Failure Time Research Articles

Data‐driven estimation for multithreshold accelerated failure time model

AbstractThis article develops a novel estimation framework for the multithreshold accelerated failure time model, which has distinct linear forms within different subdomains. One major challenge is to determine the number of threshold effects. We first show the selection consistency of a modified Bayesian information criterion under mild conditions. It is useful sometimes but heavily depends on the penalization magnitude, which usually varies from the model configuration and data distribution. To address this issue, we leverage a cross‐validation criterion alongside an order‐preserved sample‐splitting scheme to yield a consistent estimation. The new criterion is completely data driven without additional parameters and thus robust to model setting and data distributions. The asymptotic properties for the parameter estimates are also carefully established. Additionally, we propose an efficient score‐type test to examine the existence of threshold effects. The new statistic is free of estimating any potential threshold effects and is thus suitable for multithreshold scenarios. Numerical experiments validate the reliable finite‐sample performance of our methodologies, which corroborates the theoretical results.

Caries Incidence in School-Based Prevention Programs in the Presence of Interval Censoring

Background/Objectives: School-based caries prevention can increase access to critical dental services and reduce oral health inequities. However, little is known regarding the incidence of dental caries in children participating in school caries prevention, and caries diagnosis is often interval censored. Methods: In this paper, we used data from a longitudinal, school-based, randomized clinical trial of minimally invasive treatments for dental caries to estimate the per-visit incidence rate and compare the hazard of dental caries in children receiving either silver diamine fluoride or glass ionomer dental sealants. To account for interval censoring, we used semiparametric transformation models for univariate failure time data and imputed caries incidence using G-imputation. Results: There were 3040 children that met inclusion criteria for analysis, 1516 (49.9%) of which were randomly assigned to receive silver diamine fluoride and 1524 (50.1%) were assigned to receive glass ionomer dental sealants and atraumatic restorations. There were no differences in the hazard of caries between treatments (HR = 0.99, 95% CI = 0.72, 1.24), while children with caries at baseline had a significant increase in the hazard of new caries (HR = 2.54, 95% CI = 2.26, 2.83) compared to those that were caries free. The per-visit caries incidence ranged from 4.8 to 11.1 at the individual level and increased with each successive study observation. Conclusions: School-based caries prevention can positively affect caries incidence, and the results can be used to inform future program design and implementation.

Mechanical properties and energy evolution of outburst coal seams under different load regimes

AbstractCoal elasticity and gas expansion are important factors for coal and gas outburst. During the outburst process, the elastic strain energy of coal is mainly released from the stress region, and the gas expansion energy near the working face is larger, and it is not a continuous release process. To reveal the mechanical characteristics and energy evolution of outburst coal seam, uniaxial and triaxial compression tests were carried out on outburst coal seam samples under different loading methods. The experimental results show that the elastic characteristics become more obvious with the increase of loading rate, the peak strain increases, the elastic modulus is linearly related with the loading rate，and the overall degree of fragmentation increases with the increase of loading rate, which is consistent with the severity of macroscopic coal failure. The failure mode of coal under uniaxial compression conditions is often manifest as brittle failure. The strength characteristics of coal under different loading rates comply with the Mohr‐Coulomb criterion, and the peak strength is linearly related to the failure time and loading rate. With the increasing confining pressure causes the failure of coal samples to transition from ductile to brittle, and the failure mode develops from local shear to overall splitting. The elastic energy evolution curve is consistent with its stress‐strain curve. With the increase of confining pressure, the limiting elastic energy and peak total energy increase in a quasi‐linear manner. The accumulated limit elastic energy plays an important role in the failure of coal samples, and the macroscopic manifestation thereof is that the coal samples fail more severely under high confining pressure conditions than under low confining pressure conditions. The research results are of great significance for the comprehensive prevention and control of coal and gas outburst.

Cox regression model with doubly truncated and interval-censored data

Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size.

