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In prevalent cohort design, subjects who have experienced an initial event but not the failure event are preferentially enrolled and the observed failure times are often length-biased. Moreover, the prospective follow-up may not be continuously monitored and failure times are subject to interval censoring. We study the nonparametric maximum likelihood estimation for the proportional hazards model with length-biased interval-censored data. Direct maximization of likelihood function is intractable, thus we develop a computationally simple and stable expectation-maximization algorithm through introducing two layers of data augmentation. We establish the strong consistency, asymptotic normality and efficiency of the proposed estimator and provide an inferential procedure through profile likelihood. We assess the performance of the proposed methods through extensive simulations and apply the proposed methods to the Massachusetts Health Care Panel Study., (© 2018 Wiley Periodicals, Inc.)

Semi-competing risks data are often encountered in chronic disease follow-up studies that record both nonterminal events (e.g., disease landmark events) and terminal events (e.g., death). Studying the relationship between the nonterminal event and the terminal event can provide insightful information on disease progression. In this article, we propose a new sensible dependence measure tailored to addressing such an interest. We develop a nonparametric estimator, which is general enough to handle both independent right censoring and left truncation. Our strategy of connecting the new dependence measure with quantile regression enables a natural extension to adjust for covariates with minor additional assumptions imposed. We establish the asymptotic properties of the proposed estimators and develop inferences accordingly. Simulation studies suggest good finite-sample performance of the proposed methods. Our proposals are illustrated via an application to Denmark diabetes registry data., (© 2016, The International Biometric Society.)

Current status data are encountered in a wide range of applications, including tumorigenic experiments and demographic studies. In this case, each subject has one observation, and the only information obtained is whether the event of interest happened at the moment of observation. In addition to censoring, truncating is also very common in practice. This paper examines the regression analysis of current status data with informative censoring times, considering the presence of left truncation. In addition, we propose an inference approach based on sieve maximum likelihood estimation (SMLE). A copula-based approach is used to describe the relationship between the failure time of interest and the censoring time. The spline function is employed to approximate the unknown nonparametric function. We have established the asymptotic properties of the proposed estimator. Simulation studies suggest that the developed procedure works well in practice. We also applied the developed method to a real dataset derived from an AIDS cohort research. [ABSTRACT FROM AUTHOR]

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]

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 FROM AUTHOR]

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study. [ABSTRACT FROM AUTHOR]

Truncation is a statistical phenomenon that occurs in many time‐to‐event studies. For example, autopsy‐confirmed studies of neurodegenerative diseases are subject to an inherent left and right truncation, also known as double truncation. When the goal is to study the effect of risk factors on survival, the standard Cox regression model cannot be used when the survival time is subject to truncation. Existing methods that adjust for both left and right truncation in the Cox regression model require independence between the survival times and truncation times, which may not be a reasonable assumption in practice. We propose an expectation‐maximization algorithm to relax the independence assumption in the Cox regression model under left, right, or double truncation to an assumption of conditional independence on the observed covariates. The resulting regression coefficient estimators are consistent and asymptotically normal. We demonstrate through extensive simulations that the proposed estimator has little bias and has a similar or lower mean‐squared error compared to existing estimators. We implement our approach to assess the effect of occupation on survival in subjects with autopsy‐confirmed Alzheimer's disease. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Left truncation commonly occurs in many areas, and many methods have been proposed in the literature for the analysis of various types of left‐truncated failure time data. For the situation, a common approach is to conduct the analysis conditional on truncation times, and the method is relatively simple but may not be efficient. In this paper, we discuss regression analysis of such data arising from the proportional hazards model that also suffer interval censoring. For the problem, a pairwise pseudo‐likelihood approach is proposed that aims to recover some missing information in the conditional methods. The resulting estimator is shown to be consistent and asymptotically normal. A simulation study is conducted to assess the performance of the proposed method and suggests that it works well in practical situations and is indeed more efficient than the existing method. The approach is also applied to a set of real data arising from an AIDS cohort study. [ABSTRACT FROM AUTHOR]

