from analyzing all data together. Simulation studies suggest that, relative to the full-data-based approach, the proposed divide-and-combine approach has desirable advantage in terms of computation time, making it more applicable to large-scale data analysis. An application to a set of interval-censored data also demonstrates the practical utility of the proposed method. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database. [ABSTRACT FROM AUTHOR]

The article presents a novel statistical framework for COVID-19 transmission monitoring and control, which was developed and deployed at The Ohio State University main campus in Columbus during the Autumn term of 2020. Our approach effectively handles prevalence data with interval censoring and explicitly incorporates changes in transmission dynamics and human behaviour. To illustrate the methodology's usefulness, we apply it to both synthetic and actual student SARS-CoV-2 testing data collected at the OSU Columbus campus in late 2020. [ABSTRACT FROM AUTHOR]

Abstract Background Estimation of the SARS-CoV-2 incubation time distribution is hampered by incomplete data about infection. We discuss two biases that may result from incorrect handling of such data. Notified cases may recall recent exposures more precisely (differential recall). This creates bias if the analysis is restricted to observations with well-defined exposures, as longer incubation times are more likely to be excluded. Another bias occurred in the initial estimates based on data concerning travellers from Wuhan. Only individuals who developed symptoms after their departure were included, leading to under-representation of cases with shorter incubation times (left truncation). This issue was not addressed in the analyses performed in the literature. Methods We performed simulations and provide a literature review to investigate the amount of bias in estimated percentiles of the SARS-CoV-2 incubation time distribution. Results Depending on the rate of differential recall, restricting the analysis to a subset of narrow exposure windows resulted in underestimation in the median and even more in the 95th percentile. Failing to account for left truncation led to an overestimation of multiple days in both the median and the 95th percentile. Conclusion We examined two overlooked sources of bias concerning exposure information that the researcher engaged in incubation time estimation needs to be aware of.

Law enforcement agencies are tasked with crime prevention and crime reduction under limited resources. Having an accurate temporal estimate of the crime rate would be valuable to achieve such a goal. However, estimation is usually complicated by the interval censored nature of crime data. We cast the problem of intensity estimation as a Poisson regression using an EM algorithm to estimate the parameters. Two special penalties are added that provide smoothness over the time of day and day of week. This approach provides accurate intensity estimates and can also uncover day of week clusters that share the same intensity patterns. Both simulated and real crime data gathered from the city of Cincinnati and the city of Dallas are used to demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Background: Progression-free survival (PFS) is used to evaluate treatment effects in cancer clinical trials. Disease progression (DP) in patients is typically determined by radiological testing at several scheduled tumor-assessment time points. This produces a discrepancy between the true progression time and the observed progression time. When the observed progression time is considered as the true progression time, a positively biased PFS is obtained for some patients, and the estimated survival function derived by the Kaplan–Meier method is also biased. Methods: While the midpoint imputation method is available and replaces interval-censored data with midpoint data, it unrealistically assumes that several DPs occur at the same time point when several DPs are observed within the same tumor-assessment interval. We enhanced the midpoint imputation method by replacing interval-censored data with equally spaced timepoint data based on the number of observed interval-censored data within the same tumor-assessment interval. Results: The root mean square error of the median of the enhanced method is almost always smaller than that of the midpoint imputation regardless of the tumor-assessment frequency. The coverage probability of the enhanced method is close to the nominal confidence level of 95% in most scenarios. Conclusion: We believe that the enhanced method, which builds upon the midpoint imputation method, is more effective than the midpoint imputation method itself. [ABSTRACT FROM AUTHOR]