Improved machine learning models with a similarity-based approach for remaining useful life prediction

Abstract Cost efficiency is a critical factor in the competitive aviation sector. These efficiency factors force airline operators to develop new approaches in their organizations. Predictive maintenance helps to build scheduling maintenance programs for airline operators or MROs. Scheduled maintenance programs benefit cost efficiency in the aviation sector. Predictive maintenance methods predict the failure time of any equipment. Predictions can be made by analyzing the sensor values from equipment. In this paper, we predicted the remaining useful life (RUL) of turbofan engines using machine learning models and a similarity-based approach. Sensor datasets from the Prognostics Data Repository of NASA, called CMAPPS, were utilized. Using the FD0002 sub-dataset, a health index (HI) was created, and models were trained. Once the models were trained, train and test HIs were estimated. The predicted test HI was matched with the predicted train HI based on a similarity-based approach, and then a RUL prediction was made. The results obtained were compared with the actual results to calculate the accuracy, and the algorithm that resulted in the maximum accuracy was identified. We selected six machine learning algorithms and also created an ensemble model by averaging the predictions of six machine learning algorithms for comparing prediction accuracy. The different algorithms were compared to obtain the prediction model with the closest prediction of remaining useful lifecycle in terms of the number of life cycles. This experiment showed us the effect of the similarity-based approach on the basic version of machine learning models for RUL prediction.

Core Concepts in Pharmacoepidemiology: Time-To-Event Analysis Approaches in Pharmacoepidemiology.

This article provides an overview of time-to-event (TTE) analysis in pharmacoepidemiology. The key concept of censoring is reviewed, including right-, left-, interval- and informative censoring. Simple descriptive statistics are explained, including the nonparametric estimation of the TTE distribution as per Kaplan-Meier method, as well as more complex TTE regression approaches, including the parametric Accelerated Failure Time (AFT) model and the semi-parametric Cox Proportional Hazards and Restricted Mean Survival Time (RMST) models. Additional approaches and various TTE model extensions are presented as well. Finally, causal inference for TTE outcomes is addressed. A thorough review of the available concepts and methods outlines the immense variety of available and useful TTE models. There may be underused TTE concepts and methods, which are highlighted to raise awareness for researchers who aim to apply the most appropriate TTE approach for their study. This paper constitutes a modern summary of TTE analysis concepts and methods. A curated list of references is provided.

Accelerated failure time modelling in the analysis of type 2 diabetic patient data

Accelerated failure time modelling in the analysis of type 2 diabetic patient data

Prediction of landslide failure time based on moving average convergence and divergence coupling with Bayesian updating method

Prediction of landslide failure time based on moving average convergence and divergence coupling with Bayesian updating method

Predicting long-term survival among patients with HCC.

Prognosticating survival among patients with HCC and cirrhosis must account for both the tumor burden/stage, as well as the severity of the underlying liver disease. Although there are many staging systems used to guide therapy, they have not been widely adopted to predict patient-level survival after the diagnosis of HCC. We sought to develop a score to predict long-term survival among patients with early- to intermediate-stage HCC using purely objective criteria. Retrospective cohort study among patients with HCC confined to the liver, without major medical comorbidities within the Veterans Health Administration from 2014 to 2023. Tumor data were manually abstracted and combined with clinical and laboratory data to predict 5-year survival from HCC diagnosis using accelerated failure time models. The data were randomly split using a 75:25 ratio for training and validation. Model discrimination and calibration were assessed and compared to other HCC staging systems. The cohort included 1325 patients with confirmed HCC. A risk score using baseline clinical, laboratory, and HCC-related survival had excellent discrimination (integrated AUC: 0.71 in the validation set) and calibration (based on calibration plots and Brier scores). Models had superior performance to the BCLC and ALBI scores and similar performance to the combined BCLC-ALBI score. We developed a risk score using purely objective data to accurately predict long-term survival for patients with HCC. This score, if validated, can be used to prognosticate survival for patients with HCC, and, in the setting of liver transplantation, can be incorporated to consider the net survival benefit of liver transplantation versus other curative options.

Disparities in time to diagnosis of Radiographic Axial Spondyloarthritis.

