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Lee et al. in 2016 proposed a nonparametric estimator of the joint distribution of the gap time between transplant and the first infection and the following gap times between consecutive infections. In this article, we propose an alternative estimator based on the inverse-probability weighted (IPW) approach. Asymptotic properties of the proposed estimator are established. Simulation results indicate that the IPW estimator performs as well as the estimator proposed by Lee et al. We also propose an IPW estimator for estimating the joint distribution function of the gap times between consecutive recurrent events beyond the first episode. [ABSTRACT FROM AUTHOR]

In incident cohort studies, survival data often include subjects who have experienced an initiate event but have not experienced a subsequent event at the calendar time of recruitment. During the follow-up periods, subjects may undergo a series of successive events. Since the second/third duration process becomes observable only if the first/second event has occurred, the data are subject to left-truncation and dependent censoring. In this article, using the inverse-probability-weighted (IPW) approach, we propose nonparametric estimators for the estimation of the joint survival function of three successive duration times. The asymptotic properties of the proposed estimators are established. The simple bootstrapmethods are used to estimate standard deviations and construct interval estimators. A simulation study is conducted to investigate the finite sample properties of the proposed estimators. [ABSTRACT FROM AUTHOR]

Medical advancements have made it possible for patients to be cured of certain types of diseases. In follow-up studies, the disease event time can be subject to left truncation and interval censoring. In this article, we propose a semiparametric nonmixture cure model for the regression analysis of left-truncated and interval-censored (LTIC) data. We develop semiparametric maximum likelihood estimation for the nonmixture cure model with LTIC data. A simulation study is conducted to investigate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In transplant studies, the patients must survive long enough to receive a transplant, which induces left-truncation. The assumption of independence between failure and truncation times may not hold since a longer transplant waiting time can be associated with a worse survivorship. To take dependence into consideration, we utilize a semiparametric transformation model, where the truncation time is both a truncated variable and a predictor of the time to failure. Using the inverse-probability-weighted (IPW) approach, we propose an IPW estimator of the marginal distribution of waiting time. Simulation studies are conducted to investigate finite sample performance of the proposed estimator. We also apply our methods to bone marrow and heart transplant data. [ABSTRACT FROM PUBLISHER]

In this article, we propose estimating procedures for additive semiparametric transformation models with clustered doubly-censored data. A simulation study is conducted to investigate the performance of the proposed estimators. We apply the proposed methods to the dataset from the well-known Diabetic Retinopathy Study. [ABSTRACT FROM PUBLISHER]

For right-censored data, Subramanian (2001) proposed an estimatefor estimating regression parameter of “long-term” survival rate. In this article, we demonstrate that Subramanian’s estimator can be extended to left-truncated and right-censored data. When the covariate is discrete, we propose an alternative estimateand show that under logistic regression model,is asymptotically more efficient than. Based on, the chi-squared test statistic can be used for testing goodness of fit of logistic regression model. Furthermore, for a one-dimensional continuous covariate, we propose an estimatorby using a generalized product-limit estimator of conditional survival function (Iglesias-Prez and Gonzlez-Manteiga, 1999). A simulation study is conducted to investigate the performance of the proposed estimators. The proposed method is applied to the Vetran’s Administration lung cancer data reported by Prentice (1973). [ABSTRACT FROM AUTHOR]

Nonparametric estimates of the conditional distribution of a response variable given a covariate are important for data exploration purposes. In this article, we propose a nonparametric estimator of the conditional distribution function in the case where the response variable is subject to interval censoring and double truncation. Using the approach of Dehghan and Duchesne (2011), the proposed method consists in adding weights that depend on the covariate value in the self-consistency equation of Turnbull (1976), which results in a nonparametric estimator. We demonstrate by simulation that the estimator, bootstrap variance estimation and bandwidth selection all perform well in finite samples. [ABSTRACT FROM AUTHOR]

We analyze left-truncated and right-censored (LTRC) data using Aalen’s linear models. The integrated square error (ISE) is used to select an optimal bandwidth of the weighted least-squared estimator. We also consider a semiparametric approach for the case when the distribution of the left-truncated variable is parameterized. A simulation study is conducted to investigate the performance of the proposed estimators. The approaches are illustrated with the data of Stanford heart transplant. [ABSTRACT FROM AUTHOR]

Doubly truncated data play an important role in the statistical analysis of astronomical observations as well as in survival analysis. In this article, using inverse-probability-weighted (IPW) approaches, we derive the nonparametric maximum likelihood estimator (NPMLE) of joint distribution function with bivariate doubly truncated data. The asymptotic properties of the NPMLE are established. A simulation study is conducted to investigate the performance of the NPMLE. [ABSTRACT FROM PUBLISHER]

Cai and Zeng (2011) proposed an additive mixed effect model to analyze clustered right-censored data. In this article, we demonstrate that the approach of Cai and Zeng (2011) can be extended to clustered doubly censored data. Furthermore, when both left- and right-censoring variables are always observed, we propose alternative estimators using the approach of Cai and Cheng (2004). A simulation study is conducted to investigate the performance of the proposed estimators. [ABSTRACT FROM PUBLISHER]

In this article, we consider the M-estimators for the linear regression model when both response and covariate variables are subject to double censoring. The proposed estimators are constructed as some functional of three types of estimators for a bivariate survival distribution. The first two estimators are the generalizations of the Campbell and Földes (1982) and Dabrowska (1988) estimators proposed by Shen (2009). The third estimator is the generalization of the Prentice and Cai (1992) estimator. The consistency of the proposed M-estimators is established. A simulation study is conducted to investigate the performance of the proposed estimators. Furthermore, the simple bootstrap methods are used to estimate standard deviations and construct interval estimators. [ABSTRACT FROM AUTHOR]

