Cumulative Exposure Model Research Articles

Methodologies for the collection of parameters to estimate dust/soil ingestion for young children.

Heavy metals, pesticides and a host of contaminants found in dust and soil pose a health risk to young children through ingestion. Dust/soil ingestion rates for young children can be estimated using micro-level activity time series (MLATS) as model inputs. MLATS allow for the generation of frequency and duration of children's contact activities, along with sequential contact patterns. Models using MLATS consider contact types, and transfer dynamics to assign mechanisms of contact and appropriate exposure factors for cumulative estimates of ingestion rates. The objective of this study is to describe field implementation, data needs, advanced field collection, laboratory methodologies, and challenges for integrating into and updating a previously validated physical-stochastic MLATS-based model framework called the Child-Specific Aggregate Cumulative Human Exposure and Dose (CACHED) model. The manuscript focuses on describing the methods implemented in the current study. This current multidisciplinary study (Dust Ingestion childRen sTudy [DIRT]) was implemented across three US regions: Tucson, Arizona; Miami, Florida and Greensboro, North Carolina. Four hundred and fifty participants were recruited between August 2021 to June 2023 to complete a 4-part household survey, of which 100 also participated in a field study. The field study focused on videotaping children's natural play using advanced unattended 360° cameras mounted for participants' tracking and ultimately conversion to MLATS. Additionally, children's hand rinses were collected before and after recording, along with indoor dust and outdoor soil, followed by advanced mass analysis. The gathered data will be used to quantify dust/soil ingestion by region, sociodemographic variables, age groups (from 6 months to 6 years), and other variables for indoor/outdoor settings within an adapted version of the CACHED model framework. New innovative approaches for the estimation of dust/soil ingestion rates can potentially improve modeling and quantification of children's risks to contaminants from dust exposure.

Maximal entropy prior for the simple step‐stress accelerated test

AbstractThe step‐stress procedure is a popular accelerated test used to analyze the lifetime of highly reliable components. This paper considers a simple step‐stress accelerated test assuming a cumulative exposure model with uncensored lifetime data following a Weibull distribution. The maximum likelihood approach is often used to analyze accelerated stress test data. Another approach is to use the Bayesian inference, which is useful when there is limited data available. In this paper, the parameters of the model are estimated based on the objective Bayesian viewpoint using non‐informative priors. Our main aim is to propose the maximal data information prior (MDIP) presented by Zellner (1984) as an alternative prior to the conventional independent gamma priors for the unknown parameters, in situations where there is little or no a priori knowledge about the parameters. We also obtain the Bayes estimators based on both classes of priors, assuming three different loss functions: square error loss function (SELF), linear‐exponential loss function (LINEX), and generalized entropy loss function (GELF). The proposed MDIP prior is compared with the gamma priors via Monte Carlo simulations by examining their biases and mean square errors under the three loss functions, and coverage probability. Additionally, we employ the Markov Chain Monte Carlo (MCMC) algorithm to extract characteristics of marginal posterior distributions, such as the Bayes estimator and credible intervals. Finally, a real lifetime data is presented to illustrate the proposed methodology.

Predicted 25-hydroxyvitamin D over the adult lifetime and the risk of ovarian cancer.

The evidence from previous studies of serum 25-hydroxyvitamin D (25(OH)D) and ovarian cancer risk is not conclusive. However, the 25(OH)D levels were generally only measured in late adulthood, which may not capture the etiologically relevant exposure periods. We investigated predicted 25(OH)D over the adult lifetime in relation to ovarian cancer risk in a population-based case-control study conducted from 2011 to 2016 in Montreal, Canada (n = 490 cases and 896 controls). Predicted 25(OH)D was computed using previously validated regression models. Unconditional multivariable logistic regression models were used to estimate adjusted odds ratios (aORs) and 95% CIs for average predicted 25(OH)D over the adult lifetime and ovarian cancer risk. In addition, the relative importance of different periods of past 25(OH)D exposure was explored using a weighted cumulative exposure (WCE) model. For each 20-nmol/L increase in average predicted 25(OH)D over the adult lifetime, the aOR (95% CI) was 0.73 (0.55-0.96). In WCE analyses, the inverse association was strongest for exposures 5 to 20years and 35 to 55years prior to diagnosis, with aORs (95% CIs) of 0.82 (0.69-0.94) and 0.79 (0.66-1.02), respectively, for each 20-nmol/L increase in predicted 25(OH)D. These results support an inverse association between 25(OH)D levels in adulthood and ovarian cancer risk. This article is part of a Special Collection on Gynecological Cancers.