Radiographic axial spondyloarthritis (r-axSpA) has a 7-year average diagnostic delay. While the impact of sex or gender on time to diagnosis has been evaluated, the role of social determinants of health remains understudied. We assessed whether time from initial clinical documentation of r-axSpA symptoms to r-axSpA diagnosis (diagnostic delay) varies based on sex, race, ethnicity, or the presence of social needs. We studied patients with r-axSpA from a tertiary center from 2000 to 2022. The cohort was built with the Observational Health Data Sciences and Informatics (OHDSI) network. For the primary analysis, we assessed the time from back pain/spinal pain to r-axSpA diagnosis and secondarily, the time to r-axSpA from any other r-axSpA -related condition. To estimate differences in diagnostic delay, we employed a parametric survival model, accelerated failure time. We included 404 patients (mean age 49, 37% female), with 25.5% identifying as Black, 31.1% as other or unknown race and 14.1% as Hispanic. Patients with a documented social need had a 21% increase in time from back pain to r-axSpA diagnosis (95% CI 0.93, 1.56). In patients with any r-axSpA related condition, time to diagnosis increased similarly by 21% (95% CI 0.92, 1.57). Considering an average time to diagnosis of 34 months, a social need increased time to diagnosis by 7 months. This study reveals a trend toward diagnostic delay in r-axSpA related to social need, sex, race, and ethnicity. Future studies should focus on referral strategies to enable prompt diagnosis and optimize care.

Penalized Likelihood Estimation for Current Status Data with Informative Censoring

Current status data occurs when failure time of subjects in a survival study is only known to be either less or greater than the censoring time. Thus, the failure time is either left – or right – censored. Analyzing data of this structure under the Cox Proportional Hazards model with dependent censoring assumption can be challenging. To address this, a Penalized Maximum Likelihood Estimation (PMLE) approach was proposed. The unknown baseline cumulative hazard functions for both the failure time and the censoring time were estimated using splines. The advantage of penalized approach over unpenalized method is that that the desired smoothness level of the functions are controlled by their respective penalty terms. The possible dependence between the failure and censoring times was accounted for using the gamma-frailty model. An easy to implement hybrid computational algorithm is proposed to estimate the PMLEs and the Bayesian technique was employed for the estimation of the variances of the parameters. Extensive simulation studies were conducted to assess the statistical properties of the PMLEs. It was observed that the realized estimators were not only consistent, asymptotically normal and efficient, but also, were robust to the number of knots chosen, the proportion of dependent censoring used and the frailty distribution employed. The proposed PMLE method was further applied to real data obtained from tumorigenicity experiment.

Selection processes, transportability, and failure time analysis in life history studies.

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.

Relative burden of cancer and noncancer mortality among long-term survivors of differentiated thyroid cancer in the US

BackgroundLimited information is available regarding the relative risks of cancer-specific mortality and noncancer-specific mortality among long-term survivors with differentiated thyroid cancer (DTC).MethodsIn this retrospective study, nationwide data from the Surveillance, Epidemiology, and End Results database (1992-2020) were utilized. The Accelerated Failure Time Model was applied to calculate Survival Time Ratios (TR), with the primary focus on mortality resulting from DTC. The competing risks model was employed to investigate the relative risks of various outcomes in DTC patients with a survival duration of 5 years or more.ResultsIn our cohort, 279 patients succumbed to DTC, while 748 died from other diseases. Notably, in DTC cohorts, noncancer-specific mortality rates were consistently higher than DTC-specific mortality rates across different age groups and genders. The risk of DTC and noncancer-specific mortality varied based on the TNM stage. With more advanced disease stages, the risk of DTC and other cancer-specific mortality gradually increased. The cumulative mortality from other cancer-specific causes was consistently the lowest.ConclusionsIn long-term surviving DTC patients, noncancer-specific mortality outweighed DTC-specific mortality irrespective of age and gender. For stage I and II patients, increased attention should be directed toward noncancer-specific mortality in postoperative follow-ups. Conversely, for stage III and IV patients, greater consideration should be given to DTC-related causes of death. In addition, for stage III and IV DTC patients, the risk of death from other cancers was significantly higher than for stages I and II.

Performance of photovoltaic panels with different inclinations under uniform thermal loading

Integrating photovoltaic (PV) panels with different tilt angles in building envelopes or roofs is widely employed for environmental sustainability. However, little is known about the influence of different tilt angles on the thermal failure of the photovoltaic façades or roofs in fire conditions. A total of 15 four-edge shielded PV panels (300 × 300 × 4.7 mm3), with five different inclinations of 0°, 15°, 30°, 45° and 60°, were heated to fail using a uniform radiant panel. Measurements were taken to track glass thermal breakage, surface temperatures, incident heat flux and failure characteristics. The glass fracture and pyrolysis of the internal thermoplastic materials were observed under thermal radiation. The average breakage time of glass in PV panels showed an increasing trend with increasing inclination of the PV panels. Moreover, when the PV panels were tilted beyond 30°, the time to failure increased more significantly. The maximum temperature difference and heat flux that the PV panels can withstand were primarily measured within the range of 61–84 °C and 8–15 kW/m2, respectively. Finally, the test results were simulated by a finite element method (FEM) model, calculating the heat transfer and thermal stress of PV panels: the average errors concerning temperature distributions and failure times were smaller than 15 % compared with the experimental results.

