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Background: Patients with peripheral artery disease face high amputation and mortality risk. When assessing vascular outcomes, consideration of mortality as a competing risk is not routine. We hypothesize standard time-to-event methods will overestimate major amputation risk in chronic limb-threatening ischemia (CLTI) and non-CLTI. Methods: Patients undergoing peripheral vascular intervention from 2017 to 2018 were abstracted from the Vascular Quality Initiative registry and stratified by mean age (⩾ 75 vs < 75 years). Mortality and amputation data were obtained from Medicare claims. The 2-year cumulative incidence function (CIF) and risk of major amputation from standard time-to-event analysis (1 - Kaplan-Meier and Cox regression) were compared with competing risk analysis (Aalen-Johansen and Fine-Gray model) in CLTI and non-CLTI. Results: A total of 7273 patients with CLTI and 5095 with non-CLTI were included. At 2-year follow up, 13.1% of patients underwent major amputation and 33.4% died without major amputation in the CLTI cohort; 1.3% and 10.7%, respectively, in the non-CLTI cohort. In CLTI, standard time-to-event analysis overestimated the 2-year CIF of major amputation by 20.5% and 13.7%, respectively, in patients ⩾ 75 and < 75 years old compared with competing risk analysis. The standard Cox regression overestimated adjusted 2-year major amputation risk in patients ⩾ 75 versus < 75 years old by 7.0%. In non-CLTI, the CIF was overestimated by 7.1% in patients ⩾ 75 years, and the adjusted risk was overestimated by 5.1% compared with competing risk analysis. Conclusions: Standard time-to-event analysis overestimates the incidence and risk of major amputation, especially in CLTI. Competing risk analyses are alternative approaches to estimate accurately amputation risk in vascular outcomes research.

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Prior distributions, which represent one's belief in the distributions of unknown parameters before observing the data, impact Bayesian inference in a critical and fundamental way. With the ability to incorporate external information from expert opinions or historical datasets, the priors, if specified appropriately, can improve the statistical efficiency of Bayesian inference. In survival analysis, based on the concept of unit information (UI) under parametric models, we propose the unit information Dirichlet process (UIDP) as a new class of nonparametric priors for the underlying distribution of time-to-event data. By deriving the Fisher information in terms of the differential of the cumulative hazard function, the UIDP prior is formulated to match its prior UI with the weighted average of UI in historical datasets and thus can utilize both parametric and nonparametric information provided by historical datasets. With a Markov chain Monte Carlo algorithm, simulations and real data analysis demonstrate that the UIDP prior can adaptively borrow historical information and improve statistical efficiency in survival analysis.

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Forecasting mortality rates is crucial for evaluating life insurance company solvency, especially amid disruptions caused by phenomena like COVID-19. The Lee-Carter model is commonly employed in mortality modelling; however, extensions that can encompass count data with diverse distributions, such as the Generalized Autoregressive Score (GAS) model utilizing the COM-Poisson distribution, exhibit potential for enhancing time-to-event forecasting accuracy. Using mortality data from 29 countries, this research evaluates various distributions and determines that the COM-Poisson model surpasses the Poisson, binomial, and negative binomial distributions in forecasting mortality rates. The one-step forecasting capability of the GAS model offers distinct advantages, while the COM-Poisson distribution demonstrates enhanced flexibility and versatility by accommodating various distributions, including Poisson and negative binomial. Ultimately, the study determines that the COM-Poisson GAS model is an effective instrument for examining time series data on mortality rates, particularly when facing time-varying parameters and non-conventional data distributions.

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Traditional two-arm randomized trial designs have played a pivotal role in establishing the efficacy of medical interventions. However, their efficiency is often compromised when confronted with multiple experimental treatments or limited resources. In response to these challenges, the multi-arm multi-stage designs have emerged, enabling the simultaneous evaluation of multiple treatments within a single trial. In such an approach, if an arm meets efficacy success criteria at an interim stage, the whole trial stops and the arm is selected for further study. However when multiple treatment arms are active, stopping the trial at the moment one arm achieves success diminishes the probability of selecting the best arm. To address this issue, we have developed a group sequential multi-arm multi-stage survival trial design with an arm-specific stopping rule. The proposed method controls the familywise type I error in a strong sense and selects the best promising treatment arm with a high probability.