Background: Estimation of the SARS-CoV-2 incubation time distribution is hampered by incomplete data about infection. We discuss two biases that may result from incorrect handling of such data. Notified cases may recall recent exposures more precisely (differential recall). This creates bias if the analysis is restricted to observations with well-defined exposures, as longer incubation times are more likely to be excluded. Another bias occurred in the initial estimates based on data concerning travellers from Wuhan. Only individuals who developed symptoms after their departure were included, leading to under-representation of cases with shorter incubation times (left truncation). This issue was not addressed in the analyses performed in the literature. Methods: We performed simulations and provide a literature review to investigate the amount of bias in estimated percentiles of the SARS-CoV-2 incubation time distribution. Results: Depending on the rate of differential recall, restricting the analysis to a subset of narrow exposure windows resulted in underestimation in the median and even more in the 95th percentile. Failing to account for left truncation led to an overestimation of multiple days in both the median and the 95th percentile. Conclusion: We examined two overlooked sources of bias concerning exposure information that the researcher engaged in incubation time estimation needs to be aware of. [ABSTRACT FROM AUTHOR]

Many longitudinal studies are designed to monitor participants for major events related to the progression of diseases. Data arising from such longitudinal studies are usually subject to interval censoring since the events are only known to occur between two monitoring visits. In this work, we propose a new method to handle interval‐censored multistate data within a proportional hazards model framework where the hazard rate of events is modeled by a nonparametric function of time and the covariates affect the hazard rate proportionally. The main idea of this method is to simplify the likelihood functions of a discrete‐time multistate model through an approximation and the application of data augmentation techniques, where the assumed presence of censored information facilitates a simpler parameterization. Then the expectation‐maximization algorithm is used to estimate the parameters in the model. The performance of the proposed method is evaluated by numerical studies. Finally, the method is employed to analyze a dataset on tracking the advancement of coronary allograft vasculopathy following heart transplantation. [ABSTRACT FROM AUTHOR]

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

In this paper, we consider a competitive risk scenario in which the initial number of competing risks, assumed to follow a shifted Poisson distribution, is subject to a destructive element. In such settings, both the number of initial risks and risks remaining active after destruction represent missing data. Assuming the population of interest to have a cure component and the form of the data as interval-censored, we extend the destructive shifted Poisson cure model with Weibull lifetimes to accommodate interval-censored data and develop an efficient expectation maximization algorithm for this model. By using the conditional distributions of the missing data, the conditional expected complete log-likelihood function is decomposed into simpler functions which are then maximized independently. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. Also considered is the efficacy of the proposed EM algorithm as compared to direct maximization of the observed log-likelihood function. Finally, data from a crime recidivism study is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

This paper discusses variable selection when one faces general, high-dimensional interval-censored failure time data, which commonly occur in many areas such as epidemiological, medical and public health studies. Furthermore, for the situation, it is often the case that covariates may have nonlinear effects, which makes the variable selection more challenging. For the problem, we propose a novel and robust variable selection technique under a class of semiparametric additive transformation models. In particular, Bernstein polynomials are employed to approximate unknown functions and an EM algorithm is developed with the use of Poisson-based data augmentation for the implementation of the proposed method. An extensive simulation study is conducted to assess the empirical performance of the approach and suggests that it works well in practical situations. Finally, we apply the method to a set of real data arising from an Alzheimer's Disease study. [ABSTRACT FROM AUTHOR]

Multivariate panel count data arise when there are multiple types of recurrent events, and the observation for each study subject consists of the number of recurrent events of each type between two successive examinations. We formulate the effects of potentially time-dependent covariates on multiple types of recurrent events through proportional rates models, while leaving the dependence structures of the related recurrent events completely unspecified. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process, and we develop a simple and stable EM-type algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. In addition, we develop a class of graphical and numerical methods for checking the adequacy of the fitted model. Finally, we evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial. [ABSTRACT FROM AUTHOR]

Abstract Background The impact of pre-pregnancy weight and the rate of gestational weight gain (GWG) together on the risk of early GDM (

