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Landmarking is an alternative to complex multistate models when the aim is to calculate dynamic predictions. We develop the concept of landmarking for the case of left truncation and competing risks from the application background of drug safety assessment in pregnancy. The method is illustrated with a cohort study of the German Embryotox Pharmacovigilance Institute in Berlin to assess if the risk or the cumulative incidence of adverse pregnancy outcomes, like spontaneous abortions (SABs), is increased in fluoroquinolone‐exposed women. Furthermore, we conduct an extensive simulation study to compare the dynamic predictions and coefficient estimates obtained by landmarking to those from nonparametric multistate models and classical time‐dependent covariate Cox regression. The results from the simulation study indicate that attenuation of the effects is present in the landmark estimates, also in the complex setting considered here, but the estimates are still close to those from the multistate models. Regarding the Berlin fluoroquinolone data, the fluoroquinolone exposure of a pregnant woman in the first trimester seems to increase her cumulative incidence of elective termination of pregnancy over women never exposed before, but there is no evidence of a significantly increased risk or cumulative incidence in exposed women for SABs. This supports previous results on the same data, which were driven from an analysis without landmarking methods. [ABSTRACT FROM AUTHOR]

AbstractVariable selection is a fundamental tool to identify important factors from a large number of candidate covariates and has been successfully adopted in various fields. In survival analysis, developing variable selection techniques is often intractable since the failure times of interest are accompanied by censoring and other complex features, such as left truncation. Despite enormous variable selection methods for right-censored data, they seldom accommodate left truncation. In this work, for the left-truncated and right-censored data, we present a penalized composite likelihood approach to achieve variable selection and parameter estimation simultaneously in the proportional hazards model. To be specific, the composite likelihood is essentially a combination of the conditional likelihood and the pairwise likelihood that can properly take into account the marginal distribution of the observed truncation times. An explicit solution of the baseline hazard function is obtained through solving a series of self-consistent estimating equations. The sparse estimators of regression parameters under various classical penalty functions are calculated with a unified shooting algorithm. Simulation results indicate that the proposed method performs reasonably well and has some desirable advantages over the penalized conditional likelihood approach and the approach that ignores the presence of left truncation. An application to a set of left-truncated breast cancer data is also provided. [ABSTRACT FROM AUTHOR]

AbstractElectronic health records offer abundant data on various diseases and health conditions, enabling researchers to explore the relationship between disease onset age and underlying risk factors. Unlike mortality data, the event of interest is nonterminal, hence, individuals can retrospectively report their disease-onset-age upon recruitment to the study. These individuals, diagnosed with the disease before entering the study, are termed “prevalent.” The ascertainment imposes a left truncation condition, also known as a “delayed entry,” because individuals had to survive a certain period before being eligible for enrollment. The standard method to accommodate delayed entry conditions on the entire history up to recruitment, hence, the retrospective prevalent failure times are conditioned upon and cannot participate in estimating the disease-onset-age distribution. Other methods that condition on less information and allow the incorporation of the prevalent observations either bring about numerical and computational difficulties or require statistical assumptions that are violated by most biobanks. This work presents a novel estimator of the coefficients in a regression model for the age-at-onset, successfully using the prevalent data. Asymptotic results are provided, and simulations are conducted to showcase the substantial efficiency gain. In particular, the method is highly useful in leveraging large-scale repositories for replication analysis of genetic variants. Indeed, analysis of urinary bladder cancer data reveals that the proposed approach yields about twice as many replicated discoveries compared to the popular approach. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