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INTRODUCTION: Past studies suggested that Parkinson's disease (PD) patients who engage in physical activity (PA) after diagnosis have slower motor progression. Here, we examine the influence of lifetime PA prior to PD onset on motor, cognitive, and overall functional decline among PD patients. METHODS: For 495 participants in the Parkinson's Environment and Gene (PEG) studies, we collected PA-related measures through interviews and quantified these using metabolic equivalents (MET) scores. PD progression was defined as time to a Unified Parkinson's Disease Rating Scale Part III (UPDRS-III) conversion to ≥ 35 points, Hoehn and Yahr (H&Y) ≥ 3, and a 4-point decline in Mini-Mental State Examination (MMSE). We used Cox frailty models to estimate hazard ratios and inverse probability weights to account for heterogeneity by enrollment wave and censoring. RESULTS: For PD patients reporting the highest lifetime strenuous MET-h/wk (highest quartile), we estimated a lower HR for time-to-UPDRS-III-conversion (Q4 vs. Q1: HR = 0.56, 95 % CI = [0.36, 0.87]). Additionally, having engaged in any competitive sport also reduced the risk of reaching a UPDRS-III ≥ 35 points (low vs. none: HR = 0.61, 95 % CI = [0.44, 0.86]; high vs. none: HR = 0.63; 95 % CI = [0.44,0.86]); high levels of sports activities also affected progression on the H&Y scale (high vs. none: HR = 0.73; 95 % CI = [0.46,1.00]). Lifetime PA measures did not affect time-to-MMSE decline. CONCLUSION: Our study suggests that PD patients who engaged in higher levels of lifetime strenuous PA and competitive sports prior to PD diagnosis experience slower motor and overall functional decline, suggesting that lifetime PA may contribute to a physical reserve advantageous for PD patients.

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Composite endpoints defined as the time to the earliest of two or more events are often used as primary endpoints in clinical trials. Component-wise censoring arises when different components of the composite endpoint are censored differently. We focus on a composite of death and a non-fatal event where death time is right censored and the non-fatal event time is interval censored because the event can only be detected during study visits. Such data are most often analysed using methods for right censored data, treating the time the non-fatal event was first detected as the time it occurred. This can lead to bias, particularly when the time between assessments is long. We describe several approaches for estimating the event-free survival curve and the effect of treatment on event-free survival via the hazard ratio that are specifically designed to handle component-wise censoring. We apply the methods to a randomized study of breastfeeding versus formula feeding for infants of mothers infected with human immunodeficiency virus.

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A clinical trial represents a large commitment from all individuals involved and a huge financial obligation given its high cost; therefore, it is wise to make the most of all collected data by learning as much as possible. A multistate model is a generalized framework to describe longitudinal events; multistate hazards models can treat multiple intermediate/final clinical endpoints as outcomes and estimate the impact of covariates simultaneously. Proportional hazards models are fitted (one per transition), which can be used to calculate the absolute risks, that is, the probability of being in a state at a given time, the expected number of visits to a state, and the expected amount of time spent in a state. Three publicly available clinical trial datasets, colon, myeloid, and rhDNase, in the survival package in R were used to showcase the utility of multistate hazards models. In the colon dataset, a very well-known and well-used dataset, we found that the levamisole+fluorouracil treatment extended time in the recurrence-free state more than it extended overall survival, which resulted in less time in the recurrence state, an example of the classic "compression of morbidity." In the myeloid dataset, we found that complete response (CR) is durable, patients who received treatment B have longer sojourn time in CR than patients who received treatment A, while the mutation status does not impact the transition rate to CR but is highly influential on the sojourn time in CR. We also found that more patients in treatment A received transplants without CR, and more patients in treatment B received transplants after CR. In addition, the mutation status is highly influential on the CR to transplant transition rate. The observations that we made on these three datasets would not be possible without multistate models. We want to encourage readers to spend more time to look deeper into clinical trial data. It has a lot more to offer than a simple yes/no answer if only we, the statisticians, are willing to look for it.