IntroductionTo examine if perceptions of harmfulness and addictiveness of hookah and cigarettes impact the age of initiation of hookah and cigarettes, respectively, among US youth. Youth (12-17 years old) users and never users of hookah and cigarettes during their first wave of PATH participation were analyzed by each tobacco product (TP) independently. The effect of perceptions of (i) harmfulness and (ii) addictiveness at the first wave of PATH participation on the age of initiation of ever use of hookah was estimated using interval-censoring Cox proportional hazards models.MethodsUsers and never users of hookah at their first wave of PATH participation were balanced by multiplying the sampling weight and the 100 balance repeated replicate weights with the inverse probability weight (IPW). The IPW was based on the probability of being a user in their first wave of PATH participation. A Fay’s factor of 0.3 was included for variance estimation. Crude hazard ratios (HR) and 95% confidence intervals (CIs) are reported. A similar process was repeated for cigarettes.ResultsCompared to youth who perceived each TP as “a lot of harm”, youth who reported perceived “some harm” had younger ages of initiation of these tobacco products, HR: 2.53 (95% CI: 2.87-4.34) for hookah and HR: 2.35 (95% CI: 2.10-2.62) for cigarettes. Similarly, youth who perceived each TP as “no/little harm” had an earlier age of initiation of these TPs compared to those who perceived them as “a lot of harm”, with an HR: 2.23 (95% CI: 1.82, 2.71) for hookah and an HR: 1.85 (95% CI: 1.72, 1.98) for cigarettes. Compared to youth who reported each TP as “somewhat/very likely” as their perception of addictiveness, youth who reported “neither likely nor unlikely” and “very/somewhat unlikely” as their perception of addictiveness of hookah had an older age of initiation, with an HR: 0.75 (95% CI: 0.67-0.83) and an HR: 0.55 (95% CI: 0.47, 0.63) respectively.DiscussionPerceptions of the harmfulness and addictiveness of these tobacco products (TPs) should be addressed in education campaigns for youth to prevent early ages of initiation of cigarettes and hookah.

Panel count data and interval‐censored data are two types of incomplete data that often occur in event history studies. Almost all existing statistical methods are developed for their separate analysis. In this paper, we investigate a more general situation where a recurrent event process and an interval‐censored failure event occur together. To intuitively and clearly explain the relationship between the recurrent current process and failure event, we propose a failure time‐dependent mean model through a completely unspecified link function. To overcome the challenges arising from the blending of nonparametric components and parametric regression coefficients, we develop a two‐stage conditional expected likelihood‐based estimation procedure. We establish the consistency, the convergence rate and the asymptotic normality of the proposed two‐stage estimator. Furthermore, we construct a class of two‐sample tests for comparison of mean functions from different groups. The proposed methods are evaluated by extensive simulation studies and are illustrated with the skin cancer data that motivated this study. [ABSTRACT FROM AUTHOR]

In this article, a competitive risk survival model is considered in which the initial number of risks, assumed to follow a negative binomial distribution, is subject to a destructive mechanism. Assuming the population of interest to have a cure component, the form of the data as interval‐censored, and considering both the number of initial risks and risks remaining active after destruction to be missing data, we develop two distinct estimation algorithms for this model. Making use of the conditional distributions of the missing data, we develop an expectation maximization (EM) algorithm, in which the conditional expected complete log‐likelihood function is decomposed into simpler functions which are then maximized independently. A variation of the EM algorithm, called the stochastic EM (SEM) algorithm, is also developed with the goal of avoiding the calculation of complicated expectations and improving performance at parameter recovery. A Monte Carlo simulation study is carried out to evaluate the performance of both estimation methods through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We demonstrate the proposed SEM algorithm as the preferred estimation method through simulation and further illustrate the advantage of the SEM algorithm, as well as the use of a destructive model, with data from a children's mortality study. [ABSTRACT FROM AUTHOR]