In this article, we consider the estimation of distribution function for one modified form of current status data. An inverse-probability-weighted (IPW) estimator and a self-consistent estimator (SCE) are proposed. The asymptotic properties of the IPW estimator are derived. A simulation study is conducted to compare the performances among the IPW estimator, SCE, and the product-limit estimator proposed by Patilea and Rolin (2006). Simulation results indicate that when right censoring is light and left censoring is heavy, both IPW estimator and SCE can outperform the product-limit estimator. The performances of the IPW estimator and SCE are close to each other. [ABSTRACT FROM AUTHOR]

Double censoring arises when T represents an outcome variable that can only be accurately measured within a certain range, [L, U], where L and U are the left- and right-censoring variables, respectively. When L is always observed, we consider the empirical likelihood inference for linear transformation models, based on the martingale-type estimating equation proposed by Chen et al. (2002). It is demonstrated that both the approach of Lu and Liang (2006) and that of Yu et al. (2011) can be extended to doubly censored data. Simulation studies are conducted to investigate the performance of the empirical likelihood ratio methods. [ABSTRACT FROM PUBLISHER]

In this article, we consider estimating the bivariate distribution function when both components are subject to double censoring. Using an inverse-probability-weighted approach, we propose a self-consistent estimator. The asymptotic properties of the proposed estimator are derived. A simulation study is conducted to investigate the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

Consider the model φ(S(y | X)) = β(y) T X, where φ is a known link function, S(· | X) is the survival function of a response Y given a covariate X = (1, X, X 2,…, X p ), and β(y) is an unknown vector of time-dependent regression coefficients. The response Y is subject to left truncation and right censoring. We assume that given X, Y is independent of (C, T) where C and T are censoring and truncation variables with P(C ≥ T) = 1. In this article, with some modification of the assumptions in Lemmas 5 and 6 of Iglesias-Pérez and González-Manteiga (1999), we present an almost sure representation for the generalized product-limit estimator (GPL) of S(y | X). Based on the GPL and the approach of Teodorescu et al. (2010), a least squares estimator of β(y) is obtained and a bootstrap procedure is proposed to choose the optimum bandwidth. [ABSTRACT FROM PUBLISHER]

In many application, statistical data are frequently observed subject to a retrospective sampling criterion resulting in double-truncated data. For double-truncated data, the distribution of lifetime T is observable only when U ≤ T ≤ V, where U and V are the left-truncated and right-truncated time, respectively. Under the assumption of independence between T and (U, V), the nonparametric maximum likelihood estimate (NPMLE) of the distribution function of T (denoted by [image omitted] was developed by Efron and Petrosian (1999). For the special case V = U + d0, when the distribution of U is parameterized as G(x; θ) and F is left unspecified, a semiparametric MLE estimator of F (denoted by [image omitted] can be obtained using the arguments similar to those of Wang (1989). Further, we can obtain interval estimation for F using the bootstrap method (Qin and Wang, 2001) or the semiparametric likelihood ratio (SLR) method proposed by Li et al. (1997). In this article, a simulation study is conducted to compare the performance between [image omitted] and [image omitted]. Besides, the bootstrap and SLR methods are used to construct confidence intervals for F(t). Simulation results show that when G(x; θ) is correctly specified the semiparametric MLE [image omitted] outpeforms the NPMLE [image omitted] and the semiparametric bootstrap and SLR methods are more efficient than the nonparametric bootstrap method. [ABSTRACT FROM AUTHOR]

For bivariate lifetime data where both components are subject to left truncation and right censoring, Shen and Yan (2008) proposed two types of estimators as generalizations of Dabrowska and Campbell and Foldes estimators. In this note, we propose two alternative estimators, one is the generalization of the Prentice-Cai estimator, and the other is a linear combination of two expressions of Campbell and Foldes estimator. The consistency of the proposed estimators is established. A simulation study is conducted to investigate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

The complication in analyzing tumor data is that the tumors detected in a screening program tend to be slowly progressive tumors, which is the so-called length-biased sampling that is inherent in screening studies. Under the assumption that all subjects have the same tumor growth function, Ghosh (2008) developed estimation procedures for proportional hazards model. In this article, by modeling growth function as a function of covariates, we demonstrate that Ghosh (2008)'s approach can be extended to the case when each subject has a specific growth function. A simulation study is conducted to demonstrate the potential usefulness of the proposed estimators for the regression parameters in the proportional and additive hazards model. [ABSTRACT FROM AUTHOR]

In incident cohort studies, survival data often include subjects who have had an initiate event at recruitment and may potentially experience two successive events (first and second) during the follow-up period. Since the second duration process becomes observable only if the first event has occurred, left-truncation and dependent censoring arise if the two duration times are correlated. To confront the two potential sampling biases, Chang and Tzeng (2006) provided an inverse-probability-weighted (IPW) approach for estimating the joint probability function of successive duration times. In this note, an alternative IPW approach is proposed. A simulation study is conducted to compare the two IPW approaches. [ABSTRACT FROM AUTHOR]

In this article, we introduce a general class of statistics for testing the equality of two survival distribution for left-truncated and right-censored data. The class contains as special cases the extension of weighted Kaplan-Meier statistic by Pepe and Fleming (1989). The asymptotic distribution theory of the test is presented. The small-sample performance of the test is investigated under a variety of situations by means of Mone Carlo simulations. [ABSTRACT FROM AUTHOR]

In this article we consider estimating the bivariate survival function observations where one of the components is subject to left truncation and right censoring and the other is subject to right censoring only. Two types of nonparametric estimators are proposed. One is in the form of inverse-probability-weighted average (Satten and Datta, 2001) and the other is a generalization of Dabrowska's 1988 estimator. The two are then compared based on their empirical performances. [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]