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Time-to-event prediction is a key task for biological discovery, experimental medicine, and clinical care. This is particularly true for neurological diseases where development of reliable biomarkers is often limited by difficulty visualising and sampling relevant cell and molecular pathobiology. To date, much work has relied on Cox regression because of ease-of-use, despite evidence that this model includes incorrect assumptions. We have implemented a set of deep learning and spline models for time-to-event modelling within a fully customizable 'app' and accompanying online portal, both of which can be used for any time-to-event analysis in any disease by a non-expert user. Our online portal includes capacity for end-users including patients, Neurology clinicians, and researchers, to access and perform predictions using a trained model, and to contribute new data for model improvement, all within a data-secure environment. We demonstrate a pipeline for use of our app with three use-cases including imputation of missing data, hyperparameter tuning, model training and independent validation. We show that predictions are optimal for use in downstream applications such as genetic discovery, biomarker interpretation, and personalised choice of medication. We demonstrate the efficiency of an ensemble configuration, including focused training of a deep learning model. We have optimised a pipeline for imputation of missing data in combination with time-to-event prediction models. Overall, we provide a powerful and accessible tool to develop, access and share time-to-event prediction models; all software and tutorials are available at www.predictte.org.

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Stochastic curtailment tests for Phase II two-arm trials with time-to-event end points are traditionally performed using the log-rank test. Recent advances in designing time-to-event trials have utilized the Weibull distribution with a known shape parameter estimated from historical studies. As sample size calculations depend on the value of this shape parameter, these methods either cannot be used or likely underperform/overperform when the natural variation around the point estimate is ignored. We demonstrate that when the magnitude of the Weibull shape parameters changes, unblinded interim information on the shape of the survival curves can be useful to enrich the final analysis for reestimation of the sample size. For such scenarios, we propose two Bayesian solutions to estimate the natural variations of the Weibull shape parameter. We implement these approaches under the framework of the newly proposed relative time method that allows nonproportional hazards and nonproportional time. We also demonstrate the sample size reestimation for the relative time method using three different approaches (internal pilot study approach, conditional power, and predictive power approach) at the interim stage of the trial. We demonstrate our methods using a hypothetical example and provide insights regarding the practical constraints for the proposed methods.

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Early adolescent drinking onset is linked to myriad negative consequences. Using the National Consortium on Alcohol and NeuroDevelopment in Adolescence (NCANDA) baseline to year 8 data, this study (1) leveraged best subsets selection and Cox Proportional Hazards regressions to identify the most robust predictors of adolescent first and regular drinking onset, and (2) examined the clinical utility of drinking onset in forecasting later binge drinking and withdrawal effects. Baseline predictors included youth psychodevelopmental characteristics, cognition, brain structure, family, peer, and neighborhood domains. Participants (N=538) were alcohol-naïve at baseline. The strongest predictors of first and regular drinking onset were positive alcohol expectancies (Hazard Ratios [HRs]=1.67-1.87), easy home alcohol access (HRs=1.62-1.67), more parental solicitation (e.g., inquiring about activities; HRs=1.72-1.76), and less parental control and knowledge (HRs=.72-.73). Robust linear regressions showed earlier first and regular drinking onset predicted earlier transition into binge and regular binge drinking (ßs=0.57-0.95). Zero-inflated Poisson regressions revealed that delayed first and regular drinking increased the likelihood (Incidence Rate Ratios [IRR]=1.62 and IRR=1.29, respectively) of never experiencing withdrawal. Findings identified behavioral and environmental factors predicting temporal paths to youthful drinking, dissociated first from regular drinking initiation, and revealed adverse sequelae of younger drinking initiation, supporting efforts to delay drinking onset.

