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In life history analysis of data from cohort studies, it is important to address the process by which participants are identified and selected. Many health studies select or enrol individuals based on whether they have experienced certain health related events, for example, disease diagnosis or some complication from disease. Standard methods of analysis rely on assumptions concerning the independence of selection and a person's prospective life history process, given their prior history. Violations of such assumptions are common, however, and can bias estimation of process features. This has implications for the internal and external validity of cohort studies, and for the transportabilty of results to a population. In this paper, we study failure time analysis by proposing a joint model for the cohort selection process and the failure process of interest. This allows us to address both independence assumptions and the transportability of study results. It is shown that transportability cannot be guaranteed in the absence of auxiliary information on the population. Conditions that produce dependent selection and types of auxiliary data are discussed and illustrated in numerical studies. The proposed framework is applied to a study of the risk of psoriatic arthritis in persons with psoriasis., (© The authors 2024. Published by Oxford University Press.)

An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome. For example, the accelerated failure time (AFT) model structures each covariate effect as a constant multiplicative shift in the outcome distribution across all survival quantiles. Though parsimonious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model. To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model. Specifically, we embed flexible regression structures within the AFT model and derive a novel formula for interpretable effects on the quantile scale. A regression standardization scheme based on the g-formula is proposed to enable the estimation of both covariate-conditional and marginal effects for an exposure of interest. We implement a user-friendly Bayesian approach for the estimation and quantification of uncertainty while accounting for left truncation and complex censoring. We emphasize the intuitive interpretation of this model through numerical and graphical tools and illustrate its performance through simulation and application to a study of Alzheimer's disease and dementia., (© The Author 2023. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

It has become consensus that mild cognitive impairment (MCI), one of the early symptoms onset of Alzheimer's disease (AD), may appear 10 or more years after the emergence of neuropathological abnormalities. Therefore, understanding the progression of AD biomarkers and uncovering when brain alterations begin in the preclinical stage, while patients are still cognitively normal, are crucial for effective early detection and therapeutic development. In this paper, we develop a Bayesian semiparametric framework that jointly models the longitudinal trajectory of the AD biomarker with a changepoint relative to the occurrence of symptoms onset, which is subject to left truncation and right censoring, in a heterogeneous population. Furthermore, unlike most existing methods assuming that everyone in the considered population will eventually develop the disease, our approach accounts for the possibility that some individuals may never experience MCI or AD, even after a long follow-up time. We evaluate the proposed model through simulation studies and demonstrate its clinical utility by examining an important AD biomarker, ptau181, using a dataset from the Biomarkers of Cognitive Decline Among Normal Individuals (BIOCARD) study., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

Background: Shorter average lifespans for minoritized populations are hypothesized to stem from 'weathering' or accelerated health declines among minoritized individuals due to systemic marginalization. However, evidence is mixed on whether racial/ethnic differences exist in reproductive ageing, potentially due to selection biases in cohort studies that may systematically exclude 'weathered' participants. This study examines racial/ethnic disparities in the age of menopause after accounting for differential selection 'into' (left truncation) and 'out of' (right censoring) a cohort of midlife women., Methods: Using data from the Study of Women's Health Across the Nation (SWAN) cross-sectional screener (N = 15 695) and accompanying ∼20-year longitudinal cohort (N = 3302) (1995-2016), we adjusted for potential selection bias using inverse probability weighting (left truncation) to account for socio-demographic/health differences between the screening and cohort study, and multiple imputation (right censoring) to estimate racial/ethnic differences in age at menopause (natural and surgical)., Results: Unadjusted for selection, no Black/White differences in menopausal timing [hazard ratio (HR)=0.98 (0.86, 1.11)] were observed. After adjustment, Black women had an earlier natural [HR = 1.13 (1.00, 1.26)] and surgical [HR= 3.21 (2.80, 3.62)] menopause than White women with natural menopause-corresponding to a 1.2-year Black/White difference in menopause timing overall., Conclusions: Failure to account for multiple forms of selection bias masked racial/ethnic disparities in the timing of menopause in SWAN. Results suggest that there may be racial differences in age at menopause and that selection particularly affected the estimated menopausal age for women who experienced earlier menopause. Cohorts should consider incorporating methods to account for all selection biases, including left truncation, as they impact our understanding of health in 'weathered' populations., (© The Author(s) 2023; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association.)

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., (© 2022 The International Biometric Society.)

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., (© 2021 The International Biometric Society.)

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., (© 2020 The International Biometric Society.)

A time to event, [Formula: see text], is left-truncated by [Formula: see text] if [Formula: see text] can be observed only if [Formula: see text]. This often results in oversampling of large values of [Formula: see text], and necessitates adjustment of estimation procedures to avoid bias. Simple risk-set adjustments can be made to standard risk-set-based estimators to accommodate left truncation when [Formula: see text] and [Formula: see text] are quasi-independent. We derive a weaker factorization condition for the conditional distribution of [Formula: see text] given [Formula: see text] in the observable region that permits risk-set adjustment for estimation of the distribution of [Formula: see text], but not of the distribution of [Formula: see text]. Quasi-independence results when the analogous factorization condition for [Formula: see text] given [Formula: see text] holds also, in which case the distributions of [Formula: see text] and [Formula: see text] are easily estimated. While we can test for factorization, if the test does not reject, we cannot identify which factorization condition holds, or whether quasi-independence holds. Hence we require an unverifiable assumption in order to estimate the distribution of [Formula: see text] or [Formula: see text] based on truncated data. This contrasts with the common understanding that truncation is different from censoring in requiring no unverifiable assumptions for estimation. We illustrate these concepts through a simulation of left-truncated and right-censored data.

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.)

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs)., (© 2018, The International Biometric Society.)

