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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]

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]

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, samples are often selected at a later time, which results in delayed entry so that only individuals who have not yet experienced the terminal event will be included. In joint frailty models such left truncation has effects on the frailty distribution that need to be accounted for in both the recurrence process and the terminal event process, if the two are associated. We demonstrate, in a comprehensive simulation study, the effects that not adjusting for late entry can have and derive the correctly adjusted marginal likelihood, which can be expressed as a ratio of two integrals over the frailty distribution. We extend the estimation method of Liu and Huang (Stat Med 27:2665–2683, 2008. https://doi.org/10.1002/sim.3077) to include potential left truncation. Numerical integration is performed by Gaussian quadrature, the baseline intensities are specified as piecewise constant functions, potential covariates are assumed to have multiplicative effects on the intensities. We apply the method to estimate age-specific intensities of recurrent urinary tract infections and mortality in an older population. [ABSTRACT FROM AUTHOR]

Period-prevalent cohorts are often used for their cost-saving potential in epidemiological studies of survival outcomes. Under this design, prevalent patients allow for evaluations of long-term survival outcomes without the need for long follow-up, whereas incident patients allow for evaluations of short-term survival outcomes without the issue of left-truncation. In most period-prevalent survival analyses from the existing literature, patients have been recruited to achieve an overall sample size, with little attention given to the relative frequencies of prevalent and incident patients and their statistical implications. Furthermore, there are no existing methods available to rigorously quantify the impact of these relative frequencies on estimation and inference and incorporate this information into study design strategies. To address these gaps, we develop an approach to identify the optimal mix of prevalent and incident patients that maximizes precision over the entire estimated survival curve, subject to a flexible weighting scheme. In addition, we prove that inference based on the weighted log-rank test or Cox proportional hazards model is most powerful with an entirely prevalent or incident cohort, and we derive theoretical formulas to determine the optimal choice. Simulations confirm the validity of the proposed optimization criteria and show that substantial efficiency gains can be achieved by recruiting the optimal mix of prevalent and incident patients. The proposed methods are applied to assess waitlist outcomes among kidney transplant candidates., (© 2024. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

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]

It is well known that the nonparametric maximum likelihood estimator (NPMLE) can severely underestimate the survival probabilities at early times for left-truncated and interval-censored (LT-IC) data. For arbitrarily truncated and censored data, Pan and Chappel (JAMA Stat Probab Lett 38:49-57, 1998a, Biometrics 54:1053-1060, 1998b) proposed a nonparametric estimator of the survival function, called the iterative Nelson estimator (INE). Their simulation study showed that the INE performed well in overcoming the under-estimation of the survival function from the NPMLE for LT-IC data. In this article, we revisit the problem of inconsistency of the NPMLE. We point out that the inconsistency is caused by the likelihood function of the left-censored observations, where the left-truncated variables are used as the left endpoints of censoring intervals. This can lead to severe underestimation of the survival function if the NPMLE is obtained using Turnbull's (JAMA 38:290-295, 1976) EM algorithm. To overcome this problem, we propose a modified maximum likelihood estimator (MMLE) based on a modified likelihood function, where the left endpoints of censoring intervals for left-censored observations are the maximum of left-truncated variables and the estimated left endpoint of the support of the left-censored times. Simulation studies show that the MMLE performs well for finite sample and outperforms both the INE and NPMLE. [ABSTRACT FROM AUTHOR]

A semi-competing risks setting often arises in biomedical studies, involving both a nonterminal event and a terminal event. Cross quantile residual ratio (Yang and Peng in Biometrics 72:770-779, 2016) offers a flexible and robust perspective to study the dependency between the nonterminal and the terminal events which can shed useful scientific insight. In this paper, we propose a new nonparametric estimator of this dependence measure with left truncated semi-competing risks data. The new estimator overcomes the limitation of the existing estimator that is resulted from demanding a strong assumption on the truncation mechanism. We establish the asymptotic properties of the proposed estimator and develop inference procedures accordingly. Simulation studies suggest good finite-sample performance of the proposed method. Our proposal is illustrated via an application to Denmark diabetes registry data. [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]

There has been considerable interest in studying the magnitude and type of inheritance of specific diseases. This is typically derived from family or twin studies, where the basic idea is to compare the correlation for different pairs that share different amount of genes. We here consider data from the Danish twin registry and discuss how to define heritability for cancer occurrence. The key point is that this should be done taking censoring as well as competing risks due to e.g. death into account. We describe the dependence between twins on the probability scale and show that various models can be used to achieve sensible estimates of the dependence within monozygotic and dizygotic twin pairs that may vary over time. These dependence measures can subsequently be decomposed into a genetic and environmental component using random effects models. We here present several novel models that in essence describe the association in terms of the concordance probability, i.e., the probability that both twins experience the event, in the competing risks setting. We also discuss how to deal with the left truncation present in the Nordic twin registries, due to sampling only of twin pairs where both twins are alive at the initiation of the registries. [ABSTRACT FROM AUTHOR]

The cross-ratio is an important local measure that characterizes the dependence between bivariate failure times. To estimate the cross-ratio in follow-up studies where delayed entry is present, estimation procedures need to account for left truncation. Ignoring left truncation yields biased estimates of the cross-ratio. We extend the method of Hu et al., Biometrika 98:341-354 () by modifying the risk sets and relevant indicators to handle left-truncated bivariate failure times, which yields the cross-ratio estimate with desirable asymptotic properties that can be shown by the same techniques used in Hu et al., Biometrika 98:341-354 (). Numerical studies are conducted. [ABSTRACT FROM AUTHOR]