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Survival analysis (also referred to as time-to-event analysis) is the study of the time elapsed from a starting date to some event of interest. In practice, these analyses can be challenging and, if methodological errors are to be avoided, require the application of appropriate techniques. By using simulations and real-life data based on the French national registry of patients with primary immunodeficiencies (CEREDIH), we sought to highlight the basic elements that need to be handled correctly when performing the initial steps in a survival analysis. We focused on non-parametric methods to deal with right censoring, left truncation, competing risks, and recurrent events. Our simulations show that ignoring these aspects induces a bias in the results; we then explain how to analyze the data correctly in these situations using non-parametric methods. Rare disease registries are extremely valuable in medical research. We discuss the application of appropriate methods for the analysis of time-to-event from the CEREDIH registry. The objective of this tutorial article is to provide clinicians and healthcare professionals with better knowledge of the issues facing them when analyzing time-to-event data.

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Random survival forests (RSF) can be applied to many time-to-event research questions and are particularly useful in situations where the relationship between the independent variables and the event of interest is rather complex. However, in many clinical settings, the occurrence of the event of interest is affected by competing events, which means that a patient can experience an outcome other than the event of interest. Neglecting the competing event (i.e., regarding competing events as censoring) will typically result in biased estimates of the cumulative incidence function (CIF). A popular approach for competing events is Fine and Gray's subdistribution hazard model, which directly estimates the CIF by fitting a single-event model defined on a subdistribution timescale. Here, we integrate concepts from the subdistribution hazard modeling approach into the RSF. We develop several imputation strategies that use weights as in a discrete-time subdistribution hazard model to impute censoring times in cases where a competing event is observed. Our simulations show that the CIF is well estimated if the imputation already takes place outside the forest on the overall dataset. Especially in settings with a low rate of the event of interest or a high censoring rate, competing events must not be neglected, that is, treated as censoring. When applied to a real-world epidemiological dataset on chronic kidney disease, the imputation approach resulted in highly plausible predictor-response relationships and CIF estimates of renal events.

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OBJECTIVE: To investigate the association between oral contraceptive (OC) pill use and the risk of developing multiple sclerosis (MS), attempting to address the limitations present in previous studies that produced conflicting results. DESIGN: A population-based cohort study using data from the UK Biobank. PATIENTS: The study included 181,058 women of white ethnicity born in England between 1937 and 1970, among which 1,131 had an MS diagnosis. INTERVENTION: Oral contraceptive use, considering the self-reported age of initiation and discontinuation. The exposures of interest include the following: ever-use, current use, duration of current use in years, and age and year at initiation. MAIN OUTCOME MEASURES: Multiple sclerosis diagnosis (International Classification of Disease, 10th revision: G35) was used as an outcome of interest, and the associations with the exposures of interest were investigated using marginal structural models with a time-to-event approach. To adjust for confounding, we included in the models several variables, including MS polygenic risk score, education level, parity, smoking, fertility problems, obesity, and mononucleosis. We further aimed to evaluate the influence of parity using a mediation analysis. RESULTS: The association of both ever and current OC use did not result in a statistically significant MS hazard increase (ever vs. never-users, hazard ratio [HR] = 1.30 [95% confidence interval {CI}: 0.93,1.82]; current vs. never-users, HR = 1.35 [95% CI: 0.81, 2.25]). However, we highlighted parity as an effect modifier for this association. In nulliparous women, ever and current use resulted in a significant twofold and threefold MS hazard increase (HR = 2.08 [95% CI: 1.04, 4.17] and HR = 3.15 [95% CI: 1.43, 6.9]). These associations were supported by significant MS hazard increases for a higher duration of current use and for an earlier age at initiation. We further highlighted genetic MS susceptibility as another effect modifier, as a stronger OC-MS hazard association was found in women with a low MS polygenic risk score. CONCLUSION: Our findings highlighted how the association between OC use and MS varies on the basis of individual characteristics such as parity and genetic MS susceptibility. Importantly, current use in nulliparous women was found to be associated with a threefold increase in MS hazard. We acknowledge the need for cautious causal interpretation and further research to validate these findings across diverse populations and OC types.