It has attracted a great deal of interest in randomized survival studies to assess the causal treatment effect under non-compliance with time-to-event outcomes. In this paper, the problem when one faces case–cohort studies for which covariates are usually too expensive to be measured or obtained for the full cohort and also the disease rate is generally low is considered. Furthermore, only interval-censored data may be available for the failure event of interest, a situation for which there does not seem to exist an established estimation procedure. To address the problem, a sieve inverse probability weighting estimation procedure is proposed, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. In addition, the method is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Summary: Interval‐censored data often arise in prospective studies involving periodical follow‐up for monitoring the failure event occurrence. In addition to censoring, left truncation also occurs if only participants who have not experienced the failure event are enrolled in the study, which clearly induces the selection bias and makes the analysis more complicated. This work provides an efficient maximum likelihood estimation approach that appropriately adjusts the biased sampling for the proportional hazards model with left‐truncated and interval‐censored data. A flexible and stable expectation–maximisation algorithm via a two‐stage data augmentation is developed to maximise the intractable likelihood function. The asymptotic properties of the proposed estimators are established with the empirical process theory. The numerical results obtained from extensive simulations suggest that the proposed method performs satisfactorily and has some prominent advantages over the competing methods. An application to a colon cancer dataset also demonstrates the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Interval censored survival data, where the exact event time is only known to lie in an interval, is commonly encountered in practice. Furthermore, medical advancements have made it possible for a fraction of patients to be cured. In this article, we analyze interval-censored data using the Cox–Aalen model with a cure fraction, where the probability of being uncured is determined by a logistic regression model and the failure times of the uncured subjects are modelled by the Cox–Aalen model with fixed covariates. We propose a multiple imputation (MI) scheme for obtaining parameter and variance estimates for both the cure probability and survival distribution of the uncured subjects. One major advantage of the proposed MI scheme is its simplicity since it avoids computational complexity resulting from interval censoring and presence of a cure fraction. The presented approach can be implemented by using the existing software for the Cox–Aalen model with right censored data. Simulation studies indicate that the approach performs well for practical situation. We apply the proposed method to the analysis of the data from hypobaric decompression sickness (HDS) study. [ABSTRACT FROM AUTHOR]

The approximate Bernstein polynomial model, a mixture of beta distributions, is applied to obtain maximum likelihood estimates of the regression coefficients, the baseline density and the survival functions in an accelerated failure time model based on interval censored data including current status data. The estimators of the regression coefficients and the underlying baseline density function are shown to be consistent with almost parametric rates of convergence under some conditions for uncensored and/or interval censored data. Simulation shows that the proposed method is better than its competitors. The proposed method is illustrated by fitting the Breast Cosmetic and the HIV infection time data using the accelerated failure time model. [ABSTRACT FROM AUTHOR]

Length-biased failure time data occur often in various biomedical fields, including clinical trials, epidemiological cohort studies and genome-wide association studies, and their analyses have been attracting a surge of interest. In practical applications, because one may collect a large number of candidate covariates for the failure event of interest, variable selection becomes a useful tool to identify the important risk factors and enhance the estimation accuracy. In this paper, we consider Cox's proportional hazards model and develop a penalized variable selection technique with various popular penalty functions for length-biased data, in which the failure event of interest suffers from interval censoring. Specifically, a computationally stable and reliable penalized expectation-maximization algorithm via two-stage data augmentation is developed to overcome the challenge in maximizing the intractable penalized likelihood. We establish the oracle property of the proposed method and present some simulation results, suggesting that the proposed method outperforms the traditional variable selection method based on the conditional likelihood. The proposed method is then applied to a set of real data arising from the Prostate, Lung, Colorectal and Ovarian cancer screening trial. The analysis results show that African Americans and having immediate family members with prostate cancer significantly increase the risk of developing prostate cancer, while having diabetes exhibited a significantly lower risk of developing prostate cancer. [ABSTRACT FROM AUTHOR]

The Nun study is a well-known longitudinal epidemiology study of aging and dementia that recruited elderly nuns who were not yet diagnosed with dementia (i.e., incident cohort) and who had dementia prior to entry (i.e., prevalent cohort). In such a natural history of disease study, multistate modeling of the combined data from both incident and prevalent cohorts is desirable to improve the efficiency of inference. While important, the multistate modeling approaches for the combined data have been scarcely used in practice because prevalent samples do not provide the exact date of disease onset and do not represent the target population due to left-truncation. In this paper, we demonstrate how to adequately combine both incident and prevalent cohorts to examine risk factors for every possible transition in studying the natural history of dementia. We adapt a four-state nonhomogeneous Markov model to characterize all transitions between different clinical stages, including plausible reversible transitions. The estimating procedure using the combined data leads to efficiency gains for every transition compared to those from the incident cohort data only. [ABSTRACT FROM AUTHOR]