Joint regression analysis of clustered current status data with latent variables.

Clustered current status data frequently occur in many fields of survival studies. Some potential factors related to the hazards of interest cannot be directly observed but are characterized through multiple correlated observable surrogates. In this article, we propose a joint modeling method for regression analysis of clustered current status data with latent variables and potentially informative cluster sizes. The proposed models consist of a factor analysis model to characterize latent variables through their multiple surrogates and an additive hazards frailty model to investigate covariate effects on the failure time and incorporate intra-cluster correlations. We develop an estimation procedure that combines the expectation-maximization algorithm and the weighted estimating equations. The consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the proposed method is assessed via a series of simulation studies. This procedure is applied to analyze clustered current status data from the National Toxicology Program on a tumorigenicity study given by the United States Department of Health and Human Services.

Likelihood-Based Inference of Log-Logistic Accelerated Hazards Regression Models for Cross Hazards Data

ABSTRACT The proportional hazards model and accelerated failure time model are two important classes for analyzing survival data. However, the two models cannot capture time-scaled effects such as crossing hazard or the gradual effect of treatment over time. For the purpose of this detection, accelerated hazards model has been studied. In this paper, we propose the use of log-logistic distribution for the baseline hazard function of the accelerated hazards model which allows for time-dependent group effect. In particular, the log-logistic distribution gives various forms (e.g. non-monotone) of hazard function and also an easy implementation for likelihood-based model fitting due to an explicit form of hazard and survival functions. The likelihood-based estimation procedures of the accelerated hazards models are derived. Our method is demonstrated with two practical data sets, via the procedures of systematic model checking.

A semiparametric accelerated failure time-based mixture cure tree

The mixture cure rate model (MCM) is the most widely used model for the analysis of survival data with a cured subgroup. In this context, the most common strategy to model the cure probability is to assume a generalized linear model with a known link function, such as the logit link function. However, the logit model can only capture simple effects of covariates on the cure probability. In this article, we propose a new MCM where the cure probability is modeled using a decision tree-based classifier and the survival distribution of the uncured is modeled using an accelerated failure time structure. To estimate the model parameters, we develop an expectation maximization algorithm. Our simulation study shows that the proposed model performs better in capturing nonlinear classification boundaries when compared to the logit-based MCM and the spline-based MCM. This results in more accurate and precise estimates of the cured probabilities, which in-turn results in improved predictive accuracy of cure. We further show that capturing nonlinear classification boundary also improves the estimation results corresponding to the survival distribution of the uncured subjects. Finally, we apply our proposed model and the EM algorithm to analyze an existing bone marrow transplant data.

Emergent resistance-associated mutations at first- or second-line HIV-1 virologic failure with second-generation InSTIs in two- and three-drug regimens: the Virostar-1 study.