An important task in health research is to characterize time-to-event outcomes such as disease onset or mortality in terms of a potentially high-dimensional set of risk factors. For example, prospective cohort studies of Alzheimer's disease (AD) typically enroll older adults for observation over several decades to assess the long-term impact of genetic and other factors on cognitive decline and mortality. The accelerated failure time model is particularly well-suited to such studies, structuring covariate effects as "horizontal" changes to the survival quantiles that conceptually reflect shifts in the outcome distribution due to lifelong exposures. However, this modeling task is complicated by the enrollment of adults at differing ages, and intermittent follow-up visits leading to interval-censored outcome information. Moreover, genetic and clinical risk factors are not only high-dimensional, but characterized by underlying grouping structures, such as by function or gene location. Such grouped high-dimensional covariates require shrinkage methods that directly acknowledge this structure to facilitate variable selection and estimation. In this paper, we address these considerations directly by proposing a Bayesian accelerated failure time model with a group-structured lasso penalty, designed for left-truncated and interval-censored time-to-event data. We develop an R package with a Markov chain Monte Carlo sampler for estimation. We present a simulation study examining the performance of this method relative to an ordinary lasso penalty and apply the proposed method to identify groups of predictive genetic and clinical risk factors for AD in the Religious Orders Study and Memory and Aging Project prospective cohort studies of AD and dementia. [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.

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]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

From the inventory of the health insurer AOK in 2004, we draw a sample of a quarter million people and follow each person's health claims continuously until 2013. Our aim is to estimate the effect of a stroke on the dementia onset probability for Germans born in the first half of the 20th century. People deceased before 2004 are randomly left-truncated, and especially their number is unknown. Filtrations, modelling the missing data, enable circumventing the unknown number of truncated persons by using a conditional likelihood. Dementia onset after 2013 is a fixed right-censoring event. For each observed health history, Jacod's formula yields its conditional likelihood contribution. Asymptotic normality of the estimated intensities is derived, related to a sample size definition including the number of truncated people. The standard error results from the asymptotic normality and is easily computable, despite the unknown sample size. The claims data reveal that after a stroke, with time measured in years, the intensity of dementia onset increases from 0.02 to 0.07. Using the independence of the two estimated intensities, a 95% confidence interval for their difference is [0.053, 0.057]. The effect halves when we extend the analysis to an age-inhomogeneous model, but does not change further when we additionally adjust for multi-morbidity. [ABSTRACT FROM AUTHOR]

Many African nations continue to grapple with persistently high under-five child mortality rates, particularly those situated in the Sub-Saharan region, including South Africa. A multitude of socio-economic factors are identified as key contributors to the elevated under-five child mortality in numerous African nations. This research endeavors to investigate various factors believed to be associated with child mortality by employing advanced statistical models. This study utilizes child-level survival data from South Africa, characterized by left truncation and right censoring, to fit a Cox proportional hazards model under the assumption of working independence. Additionally, a shared frailty model is applied, clustering children based on their mothers. Comparative analysis is performed between the results obtained from the shared frailty model and the Cox proportional hazards model under the assumption of working independence. Within the scope of this analysis, several factors stand out as significant contributors to under-five child mortality in the study area, including gender, birth province, birth year, birth order, and twin status. Notably, the shared frailty model demonstrates superior performance in modeling the dataset, as evidenced by a lower likelihood cross-validation score compared to the Cox proportional hazards model assuming independence. This improvement can be attributed to the shared frailty model’s ability to account for heterogeneity among mothers and the inherent association between siblings born to the same mother, ultimately enhancing the quality of the study’s conclusions.

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards model. The principal advantage of the proposed model is that it does not depend on restrictive parametric assumptions while being flexible and data‐driven. Likelihood inference for the model is developed. Through detailed simulation studies, the robustness property of the model is studied by fitting it to LTRC data generated from different processes covering a wide range of lifetime distributions. A sensitivity analysis is also carried out by fitting the model to LTRC data generated from a process with a piecewise constant baseline hazard. It is observed that the performance of the model is quite satisfactory in all those cases. Analyses of two real LTRC datasets by using the model are provided as illustrative examples. Applications of the model in some practical prediction issues are discussed. In summary, the proposed model provides a comprehensive and flexible approach to model a general structure for LTRC lifetime data. [ABSTRACT FROM AUTHOR]