Background: Composite time-to-event endpoints are beneficial for assessing related outcomes jointly in clinical trials, but components of the endpoint may have different censoring mechanisms. For example, in the PRagmatic EValuation of evENTs And Benefits of Lipid-lowering in oldEr adults (PREVENTABLE) trial, the composite outcome contains one endpoint that is right censored (all-cause mortality) and two endpoints that are interval censored (dementia and persistent disability). Although Cox regression is an established method for time-to-event outcomes, it is unclear how models perform under differing component-wise censoring schemes for large clinical trial data. The goal of this article is to conduct a simulation study to investigate the performance of Cox models under different scenarios for composite endpoints with component-wise censoring. Methods: We simulated data by varying the strength and direction of the association between treatment and outcome for the two component types, the proportion of events arising from the components of the outcome (right censored and interval censored), and the method for including the interval-censored component in the Cox model (upper value and midpoint of the interval). Under these scenarios, we compared the treatment effect estimate bias, confidence interval coverage, and power. Results: Based on the simulation study, Cox models generally have adequate power to achieve statistical significance for comparing treatments for composite outcomes with component-wise censoring. In our simulation study, we did not observe substantive bias for scenarios under the null hypothesis or when the treatment has a similar relative effect on each component outcome. Performance was similar regardless of if the upper value or midpoint of the interval-censored part of the composite outcome was used. Conclusion: Cox regression is a suitable method for analysis of clinical trial data with composite time-to-event endpoints subject to different component-wise censoring mechanisms. [ABSTRACT FROM AUTHOR]

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right‐censored data. No formal goodness‐of‐fit (GOF) test exists for interval‐censored or recurrent events data. We develop a general GOF test for copula‐based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D‐vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type‐I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of model fitness. [ABSTRACT FROM AUTHOR]

The Botswana Combination Prevention Project was a cluster‐randomized HIV prevention trial whose follow‐up period coincided with Botswana's national adoption of a universal test and treat strategy for HIV management. Of interest is whether, and to what extent, this change in policy modified the preventative effects of the study intervention. To address such questions, we adopt a stratified proportional hazards model for clustered interval‐censored data with time‐dependent covariates and develop a composite expectation maximization algorithm that facilitates estimation of model parameters without placing parametric assumptions on either the baseline hazard functions or the within‐cluster dependence structure. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal. We also propose and provide theoretical justification for the use of the profile composite likelihood function to construct a robust sandwich estimator for the variance. We characterize the finite‐sample performance and robustness of these estimators through extensive simulation studies. Finally, we conclude by applying this stratified proportional hazards model to a re‐analysis of the Botswana Combination Prevention Project, with the national adoption of a universal test and treat strategy now modeled as a time‐dependent covariate. [ABSTRACT FROM AUTHOR]

Alzheimer's disease (AD) is a progressive and polygenic disorder that affects millions of individuals each year. Given that there have been few effective treatments yet for AD, it is highly desirable to develop an accurate model to predict the full disease progression profile based on an individual's genetic characteristics for early prevention and clinical management. This work uses data composed of all four phases of the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, including 1740 individuals with 8 million genetic variants. We tackle several challenges in this data, characterized by large‐scale genetic data, interval‐censored outcome due to intermittent assessments, and left truncation in one study phase (ADNIGO). Specifically, we first develop a semiparametric transformation model on interval‐censored and left‐truncated data and estimate parameters through a sieve approach. Then we propose a computationally efficient generalized score test to identify variants associated with AD progression. Next, we implement a novel neural network on interval‐censored data (NN‐IC) to construct a prediction model using top variants identified from the genome‐wide test. Comprehensive simulation studies show that the NN‐IC outperforms several existing methods in terms of prediction accuracy. Finally, we apply the NN‐IC to the full ADNI data and successfully identify subgroups with differential progression risk profiles. Data used in the preparation of this article were obtained from the ADNI database. [ABSTRACT FROM AUTHOR]

Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We construct the nonparametric pseudolikelihood under the working assumption that all event times are independent, and we provide a simple and stable EM-type algorithm. The resulting nonparametric maximum pseudolikelihood estimators for the regression parameters are shown to be consistent and asymptotically normal, with a limiting covariance matrix that can be consistently estimated by a sandwich estimator under arbitrary dependence structures for the related event times. We evaluate the performance of the proposed methods through extensive simulation studies and present an application to data from the Atherosclerosis Risk in Communities Study. [ABSTRACT FROM AUTHOR]