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Graft failure and recipient death with functioning graft are important competing outcomes after kidney transplantation. Risk prediction models typically censor for the competing outcome thereby overestimating the cumulative incidence. The magnitude of this overestimation is not well described in real-world transplant data. This retrospective cohort study analyzed data from the European Collaborative Transplant Study (n = 125 250) and from the American Scientific Registry of Transplant Recipients (n = 190 258). Separate cause-specific hazard models using donor and recipient age as continuous predictors were developed for graft failure and recipient death. The hazard of graft failure increased quadratically with increasing donor age and decreased decaying with increasing recipient age. The hazard of recipient death increased linearly with increasing donor and recipient age. The cumulative incidence overestimation due to competing risk-censoring was largest in high-risk populations for both outcomes (old donors/recipients), sometimes amounting to 8.4 and 18.8 percentage points for graft failure and recipient death, respectively. In our illustrative model for posttransplant risk prediction, the absolute risk of graft failure and death is overestimated when censoring for the competing event, mainly in older donors and recipients. Prediction models for absolute risks should treat graft failure and death as competing events.

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Delayed sputum conversion has been associated with a higher risk of treatment failure or relapse among drug susceptible smear-positive pulmonary tuberculosis patients. Several contributing factors have been identified in many studies, but the results varied across regions and countries. Therefore, the current study aimed to develop a predictive model that explained the factors affecting time to sputum conversion within two months after initiating antituberculosis agents among Malaysian with drug-susceptible smear-positive pulmonary tuberculosis patients. Retrospective data of pulmonary tuberculosis patients followed up at a tertiary hospital in the Northern region of Malaysia from 2013 until 2018 were collected and analysed. Nonlinear mixed-effect modelling software (NONMEM 7.3.0) was used to develop parametric survival models. The final model was further validated using Kaplan-Meier-visual predictive check (KM-VPC) approach, kernel-based hazard rate estimation method and sampling-importance resampling (SIR) method. A total of 224 patients were included in the study, with 34.4 % (77/224) of the patients remained positive at the end of 2 months of the intensive phase. Gompertz hazard function best described the data. The hazard of sputum conversion decreased by 39 % and 33 % for moderate and advanced lesions as compared to minimal baseline of chest X-ray severity, respectively (adjusted hazard ratio (aHR), 0.61; 95 % confidence intervals (95 % CI), (0.44-0.84) and 0.67, 95 % CI (0.53-0.84)). Meanwhile, the hazard also decreased by 59 % (aHR, 0.41; 95 % CI, (0.23-0.73)) and 48 % (aHR, 0.52; 95 % CI, (0.35-0.79)) between active and former drug abusers as compared to non-drug abuser, respectively. The successful development of the internally and externally validated final model allows a better estimation of the time to sputum conversion and provides a better understanding of the relationship with its predictors.

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Many clinical trials assess time-to-event endpoints. To describe the difference between groups in terms of time to event, we often employ hazard ratios. However, the hazard ratio is only informative in the case of proportional hazards (PHs) over time. There exist many other effect measures that do not require PHs. One of them is the average hazard ratio (AHR). Its core idea is to utilize a time-dependent weighting function that accounts for time variation. Though propagated in methodological research papers, the AHR is rarely used in practice. To facilitate its application, we unfold approaches for sample size calculation of an AHR test. We assess the reliability of the sample size calculation by extensive simulation studies covering various survival and censoring distributions with proportional as well as nonproportional hazards (N-PHs). The findings suggest that a simulation-based sample size calculation approach can be useful for designing clinical trials with N-PHs. Using the AHR can result in increased statistical power to detect differences between groups with more efficient sample sizes.