Purpose: In analyzing pregnancy data concerning drug exposure in the first trimester, the risk of spontaneous abortions is of primary interest. For estimating the cumulative incidence function, the Aalen–Johansen estimator is typically used, and competing risks such as induced abortion and livebirth are considered. However, the delayed study entry can lead to overly small risk sets for the first events. This results in large jumps in the estimated cumulative incidence function of spontaneous abortions or induced abortions using the Aalen–Johansen estimator, and consequently in an overestimation of the probability. Methods: Several approaches account for early overly small risk sets. The first approach is conditioning on the event time being greater than the event time causing the large jump. Second, the events can be ignored by censoring them. Third, the events can be postponed until a large enough number is at risk. These three approaches are compared. Results: All approaches are applied using data of 54 lacosamide‐exposed pregnancies. The Aalen–Johansen estimate of the probability of spontaneous abortion is 22.64%, which is relatively large for only three spontaneous abortions in the dataset. The conditional approach and the ignore approach have an estimated probability of 7.17%. In contrast, the estimate of the postpone approach is 16.45%. In this small sample, bootstrapped confidence intervals seem more accurate. Conclusions: In the analyses of pregnancy data with rare events, the postpone approach is favorable as no events are excluded. However, the approach that ignores early events has the narrowest confidence interval. [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]

Many African nations continue to grapple with persistently high under-five child mortality rates, particularly those situated in the Sub-Saharan region, including South Africa. A multitude of socio-economic factors are identified as key contributors to the elevated under-five child mortality in numerous African nations. This research endeavors to investigate various factors believed to be associated with child mortality by employing advanced statistical models. This study utilizes child-level survival data from South Africa, characterized by left truncation and right censoring, to fit a Cox proportional hazards model under the assumption of working independence. Additionally, a shared frailty model is applied, clustering children based on their mothers. Comparative analysis is performed between the results obtained from the shared frailty model and the Cox proportional hazards model under the assumption of working independence. Within the scope of this analysis, several factors stand out as significant contributors to under-five child mortality in the study area, including gender, birth province, birth year, birth order, and twin status. Notably, the shared frailty model demonstrates superior performance in modeling the dataset, as evidenced by a lower likelihood cross-validation score compared to the Cox proportional hazards model assuming independence. This improvement can be attributed to the shared frailty model's ability to account for heterogeneity among mothers and the inherent association between siblings born to the same mother, ultimately enhancing the quality of the study's conclusions. [ABSTRACT FROM AUTHOR]

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. [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]

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]

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]

The analysis of left truncated and right censored data is very common in survival and reliability analysis. In lifetime studies patients are often subject to left truncation in addition to right censoring. For example, in bone marrow transplant studies based on International Bone Marrow Transplant Registry (IBMTR), the patients who die while waiting for the transplants will not be reported to the IBMTR. In this paper, we develop novel U-statistics under left truncation and right censoring. We prove the n -consistency of the proposed U-statistics. We derive the asymptotic distribution of the U-statistics using the counting process technique. As an application of the U-statistics, we develop a simple non-parametric test for testing the independence between time to failure and cause of failure in competing risks when the observations are subject to left truncation and right censoring. The finite sample performance of the proposed test is evaluated through a Monte Carlo simulation study. Finally, we illustrate our test procedure using the lifetime data of transformers. [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.

A platform trial is a trial involving an innovative adaptive design with a single master protocol to efficiently evaluate multiple interventions. It offers flexible features such as dropping interventions for futility and adding new interventions to be evaluated during the course of a trial. Although there is a consensus that platform trials can identify beneficial interventions with fewer patients, less time, and a higher probability of success than traditional trials, there remains debate on certain issues, one of which is whether (and how) the non-concurrent control (NCC) (i.e., patients in the control group recruited prior to the new interventions) can be combined with the current control (CC) in the analysis, especially if there is a change of standard of care during the trial. Methods: In this paper, considering time-to-event endpoints under the proportional hazard model assumption, we introduce a new concept of NCC concurrent observation time (NCC COT), and propose to borrow NCC COT through left truncation. This assumes that the NCC COT and CC are comparable. If the protocol does not prohibit NCC patients to change the standard of care while on study, NCC COT and CC likely will share the same standard of care. A simulated example is provided to demonstrate the approach. Results: Using exponential distributions, the simulated example assumes that NCC COT and CC have the same hazard, and the treatment group has a lower hazard. The estimated HR comparing treatment to the pooled control group is 0.744 (95% CI 0.575, 0.962), whereas the comparison to the CC group alone is 0.755 (95% CI 0.566, 1.008), with corresponding p-values of 0.024 versus 0.057, respectively. This suggests that borrowing NCC COT can improve statistical efficiency when the exchangeability assumption holds. Conclusion: This article proposes an innovative approach of borrowing NCC COT to enhance statistical inference in platform trials under appropriate scenarios.