Truncation is a mechanism that permits observation of selected subjects from a source population; subjects are excluded if their event times are not contained within subject-specific intervals. Standard survival analysis methods for estimation of the distribution of the event time require quasi-independence of failure and truncation. When quasi-independence does not hold, alternative estimation procedures are required; currently, there is a copula model approach that makes strong modeling assumptions, and a transformation model approach that does not allow for right censoring. We extend the transformation model approach to accommodate right censoring. We propose a regression diagnostic for assessment of model fit. We evaluate the proposed transformation model in simulations and apply it to the National Alzheimer's Coordinating Centers autopsy cohort study, and an AIDS incubation study. Our methods are publicly available in an R package, tranSurv. [ABSTRACT FROM AUTHOR]

Scheike and Zhang [An additive-multiplicative Cox-Aalen regression model. Scand J Stat. 2002;29:75–88] proposed a flexible additive-multiplicative hazard model, called the Cox-Aalen model, by replacing the baseline hazard function in the well-known Cox model with a covariate-dependent Aalen model, which allows for both fixed and dynamic covariate effects. In this paper, based on left-truncated and mixed interval-censored (LT-MIC) data, we consider maximum likelihood estimation for the Cox-Aalen model with fixed covariates. We propose expectation-maximization (EM) algorithms for obtaining the conditional maximum likelihood estimators (cMLE) of the regression coefficients for the Cox-Aalen model. We establish the consistency of the cMLE. Numerical studies show that estimation via the EM algorithms performs well. [ABSTRACT FROM AUTHOR]

We analyze left-truncated and right-censored (LTRC) data using an additive-multiplicative Cox-Aalen model proposed by Scheike and Zhang (2002), which extends the Cox regression model as well as the additive Aalen model. Based on the conditional likelihood function, we derive the weighted least-squared (WLS) estimators for the regression parameters and cumulative intensity functions of the model. The estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to investigate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

The hazard ratios resulting from a Cox's regression hazards model are hard to interpret and to be converted into prolonged survival time. As the main goal is often to study survival functions, there is increasing interest in summary measures based on the survival function that are easier to interpret than the hazard ratio; the residual mean time is an important example of those measures. However, because of the presence of right censoring, the tail of the survival distribution is often difficult to estimate correctly. Therefore, we consider the restricted residual mean time, which represents a partial area under the survival function, given any time horizon τ, and is interpreted as the residual life expectancy up to τ of a subject surviving up to time t. We present a class of regression models for this measure, based on weighted estimating equations and inverse probability of censoring weighted estimators to model potential right censoring. Furthermore, we show how to extend the models and the estimators to deal with delayed entries. We demonstrate that the restricted residual mean life estimator is equivalent to integrals of Kaplan-Meier estimates in the case of simple factor variables. Estimation performance is investigated by simulation studies. Using real data from Danish Monitoring Cardiovascular Risk Factor Surveys, we illustrate an application to additive regression models and discuss the general assumption of right censoring and left truncation being dependent on covariates. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For the past several decades, nonparametric and semiparametric modeling for conventional right-censored survival data has been investigated intensively under a noninformative censoring mechanism. However, these methods may not be applicable for analyzing right-censored survival data that arise from prevalent cohorts when the failure times are subject to length-biased sampling. This review article is intended to provide a summary of some newly developed methods as well as established methods for analyzing length-biased data. [ABSTRACT FROM AUTHOR]

Truncated data are commonly seen in studies of biomedicine, epidemiology, astronomy and econometrics. Existing regression methods for analyzing left-truncated and right-censored data have been developed under the assumption that the lifetime variable of interest is independent of both truncation and censoring variables. In this article, we propose a semiparametric accelerated failure time model that incorporates both covariates and the truncation variable as regressors. The proposed model utilizes the truncation information in statistical modeling and hence allows for dependent truncation. For estimation, we develop a set of estimating equations constructed from the log-rank and quasi-independence test statistics. We show that the resulting estimators are consistent and asymptotically normal. We also propose an explicit formula for variance estimation based on a kernel method. Finite-sample performances of the estimators are studied by simulations. The proposed methodology is applied to analyze a real data for illustration. [ABSTRACT FROM AUTHOR]

For a linear regression model subject to left-truncation and right-censoring where the truncation and censoring points are known constants (or always observed if random), Karlsson and Laitila (Stat Probab Lett 78:2567-2571, ) proposed a semiparametric estimator which deals with left-truncation by trimming and right-censoring by 'winsorizing'. The estimator was motivated by a zero moment condition where a transformed error term appears with trimmed and winsorized tails. This paper takes the semiparametric estimator further by deriving the asymptotic distribution that was not shown in Karlsson and Laitila (Stat Probab Lett 78:2567-2571, ) and discusses its implementation aspects in practice, albeit brief. [ABSTRACT FROM AUTHOR]