Background: The impact of pre-pregnancy weight and the rate of gestational weight gain (GWG) together on the risk of early GDM (< 24 weeks gestation; eGDM) has not been studied in the Indian context. We aimed to study the influence of (1) pre-pregnancy weight on the risk of eGDM diagnosed in two time intervals; and (2) in addition, the rate of GWG by 12 weeks on the risk of eGDM diagnosed in 19–24 weeks. Method: Our study utilized real-world clinical data on pregnant women routinely collected at an antenatal care clinic at a private tertiary hospital, in Pune, India. Women registering before 12 weeks of gestation (v1), with a singleton pregnancy, and having a follow-up visit between 19–24 weeks (v2) were included (n = 600). The oral glucose tolerance test was conducted universally as per Indian guidelines (DIPSI) at v1 and v2 for diagnosing eGDM. The data on the onset time of eGDM were interval censored; hence, we modeled the risk of eGDM using binomial regression to assess the influence of pre-pregnancy weight on the risk of eGDM in the two intervals. The rate of GWG by 12 weeks was added to assess its impact on the risk of eGDM diagnosed in v2. Result: Overall, 89 (14.8%) women (age 32 ± 4 years) were diagnosed with eGDM by 24 weeks, of which 59 (9.8%) were diagnosed before 12 weeks and 30 of 541 (5.5%) women were diagnosed between 19–24 weeks. Two-thirds (66%) of eGDM were diagnosed before 12 weeks of gestation. Women's pre-pregnancy weight was positively associated with the risk of GDM in both time intervals though the lower confidence limit was below zero in v1. The rate of GWG by 12 weeks was not observed to be associated with the risk of eGDM diagnosed between 19–24 weeks of gestation. These associations were independent of age, height, and parity. Conclusion: Health workers may focus on pre-pregnancy weight, a modifiable risk factor for eGDM. A larger community-based study measuring weight and GDM status more frequently may be warranted to deepen the understanding of the role of GWG as a risk factor for GDM. [ABSTRACT FROM AUTHOR]

Abstract Background Failure time data frequently occur in many medical studies and often accompany with various types of censoring. In some applications, left truncation may occur and can induce biased sampling, which makes the practical data analysis become more complicated. The existing analysis methods for left-truncated data have some limitations in that they either focus only on a special type of censored data or fail to flexibly utilize the distribution information of the truncation times for inference. Therefore, it is essential to develop a reliable and efficient method for the analysis of left-truncated failure time data with various types of censoring. Method This paper concerns regression analysis of left-truncated failure time data with the proportional hazards model under various types of censoring mechanisms, including right censoring, interval censoring and a mixture of them. The proposed pairwise pseudo-likelihood estimation method is essentially built on a combination of the conditional likelihood and the pairwise likelihood that eliminates the nuisance truncation distribution function or avoids its estimation. To implement the presented method, a flexible EM algorithm is developed by utilizing the idea of self-consistent estimating equation. A main feature of the algorithm is that it involves closed-form estimators of the large-dimensional nuisance parameters and is thus computationally stable and reliable. In addition, an R package LTsurv is developed. Results The numerical results obtained from extensive simulation studies suggest that the proposed pairwise pseudo-likelihood method performs reasonably well in practical situations and is obviously more efficient than the conditional likelihood approach as expected. The analysis results of the MHCPS data with the proposed pairwise pseudo-likelihood method indicate that males have significantly higher risk of losing active life than females. In contrast, the conditional likelihood method recognizes this effect as non-significant, which is because the conditional likelihood method often loses some estimation efficiency compared with the proposed method. Conclusions The proposed method provides a general and helpful tool to conduct the Cox’s regression analysis of left-truncated failure time data under various types of censoring.