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]

Background: Cancer survival is an important indicator for evaluating cancer prognosis and cancer care outcomes. The incidence dates used in calculating survival differ between population-based registries and hospital-based registries. Studies examining the effects of the left truncation of incidence dates and delayed reporting on survival estimates are scarce in real-world applications. Methods: Cancer cases hospitalized at Nantong Tumor Hospital during the years 2002-2017 were traced with their records registered in the Qidong Cancer Registry. Survival was calculated using the life table method for cancer patients with the first visit dates recorded in the hospital-based cancer registry (HBR) as the diagnosis date (OSH), those with the registered dates of population-based cancer (PBR) registered as the incidence date (OSP), and those with corrected dates when the delayed report dates were calibrated (OSC). Results: Among 2,636 cases, 1,307 had incidence dates registered in PBR prior to the diagnosis dates of the first hospitalization registered in HBR, while 667 cases with incidence dates registered in PBR were later than the diagnosis dates registered in HBR. The 5-year OSH, OSP, and OSC were 36.1%, 37.4%, and 39.0%, respectively. The "lost" proportion of 5-year survival due to the left truncation for HBR data was estimated to be between 3.5% and 7.4%, and the "delayed-report" proportion of 5-year survival for PBR data was found to be 4.1%. Conclusion: Left truncation of survival in HBR cases was demonstrated. The pseudo-left truncation in PBR should be reduced by controlling delayed reporting and maximizing completeness. Our study provides practical references and suggestions for evaluating the survival of cancer patients with HBR and PBR. [ABSTRACT FROM AUTHOR]

Unmeasured baseline information in left-truncated data situations frequently occurs in observational time-to-event analyses. For instance, a typical timescale in trials of antidiabetic treatment is "time since treatment initiation", but individuals may have initiated treatment before the start of longitudinal data collection. When the focus is on baseline effects, one widespread approach is to fit a Cox proportional hazards model incorporating the measurements at delayed study entry. This has been criticized because of the potential time dependency of covariates. We tackle this problem by using a Bayesian joint model that combines a mixed-effects model for the longitudinal trajectory with a proportional hazards model for the event of interest incorporating the baseline covariate, possibly unmeasured in the presence of left truncation. The novelty is that our procedure is not used to account for non-continuously monitored longitudinal covariates in right-censored time-to-event studies, but to utilize these trajectories to make inferences about missing baseline measurements in left-truncated data. Simulating times-to-event depending on baseline covariates we also compared our proposal to a simpler two-stage approach which performed favorably. Our approach is illustrated by investigating the impact of baseline blood glucose levels on antidiabetic treatment failure using data from a German diabetes register. [ABSTRACT FROM AUTHOR]

Female sex in patients with atrial fibrillation (AF) is a controversial and paradoxical risk factor for stroke—controversial because it increases the risk of stroke only among older women of some ethnicities and paradoxical because it appears to contradict male predominance in cardiovascular diseases. However, the underlying mechanism remains unclear. We conducted simulations to examine the hypothesis that this sex difference is generated non-causally through left truncation due to competing risks (CR) such as coronary artery diseases, which occur more frequently among men than among women and share common unobserved causes with stroke. We modeled the hazards of stroke and CR with correlated heterogeneous risk. We assumed that some people died of CR before AF diagnosis and calculated the hazard ratio of female sex in the left-truncated AF population. In this situation, female sex became a risk factor for stroke in the absence of causal roles. The hazard ratio was attenuated in young populations without left truncation and in populations with low CR and high stroke incidence, which is consistent with real-world observations. This study demonstrated that spurious risk factors can be identified through left truncation due to correlated CR. Female sex in patients with AF may be a paradoxical risk factor for stroke. [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]