Semi-competing risks data frequently arise in biomedical studies when time to a disease landmark event is subject to dependent censoring by death, the observation of which however is not precluded by the occurrence of the landmark event. In observational studies, the analysis of such data can be further complicated by left truncation. In this work, we study a varying coefficient subdistribution regression model for left-truncated semi-competing risks data. Our method appropriately accounts for the specifical truncation and censoring features of the data, and moreover has the flexibility to accommodate potentially varying covariate effects. The proposed method can be easily implemented and the resulting estimators are shown to have nice asymptotic properties. We also present inference, such as Kolmogorov–Smirnov type and Cramér–Von-Mises type hypothesis testing procedures for the covariate effects. Simulation studies and an application to the Denmark diabetes registry demonstrate good finite-sample performance and practical utility of the proposed method. [ABSTRACT FROM AUTHOR]

Quantile regression methods have been used to estimate upper and lower quantile reference curves as the function of several covariates. In this article, it is demonstrated that the estimating equation of Zhou [A weighted quantile regression for randomly truncated data, Comput. Stat. Data Anal. 55 (2011), pp. 554–566.] can be extended to analyse left-truncated and right-censored data. We evaluate the finite sample performance of the proposed estimators through simulation studies. The proposed estimator βˆ(q) is applied to the Veteran's Administration lung cancer data reported by Prentice [Exponential survival with censoring and explanatory variables, Biometrika 60 (1973), pp. 279–288]. [ABSTRACT FROM AUTHOR]

This paper considers the estimation of the regression coefficients in the Cox proportional hazards model with left-truncated and interval-censored data. Using the approaches of Pan [A multiple imputation approach to Cox regression with interval-censored data, Biometrics 56 (2000), pp. 199–203] and Heller [Proportional hazards regression with interval censored data using an inverse probability weight, Lifetime Data Anal. 17 (2011), pp. 373–385], we propose two estimates of the regression coefficients. The first estimate is based on a multiple imputation methodology. The second estimate uses an inverse probability weight to select event time pairs where the ordering is unambiguous. A simulation study is conducted to investigate the performance of the proposed estimators. The proposed methods are illustrated using the Centers for Disease Control and Prevention (CDC) acquired immunodeficiency syndrome (AIDS) Blood Transfusion Data. [ABSTRACT FROM PUBLISHER]

In longitudinal studies, the additive hazard model is often used to analyze covariate effects on the duration time, defined as the elapsed time between the first and the second event. In this article, we consider the situation when the first event suffers partly interval censoring and the second event suffers left truncation and right-censoring. We proposed a two-step estimation procedure for estimating the regression coefficients of the additive hazards model. A simulation study is conducted to investigate the performance of the proposed estimator. The proposed method is applied to the Centers for Disease Control acquired immune deficiency syndrome blood transfusion data. [ABSTRACT FROM PUBLISHER]

Abstract: We study the problem of fitting a heteroscedastic median regression model from left-truncated and right-censored data. It is demonstrated that the adapted Efron''s self-consistency equation of can be extended to analyze left-truncated and right-censored data. We evaluate the finite sample performance of the proposed estimators through simulation studies. [Copyright &y& Elsevier]

We analyze left-truncated and right-censored (LTRC) data using semiparametric transformation models. It is demonstrated that the approach of Chen et al. (Biometrika 89: 659-668, ) can be extended to LTRC data. Furthermore, when covariates are discrete, similar to the approach of Cai and Cheng (Biometrika 91: 277-290, ), we propose an alternative estimator. A simulation study is conducted to investigate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Although many authors have proposed different approaches to the analysis of length-biased survival data, a number of issues have not been fully addressed. The most important among these issues is perhaps that regarding inclusion of covariates into the analysis of length-biased lifetime data collected through cross-sectional sampling of a population. One aspect of this problem, which appears to have been neglected in the literature, concerns the effect of length bias on the sampling distribution of the covariates. In most regression analyses, it is conventional to condition on the observed covariate values; however, certain covariate values could be preferentially selected into the sample, being linked to the long-term survivors, who themselves are favored by the sampling mechanism. This observation raises two questions: (1) Does the conditional analysis of covariates lead to biased estimators of regression coefficients?; and (2) does inference through the joint I likelihood of covariates and failure times yield more efficient estimators of the regression parameters? We present a joint likelihood approach and study the large-sample behavior of the resulting maximum likelihood estimators (MLEs). We find that these MLEs are more efficient than their conditional counterparts even though the two MLEs are asymptotically equal. Our results are illustrated using data on survival with dementia, collected as part of the Canadian Study of Health and Aging. [ABSTRACT FROM AUTHOR]