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Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffers from biased estimation. Therefore, we propose the multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from nonconjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.

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Spatial scan statistics are well-known methods widely used to detect spatial clusters of events. Furthermore, several spatial scan statistics models have been applied to the spatial analysis of time-to-event data. However, these models do not take account of potential correlations between the observations of individuals within the same spatial unit or potential spatial dependence between spatial units. To overcome this problem, we have developed a scan statistic based on a Cox model with shared frailty and that takes account of the spatial dependence between spatial units. In simulation studies, we found that (i) conventional models of spatial scan statistics for time-to-event data fail to maintain the type I error in the presence of a correlation between the observations of individuals within the same spatial unit and (ii) our model performed well in the presence of such correlation and spatial dependence. We have applied our method to epidemiological data and the detection of spatial clusters of mortality in patients with end-stage renal disease in northern France.

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Preeclampsia is a pregnancy-associated condition posing risks of both fetal and maternal mortality and morbidity that can only resolve following delivery and removal of the placenta. Because in its typical form preeclampsia can arise before delivery, but not after, these two events exemplify the time-to-event setting of "semi-competing risks" in which a non-terminal event of interest is subject to the occurrence of a terminal event of interest. The semi-competing risks framework presents a valuable opportunity to simultaneously address two clinically meaningful risk modeling tasks: (i) characterizing risk of developing preeclampsia, and (ii) characterizing time to delivery after onset of preeclampsia. However, some people with preeclampsia deliver immediately upon diagnosis, while others are admitted and monitored for an extended period before giving birth, resulting in two distinct trajectories following the non-terminal event, which we call "clinically immediate" and "non-immediate" terminal events. Though such phenomena arise in many clinical contexts, to-date there have not been methods developed to acknowledge the complex dependencies between such outcomes, nor leverage these phenomena to gain new insight into individualized risk. We address this gap by proposing a novel augmented frailty-based illness-death model with a binary submodel to distinguish risk of immediate terminal event following the non-terminal event. The model admits direct dependence of the terminal event on the non-terminal event through flexible regression specification, as well as indirect dependence via a shared frailty term linking each submodel. We develop an efficient Bayesian sampler for estimation and corresponding model fit metrics, and derive formulae for dynamic risk prediction. In an extended example using pregnancy outcome data from an electronic health record, we demonstrate the proposed model's direct applicability to address a broad range of clinical questions.

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OBJECTIVES: This paper discusses methodological challenges in epidemiological association analysis of a time-to-event outcome and hypothesized risk factors, where age/time at the onset of the outcome may be missing in some cases, a condition commonly encountered when the outcome is self-reported. STUDY DESIGN AND SETTING: A cohort study with long-term follow-up for outcome ascertainment such as the Childhood Cancer Survivor Study (CCSS), a large cohort study of 5-year survivors of childhood cancer diagnosed in 1970-1999 in which occurrences and age at onset of various chronic health conditions (CHCs) are self-reported in surveys. Simple methods for handling missing onset age and their potential bias in the exposure-outcome association inference are discussed. The interval-censored method is discussed as a remedy for handling this problem. The finite sample performance of these approaches is compared through Monte Carlo simulations. Examples from the CCSS include four CHCs (diabetes, myocardial infarction, osteoporosis/osteopenia, and growth hormone deficiency). RESULTS: The interval-censored method is useable in practice using the standard statistical software. The simulation study showed that the regression coefficient estimates from the 'Interval censored' method consistently displayed reduced bias and, in most cases, smaller standard deviations, resulting in smaller mean square errors, compared to those from the simple approaches, regardless of the proportion of subjects with an event of interest, the proportion of missing onset age, and the sample size. CONCLUSION: The interval-censored method is a statistically valid and practical approach to the association analysis of self-reported time-to-event data when onset age may be missing. While the simpler approaches that force such data into complete data may enable the standard analytic methods to be applicable, there is considerable loss in both accuracy and precision relative to the interval-censored method.