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status. [ABSTRACT FROM AUTHOR]

A platform trial is a trial involving an innovative adaptive design with a single master protocol to efficiently evaluate multiple interventions. It offers flexible features such as dropping interventions for futility and adding new interventions to be evaluated during the course of a trial. Although there is a consensus that platform trials can identify beneficial interventions with fewer patients, less time, and a higher probability of success than traditional trials, there remains debate on certain issues, one of which is whether (and how) the non-concurrent control (NCC) (i.e., patients in the control group recruited prior to the new interventions) can be combined with the current control (CC) in the analysis, especially if there is a change of standard of care during the trial. Methods: In this paper, considering time-to-event endpoints under the proportional hazard model assumption, we introduce a new concept of NCC concurrent observation time (NCC COT), and propose to borrow NCC COT through left truncation. This assumes that the NCC COT and CC are comparable. If the protocol does not prohibit NCC patients to change the standard of care while on study, NCC COT and CC likely will share the same standard of care. A simulated example is provided to demonstrate the approach. Results: Using exponential distributions, the simulated example assumes that NCC COT and CC have the same hazard, and the treatment group has a lower hazard. The estimated HR comparing treatment to the pooled control group is 0.744 (95% CI 0.575, 0.962), whereas the comparison to the CC group alone is 0.755 (95% CI 0.566, 1.008), with corresponding p-values of 0.024 versus 0.057, respectively. This suggests that borrowing NCC COT can improve statistical efficiency when the exchangeability assumption holds. Conclusion: This article proposes an innovative approach of borrowing NCC COT to enhance statistical inference in platform trials under appropriate scenarios. [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]

Time‐to‐event data such as time to death are broadly used in medical research and drug development to understand the efficacy of a therapeutic. For time‐to‐event data, right censoring (data only observed up to a certain point of time) is common and easy to recognize. Methods that use right censored data, such as the Kaplan–Meier estimator and the Cox proportional hazard model, are well established. Time‐to‐event data can also be left truncated, which arises when patients are excluded from the sample because their events occur before a specific milestone, potentially resulting in an immortal time bias. For example, in a study evaluating the association between biomarker status and overall survival, patients who did not live long enough to receive a genomic test were not observed in the study. Left truncation causes selection bias and often leads to an overestimate of survival time. In this tutorial, we used a nationwide electronic health record‐derived de‐identified database to demonstrate how to analyze left truncated and right censored data without bias using example code from SAS and R. [ABSTRACT FROM AUTHOR]

Vaginal implant transmitters (VITs) are a popular tool in ungulate parturition studies and have been used in moose (Alces alces), but their potential impact on animal performance has not been thoroughly assessed. We looked at potential short‐term impacts of VIT use on maternal condition through assessments of neonate calf mass, early calf survival, and parturition date. We also assessed long‐term impacts of VIT use on future reproduction and the inflammatory response after prolonged VIT retention through qualifying discharge at VIT removal and measures of acute phase proteins haptoglobin and ceruloplasmin. We captured 54 neonates and assessed over 900 potential parturition events of 278 adult moose over multiple years and we did not detect any evidence of a negative impact of VIT use on neonate calf mass, parturition date, or future reproduction. We did find elevated haptoglobin and ceruloplasmin levels in non‐pregnant individuals that had unintentional VIT retention past parturition, but this was not universal across all cases. We found a potential negative impact of VIT use on early calf survival which was likely driven by biased sampling. A bias can exist (i.e., left truncation) if sampling is mixed between cows that had a VIT (and, therefore, a known parturition time) and those without a VIT that were sampled opportunistically. Future evaluations need to overcome this bias when assessing early calf survival. With that caveat, we did not detect clear negative impacts of VIT use on moose and recommend late winter to early spring VIT insertion in pregnant females to minimize retention time. [ABSTRACT FROM AUTHOR]

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.