Satten et al. [Satten, G. A., Datta, S., Robins, J. M. (2001). Estimating the marginal survival function in the presence of time dependent covariates. Statis. Prob. Lett. 54: 397--403] proposed an estimator [denoted byŝ(t)] of survival function of failure times that is in the class of survival function estimators proposed by Robins [Robins, J. M. (1993). Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. In: Proceedings of the American Statistical Association-Biopharmaceutical Section. Alexandria, VA: ASA, pp. 24--33]. The estimator is appropriate when data are subject to dependent censoring. In this article, it is demonstrated that the estimatorŝ(t) can be extended to estimate the survival function when data are subject to dependent censoring and left truncation. In addition, we propose an alternative estimator of survival function [denoted byŝw(t)] that is represented as an inverse-probability-weighted average Satten and Datta [Satten, G. A., Datta, S. (2001). The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass. 55: 207--210]. Simulation results show that when truncation is not severe the mean squared error ofŝ(t) is smaller than that ofŝw(t), except for the case when censoring is light. However, when truncation is severe,ŝw(t) has the advantage of less bias and the situation can be reversed. [ABSTRACT FROM AUTHOR]

In this paper we consider nonparametric regression with left-truncated and right-censored data. An estimator of the regression function is developed when censoring and truncation are independent of covariates and the response. The estimation is based on the product limit estimator of the response variable. Under certain conditions, the L2 rate of convergence of the estimated regression function is obtained when tensor products of B-splines are used. [Copyright &y& Elsevier]

Retrospectively ascertained data are common in many areas, including demography, epidemiology, and actuarial science. The main objective of this article is to study the effect of retrospective ascertainment on inference regarding recurrent events of time to pregnancy (TTP) data. For the particular TTP dataset that we consider, couples are included retrospectively based on their first pregnancy and then followed prospectively to a second pregnancy or to end of study. We consider a conditional model for the recurrent events data where the second TTP is included only if it is observed and a full model where the nonobserved second TTPs are included as suitably right censored. We furthermore consider two different approaches to modeling the dependencies of the recurrent events. A traditional frailty model, where the frailty enters the model as an unobserved covariate, and a marginal frailty model are applied. We find that efficiency is gained from including the second TTPs, with the full model being the most efficient. Further, the marginal frailty model is preferred over the traditional frailty model because estimates of covariate effects are easier to interpret and are more robust to changes in the frailty distribution. [ABSTRACT FROM AUTHOR]

Background: Cohort-type data are increasingly used to compare health outcomes of immigrants between countries, e.g. to assess the effects of different national integration policies. In such international comparisons, small differences in cardiovascular diseases risk or mortality rates have been interpreted as showing effects of different policies. We conjecture that cohort-type data sets available for such comparisons might not provide unbiased relative risk estimates between countries because of differentials in migration patterns occurring before the cohorts are being observed.Method: Two simulation studies were performed to assess whether comparisons are biased if there are differences in 1. the way migrants arrived in the host countries, i.e. in a wave or continuously; 2. the effects on health of exposure to the host country; or 3., patterns of return-migration before a cohort is recruited. In the first simulation cardiovascular disease was the outcome and immortality in the second. Bias was evaluated using a Cox regression model adjusted for age and other dependant variables.Results: Comparing populations from wave vs. continuous migration may lead to bias only if the duration of stay has a dose-response effect (increase in simulated cardiovascular disease risk by 5% every 5 years vs. no risk: hazard-ratio 1.20(0.15); by 10% every 5 years: 1.47(0.14)). Differentials in return-migration patterns lead to bias in mortality rate ratios (MRR). The direction (under- or overestimation) and size of the bias depends on the model (MRR from 0.92(0.01) to 1.09(0.01)).Conclusion: The order of magnitude of the effects interpreted as due to integration policies in the literature is the same as the bias in our simulations. Future studies need to take into account duration and relevance of exposure and return-migration to make valid inferences about the effects of integration policies on the health of immigrants. [ABSTRACT FROM AUTHOR]