Evaluating and understanding the risk and safety of using medications for autoimmune disease in a woman during her pregnancy will help both clinicians and pregnant women to make better treatment decisions. However, utilizing spontaneous abortion (SAB) data collected in observational studies of pregnancy to derive valid inference poses two major challenges. First, the data from the observational cohort are not random samples of the target population due to the sampling mechanism. Pregnant women with early SAB are more likely to be excluded from the cohort, and there may be substantial differences between the observed SAB time and those in the target population. Second, the observed data are heterogeneous and contain a "cured" proportion. In this article, we consider semiparametric models to simultaneously estimate the probability of being cured and the distribution of time to SAB for the uncured subgroup. To derive the maximum likelihood estimators, we appropriately adjust the sampling bias in the likelihood function and develop an expectation-maximization algorithm to overcome the computational challenge. We apply the empirical process theory to prove the consistency and asymptotic normality of the estimators. We examine the finite sample performance of the proposed estimators in simulation studies and illustrate the proposed method through an application to SAB data from pregnant women., (© The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Recurrent events together with longitudinal measurements are commonly observed in follow-up studies where the observation is terminated by censoring or a primary failure event. In this article, we developed a joint model where the dependence of longitudinal measurements, recurrent event process and time to failure event is modeled through rescaling the time index. The general idea is that the trajectories of all biology processes of subjects in the survivors' population are elongated or shortened by the rate identified from a model for the failure event. To avoid making disputing assumptions on recurrent events or biomarkers after the failure event (such as death), the model is constructed on the basis of survivors' population. The model also possesses a specific feature that, by aligning failure events as time origins, the backward-in-time model of recurrent events and longitudinal measurements shares the same parameter values with the forward time model. The statistical properties, simulation studies and real data examples are conducted. The proposed method can be generalized to analyze left-truncated data., (© 2017, The International Biometric Society.)

In the standard analysis of competing risks data, proportional hazards models are fit to the cause-specific hazard functions for all causes on the same time scale. These regression analyses are the foundation for predictions of cause-specific cumulative incidence functions based on combining the estimated cause-specific hazard functions. However, in predictions arising from disease registries, where only subjects with disease enter the database, disease-related mortality may be more naturally modeled on the time since diagnosis time scale while death from other causes may be more naturally modeled on the age time scale. The single time scale methodology may be biased if an incorrect time scale is employed for one of the causes and an alternative methodology is not available. We propose inferences for the cumulative incidence function in which regression models for the cause-specific hazard functions may be specified on different time scales. Using the disease registry data, the analysis of other cause mortality on the age scale requires left truncating the event time at the age of disease diagnosis, complicating the analysis. In addition, standard Martingale theory is not applicable when combining regression models on different time scales. We establish that the covariate conditional predictions are consistent and asymptotically normal using empirical process techniques and propose consistent variance estimators for constructing confidence intervals. Simulation studies show that the proposed two time scales method performs well, outperforming the single time-scale predictions when the time scale is misspecified. The methods are illustrated with stage III colon cancer data obtained from the Surveillance, Epidemiology, and End Results program of National Cancer Institute., (© The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

To shed light on the etiology of metabolic syndrome development, it is important to understand whether its 5 component disorders follow certain onset sequences. To explore disease progression of the syndrome, we studied the ages at onset of 5 cardiometabolic diseases: abdominal obesity, diabetes, hypertension, hypertriglyceridemia, and hypo-α-lipoproteinemia. In analyzing longitudinal data from the Cardiovascular Disease Risk Factors Two-Township Study (1989-2002) in Taiwan, we adjusted for nonsusceptibility, utilizing the logistic-accelerated failure time location-scale mixture regression models for left-truncated and interval-censored data to simultaneously estimate the associations of township and sex with the susceptibility probability and the age-at-onset distribution of susceptible individuals for each disease. We then validated the onset sequences of 5 cardiometabolic diseases by comparing the overall probability density curves across township-sex strata. Visualization of these curves indicates that women tended to have onsets of abdominal obesity and hypo-α-lipoproteinemia in young adulthood, hypertension and hypertriglyceridemia in middle age, and diabetes later; men tended to have onsets of abdominal obesity, hypo-α-lipoproteinemia, and hypertriglyceridemia in young adulthood, hypertension in middle age, and diabetes later. Different onset patterns of abdominal obesity, hypo-α-lipoproteinemia, and male hypertension were identified between townships. Our proposed method provides a novel strategy for investigating both pathogenesis and preventive measures of complex syndromes., (© The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

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.)

Analyses of observational data aimed at supporting decision-making are ideally framed as a contrast between well-defined treatment strategies. These analyses compare individuals' outcomes from the start of the treatment strategies under consideration. Exceptions to this synchronizing of the start of follow-up and the treatment strategies may be justified on a case-by-case basis., (© The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

The idea that epidemiologic studies should start from first exposure onward has been advocated in the past few years. The study of incident exposures is contrasted with studies of prevalent exposures in which follow-up may commence after first exposure. The former approach is seen as a hallmark of a good study and necessary for causal inference. We argue that studying incident exposures may be necessary in some situations, but it is not always necessary and is not the preferred option in many instances. Conducting a study involves decisions as to which person-time experience should be included. Although studies of prevalent exposures involve left truncation (missingness on the left), studies of incident exposures may involve right censoring (missingness on the right) and therefore may not be able to assess the long-term effects of exposure. These considerations have consequences for studies of dynamic (open) populations that involve a mixture of prevalent and incident exposures. We argue that studies with prevalent exposures will remain a necessity for epidemiology. The purpose of this paper is to restore the balance between the emphasis on first exposure cohorts and the richness of epidemiologic information obtained when studying prevalent exposures., (© The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.)