Abstract Unbiased mortality estimates are fundamental for testing ecological and evolutionary theory as well as for developing effective conservation actions. However, mortality estimates are often confounded by dispersal, especially in studies where dead‐recovery is not possible. In such instances, missing individuals (i.e. individuals with unobserved time of death) may have died or permanently emigrated from a study area, making inferences about their fate difficult. Mortality before and during dispersal, as well as the decision to disperse, usually depend on a suite of individual, social and environmental covariates, which in turn can be used to draw conclusions about the fate of missing individuals. Here, we propose a Bayesian hierarchical model that takes into account time‐varying covariates to estimate transitions between life‐history states and mortality in each state using mark‐resighting data with missing individuals. Specifically, our framework estimates mortality rates in two states (resident and dispersing state) by treating the fate of missing individuals as a latent (i.e. unobserved) variable that is statistically inferred based on information from individuals with a known fate and given the individual, social and environmental conditions at the time of disappearance. Our model also estimates rates of state transition (i.e. emigration) to assess whether a missing individual was more likely to have died or survived due to unobserved emigration from the study area. We used simulations to check the validity of our model and assessed its performance with data of varying degrees of uncertainty. Our modelling framework provided accurate mortality and emigration estimates for simulated data of different sample sizes, proportions of missing individuals, and resighting intervals. Variation in sample size appeared to affect the precision of estimated parameters the most. Our approach offers a solution to estimating unbiased mortality of both resident and dispersing individuals as well as the probability of emigration using mark‐resighting data with incomplete death records. Conditional on the availability of data on known‐fate individuals and relevant time‐varying covariates, our model can reconstruct the fate (death or emigration) of missing individuals. The modularity of our framework allows mortality analyses to be tailored to a variety of species‐specific life histories.

Interval-censored failure time data arise commonly in various scientific studies where the failure time of interest is only known to lie in a certain time interval rather than observed exactly. In addition, left truncation on the failure event may occur and can greatly complicate the statistical analysis. In this paper, we investigate regression analysis of left-truncated and interval-censored data with the commonly used additive hazards model. Specifically, we propose a conditional estimating equation approach for the estimation, and further improve its estimation efficiency by combining the conditional estimating equation and the pairwise pseudo-score-based estimating equation that can eliminate the nuisance functions from the marginal likelihood of the truncation times. Asymptotic properties of the proposed estimators are discussed including the consistency and asymptotic normality. Extensive simulation studies are conducted to evaluate the empirical performance of the proposed methods, and suggest that the combined estimating equation approach is obviously more efficient than the conditional estimating equation approach. We then apply the proposed methods to a set of real data for illustration. [ABSTRACT FROM AUTHOR]

Length‐biased data occur often in many scientific fields, including clinical trials, epidemiology surveys and genome‐wide association studies, and many methods have been proposed for their analysis under various situations. In this article, we consider the situation where one faces length‐biased and partly interval‐censored failure time data under the proportional hazards model, for which it does not seem to exist an established method. For the estimation, we propose an efficient nonparametric maximum likelihood method by incorporating the distribution information of the observed truncation times. For the implementation of the method, a flexible and stable EM algorithm via two‐stage data augmentation is developed. By employing the empirical process theory, we establish the asymptotic properties of the resulting estimators. A simulation study conducted to assess the finite‐sample performance of the proposed method suggests that it works well and is more efficient than the conditional likelihood approach. An application to an AIDS cohort study is also provided. [ABSTRACT FROM AUTHOR]

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 fracture risk. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

There are few computational and methodological tools available for the analysis of general multi-state models with interval censoring. Here, we propose a general framework for parametric inference with interval censored multi-state data. Our framework can accommodate any parametric model for the transition times, and covariates may be included in various ways. We present a general method for constructing the likelihood, which we have implemented in a ready-to-use R package, smms, available on GitHub. The R package also computes the required high-dimensional integrals in an efficient manner. Further, we explore connections between our modelling framework and existing approaches: our models fall under the class of semi-Markovian multi-state models, but with a different, and sparser parameterisation than what is often seen. We illustrate our framework through a dataset monitoring heart transplant patients. Finally, we investigate the effect of some forms of misspecification of the model assumptions through simulations. [ABSTRACT FROM AUTHOR]