Second-generation integrase strand transfer inhibitors (InSTIs) have a high barrier to resistance and potent antiretroviral activity. They are recommended as first- or second-line (FL and SL) options in two- and three-drug regimens (2DR and 3DR) in international treatment guidelines. However, there are limited real-world data on emerging resistance at the time of virological failure (VF) with these regimens. The Virostar-1 study objective is to analyse the emergence of resistance-associated mutations (RAMs) over 3 years with DTG-based 2DRs and DTG- or bictegravir (BIC)-based 3DRs in people living with HIV (PLWH) experiencing a VF (FL or SL). Retrospective analysis of genotypic resistance detected at the time of a FL or SL VF with BIC/FTC/TAF, DTG/ABC/3TC, DTG/3TC and DTG/RPV between 2019 and 2022 was conducted from a French multicentre database. VF was defined as two consecutive HIV-1 plasma viral loads > 50 c/mL. Sanger assays were performed at VF within standard clinical care. Resistance mutations were reported using the ANRS algorithm. Selection biases prevent group comparisons. During the period, N = 5986 PLWH were followed either in FL or SL. The VF rate was overall low: BIC/FTC/TAF, 6.8%; DTG/ABC/3TC, 7.5%; DTG/3TC, 5.1%; and DTG/RPV, 2.1%. Some emergent InSTI or NRTI RAMs were detected with BIC/FTC/TAF 4%, DTG/ABC/3TC 8.5%, DTG/3TC 18% and 39% emergent NNRTI RAMs with DTG/RPV. However, a complete absence of dual resistance against NRTIs and InSTIs was observed. We detected rare emergent InSTI RAMs and few emergent NRTI RAMs in PLWH failing DTG- or BIC-based regimens in FL or SL. The observed rates of emergent RAMs at VF were 4% with BIC/FTC/TAF, 8.5% with DTG/ABC/3TC, 18% with DTG/3TC and 39% with DTG/RPV.

Physics informed neural network can retrieve rate and state friction parameters from acoustic monitoring of laboratory stick-slip experiments

Various machine learning (ML) and deep learning (DL) techniques have been recently applied to the forecasting of laboratory earthquakes from friction experiments. The magnitude and timing of shear failures in stick-slip cycles are predicted using features extracted from the recorded ultrasonic or acoustic emission (AE) signals. In addition, the Rate and State Friction (RSF) constitutive laws are extensively used to model the frictional behavior of faults. In this work, we use data from shear experiments coupled with passive acoustic (variance, kurtosis, and AE rate) interleaved with active source ultrasonic monitoring (transmitted wave amplitude) to develop physics-informed neural network (PINN) models incorporating the RSF law and AE rate generation equation with wave amplitude serving as a proxy for friction state variable. This PINN framework allows learning RSF parameters from stick-slip experiments rather than measuring them through a series of velocity step experiments. We observe that when the stick-slip cycles are irregular, the PINN models outperform the data-driven DL models. Transfer learning (TL) PINN models are also developed by pre-training on data collected at one normal stress level followed by forecasting shear failures and retrieving RSF parameters at other stress levels (i.e., with different recurrence intervals) after retraining on a limited amount of new data. Our findings suggest that TL models perform better compared to standalone models. Both standalone and TL PINN-estimated RSF parameters and their ground truth values show excellent agreements thus demonstrating that RSF parameters can be retrieved from laboratory stick-slip experiments using the corresponding acoustic data and that the transmitted wave amplitude provides a good representation of the evolving frictional state during stick-slips.

Association between periodontitis with the all-cause and cause specific mortality among the population with hyperlipidemia

BackgroundTo explore the association between periodontitis and all-cause as well as cause-specific mortality rates in U.S. adults with hyperlipidemia.MethodsParticipants were extracted from NHANES during 1988–1994, 1999–2004 and 2009–2014 periods. To assess the association between moderate-to-severe periodontitis and mortality rates for both all-cause and cause-specific mortality, hazard ratios (HRs), time ratios (TRs), and their respective 95% confidence intervals (CIs) were calculated using Cox proportional hazards and Weibull accelerated failure time (AFT) models.ResultsOver a median follow-up duration of 11.83 years, 4,623 deaths of 16,848 participants were recorded. Multivariate Cox regression and AFT analyses showed moderate-to-severe periodontitis were associated with an increased risk of all-cause (HR: 1.31, 95% CI: 1.20–1.44, P < 0.001; TR: 0.85, 95% CI: 0.80–0.90, P < 0.001), cardiovascular disease (CVD)-related (HR: 1.36, 95% CI: 1.14–1.63, P = 0.001; TR: 0.83, 95% CI: 0.75–0.92, P < 0.001) and cancer-related mortality ( HR: 1.35, 95% CI: 1.12–1.63, P = 0.002; TR: 0.82, 95% CI: 0.72–0.93, P = 0.002). Meanwhile, there was a significant upward trend in the risk of mortality with increasing severity of periodontitis (P for trend < 0.001).ConclusionsOur study highlights the moderate-to-severe periodontitis is associated with an increased risk of all-cause, CVD-related and cancer-related mortality among U.S. adults with hyperlipidemia. And the mortality risk increasing alongside the severity of periodontitis.