Databases derived from electronic health records (EHRs) are commonly subject to left truncation, a type of selection bias that occurs when patients need to survive long enough to satisfy certain entry criteria. Standard methods to adjust for left truncation bias rely on an assumption of marginal independence between entry and survival times, which may not always be satisfied in practice. In this work, we examine how a weaker assumption of conditional independence can result in unbiased estimation of common statistical parameters. In particular, we show the estimability of conditional parameters in a truncated dataset, and of marginal parameters that leverage reference data containing non‐truncated data on confounders. The latter is complementary to observational causal inference methodology applied to real‐world external comparators, which is a common use case for real‐world databases. We implement our proposed methods in simulation studies, demonstrating unbiased estimation and valid statistical inference. We also illustrate estimation of a survival distribution under conditionally independent left truncation in a real‐world clinico‐genomic database. [ABSTRACT FROM AUTHOR]

Excess hazard modelling is one of the main tools in population‐based cancer survival research. Indeed, this setting allows for direct modelling of the survival due to cancer even in the absence of reliable information on the cause of death, which is common in population‐based cancer epidemiology studies. We propose a unifying link‐based additive modelling framework for the excess hazard that allows for the inclusion of many types of covariate effects, including spatial and time‐dependent effects, using any type of smoother, such as thin plate, cubic splines, tensor products and Markov random fields. In addition, this framework accounts for all types of censoring as well as left truncation. Estimation is conducted by using an efficient and stable penalized likelihood‐based algorithm whose empirical performance is evaluated through extensive simulation studies. Some theoretical and asymptotic results are discussed. Two case studies are presented using population‐based cancer data from patients diagnosed with breast (female), colon and lung cancers in England. The results support the presence of non‐linear and time‐dependent effects as well as spatial variation. The proposed approach is available in the R package GJRM. [ABSTRACT FROM AUTHOR]

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.

Objectives Restriction to the analysis of births that survive past a specified gestational age (typically 20 weeks gestation) can lead to biased exposure-outcome associations. The objective is to estimate the influence of bias resulting from using a left truncated dataset to ascertain exposure-outcome associations in perinatal studies. Approach We simulated the magnitude of bias under a collider-stratification mechanism for the association between the exposure of advancing maternal age (≥ 35 years) and the outcome of stillbirth. This bias occurs when the cause of restriction (early pregnancy loss) is influenced by both the exposure and unmeasured factors that also affect the outcome. Simulation parameters were based on an original birth cohort from Western Australia and a range of plausible values for the prevalence of early pregnancy loss (< 20 gestational weeks), an unmeasured factor U and the odds ratios for the selection effects. Selection effects included the effects of maternal age on early pregnancy loss, U on early pregnancy loss, and U on stillbirth. We then compared the simulated scenarios with the results from the original cohort in which bias was unadjusted. Results We found the overall magnitude of bias to be minimal in the association between advancing maternal age and stillbirth. The findings indicate that the stronger the effect of the unmeasured U on early pregnancy loss and stillbirth, the greater the departure from the null. When we compared the simulated model with the results of the original cohort, we found evidence of marginal downward bias which was most prominent for women aged 40+ years. Discussion Our simulations demonstrated a marginal downward bias in the association between advancing maternal age and stillbirth. We recommend that future studies should quantify the extent of such bias when using left truncated birth datasets to determine exposure-outcome associations.

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]

In this article, we consider nonparametric estimation of the cumulative incidence function (CIF) for left-truncated and interval-censored competing risks (LT-ICC) data. To reduce the bias of the pseudo-likelihood estimator (PLE) of CIF in the literature, we proposed two alternative estimators. The first estimator, called the modified PLE (MPLE), is obtained based on the modified NPMLE of F(t). The second estimator, called the modified maximum likelihood estimator (MMLE), is derived using modified likelihood functions for LT-ICC data, where the left endpoints of the intervals for left-censored observations with failure type j are the maximum of left-truncated variables and the estimated left endpoint of the support of the observations. Simulation studies show that the MPLE and MMLE are less biased than the PLE for most of the cases considered and their standard deviations are significantly smaller than that of the PLE. [ABSTRACT FROM AUTHOR]

Lifetime risk measures the cumulative risk for developing a disease over one's lifespan. Modeling the lifetime risk must account for left truncation, the competing risk of death, and inference at a fixed age. In addition, statistical methods to predict the lifetime risk should account for covariate-outcome associations that change with age. In this paper, we review and compare statistical methods to predict the lifetime risk. We first consider a generalized linear model for the lifetime risk using pseudo-observations of the Aalen-Johansen estimator at a fixed age, allowing for left truncation. We also consider modeling the subdistribution hazard with Fine-Gray and Royston-Parmar flexible parametric models in left truncated data with time-covariate interactions, and using these models to predict lifetime risk. In simulation studies, we found the pseudo-observation approach had the least bias, particularly in settings with crossing or converging cumulative incidence curves. We illustrate our method by modeling the lifetime risk of atrial fibrillation in the Framingham Heart Study. We provide technical guidance to replicate all analyses in R. [ABSTRACT FROM AUTHOR]

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.)

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]

In epidemiology, left-truncated data may bias exposure effect estimates. We analyzed the bias induced by left truncation in estimating breast cancer risk associated with exposure to airborne dioxins. Simulations were run with exposure estimates from a Geographic Information System (GIS)-based metric and considered two hypotheses for historical exposure, three scenarios for intra-individual correlation of annual exposures, and three exposure-effect models. For each correlation/model combination, 500 nested matched case–control studies were simulated and data fitted using a conditional logistic regression model. Bias magnitude was assessed by estimated odds-ratios (ORs) versus theoretical relative risks (TRRs) comparisons. With strong intra-individual correlation and continuous exposure, left truncation overestimated the Beta parameter associated with cumulative dioxin exposure. Versus a theoretical Beta of 4.17, the estimated mean Beta (5%; 95%) was 73.2 (67.7; 78.8) with left-truncated exposure and 4.37 (4.05; 4.66) with lifetime exposure. With exposure categorized in quintiles, the TRR was 2.0, the estimated ORQ5 vs. Q1 2.19 (2.04; 2.33) with truncated exposure versus 2.17 (2.02; 2.32) with lifetime exposure. However, the difference in exposure between Q5 and Q1 was 18× smaller with truncated data, indicating an important overestimation of the dose effect. No intra-individual correlation resulted in effect dilution and statistical power loss. Left truncation induced substantial bias in estimating breast cancer risk associated with exposure with continuous and categorical models. With strong intra-individual exposure correlation, both models detected associations, but categorical models provided better estimates of effect trends. This calls for careful consideration of left truncation-induced bias in interpreting environmental epidemiological data. [ABSTRACT FROM AUTHOR]

Typically, case-control studies to estimate odds-ratios associating risk factors with disease incidence only include newly diagnosed cases. Recently proposed methods allow incorporating information on prevalent cases, individuals who survived from disease diagnosis to sampling, into cross-sectionally sampled case-control studies under parametric assumptions for the survival time after diagnosis. Here we propose and study methods to additionally use prospectively observed survival times fromprevalent and incident cases to adjust logistic models for the time between diagnosis and sampling, the backward time, for prevalent cases. This adjustment yields unbiased odds-ratio estimates from case-control studies that include prevalent cases.We propose a computationally simple two-step generalized method-of-moments estimation procedure. First, we estimate the survival distribution assuming a semiparametric Cox model using an expectation-maximization algorithm that yields fully efficient estimates and accommodates left truncation for prevalent cases and right censoring. Then, we use the estimated survival distribution in an extension of the logistic model to three groups (controls, incident, and prevalent cases), to adjust for the survival bias in prevalent cases. In simulations, under modest amounts of censoring, odds-ratios from the two-step procedure were equally efficient as those estimated from a joint logistic and survival data likelihood under parametric assumptions. This indicates that utilizing the cases' prospective survival data lessens model dependencies and improves precision of association estimates for case-control studies with prevalent cases. We illustrate the methods by estimating associations between single nucleotide polymorphisms and breast cancer risk using controls, and incident and prevalent cases sampled from the US Radiologic Technologists Study cohort. [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]