Disability and the widening gap in mid-life wealth accumulation: A longitudinal examination

Research suggests that persons living with a disability are disadvantaged in terms of employment outcomes and experience greater economic vulnerability. Despite our understanding of wealth inequality in later life as the result of an accumulative process of resource acquisition that occurs across the life course, conclusions about economic inequality associated with disability are mainly based on cross-sectional research or very short-term panel studies. In this paper, we examine the extent to which work disability in mid-life creates a cumulative disadvantage in wealth accumulation that grows with age. Using long-term longitudinal data from the Panel Study of Income Dynamics (PSID), we follow respondents from their 40 s into their 60 s to understand the relationship between work disability and wealth accumulation over time. Growth curve models include two specifications of trajectories of household wealth accumulation; as a function of time-varying work disability and also as a function of cumulative exposure to work disability in mid-life. Although both specifications indicate a disability penalty to wealth accumulation, the cumulative exposure model shows that initial wealth disparities associated with disability grow substantially with age, resulting in a widening gap in household wealth at the threshold of traditional retirement age for those with histories of temporary or persistent work disability in midlife.

Importance of accounting for timing of time-varying exposures in association studies: Hydrochlorothiazide and non-melanoma skin cancer.

Hydrochlorothiazide (HCTZ), a widely prescribed antihypertensive drug with photosensitising properties, has been linked with non-melanoma skin cancer (NMSC) risk. However, previous analyses did not fully explore if and how the impact of past HCTZ exposures accumulates with prolonged use and/or depends on time elapsed since exposures. Therefore, we used different models to more comprehensively assess how NMSC risk vary with HCTZ exposure, and explore how the results may depend on modeling strategies. We used different parametric models with alternative time-varying exposure metrics, and the flexible weighted cumulative exposure model (WCE) to estimate associations between HCTZ exposures and NMSC risk in a population-based cohort of HCTZ users over 65 years old, in the province of Ontario, Canada. Among 3844 HCTZ users, 273 developed NMSC during up to 8 years of follow-up. In parametric models, based on all exposures, increased duration of past HCTZ use was associated with an increase of NMSC risk but cumulative dose showed no systematic association. Yet, WCE results suggested that only exposures taken 2.5-4 years in the past were associated with the current NMSC hazard. This finding led us to re-define the parametric models, which also confirmed that any HCTZ dose taken outside this time-window were not systematically associated with NMSC incidence. Our analyses illustrate how flexible modeling may yield new insights into complex temporal relationships between a time-varying drug exposure and risks of adverse events. Duration and recency of antihypertensive agents exposures must be taken into account in evaluating risk and benefits.

Optimal scheme and estimation for a bivariate step‐stress accelerated life test with the inverse Weibull distribution under type‐I progressive censored samples

AbstractIn this paper, we provide an optimization design for a step‐stress accelerated life test (ALT) with two stress variables when the lifespan of test units is assumed to follow the inverse Weibull (IW) distribution. We first utilize progressive type‐I censoring and accelerated life testing to shorten the time and reduce cost of testing and then adopt a cumulative exposure (CE) model to look at the impact of varying stress levels. A log‐linear relationship between the scale parameter of the IW distribution and stress has been postulated. We obtain the maximum likelihood estimators and Bayes estimators of the unknown model parameters. Under normal operating conditions, we design an optimal test plan via minimizing the asymptotic variance (AV) of the percentile life. We carry out simulation studies to illustrate the performance and optimality of the proposed model. Finally, a real‐life data is analyzed for illustrative purposes.

Reverse causation biases weighted cumulative exposure model estimates, but can be investigated in sensitivity analyses

ObjectivesTo examine the effects of reverse causation on estimates from the weighted cumulative exposure (WCE) model that is used in pharmacoepidemiology to explore drug-health outcome associations, and to identify sensitivity analyses for revealing such effects. Study Design and Setting314,099 patients with diabetes under Clalit Health Services, Israel, were followed over 2002–2012. The association between metformin and pancreatic cancer (PC) was explored using a WCE model within the framework of discrete-time Cox regression. We used computer simulations to explore the effects of reverse causation on estimates of a WCE model and to examine sensitivity analyses for revealing and adjusting for reverse causation. We then applied those sensitivity analyses to our data. ResultsSimulation demonstrated bias in the weighted cumulative exposure model and showed that sensitivity analysis could reveal and adjust for these biases. In our data, a positive association was observed (hazard ratio (HR) = 3.24, 95% confidence interval (CI): 2.24–4.73) with metformin exposure in the previous 2 years. After applying sensitivity analysis, assuming reverse causation operated up to 4 years before cancer diagnosis, the association between metformin and PC was no longer apparent. ConclusionReverse causation can cause substantial bias in the WCE model. When suspected, sensitivity analyses based on causal analysis are advocated.

A cumulative exposure model for remaining useful life prediction of pitot tube based on dynamic operating data

AbstractThe data measured by the pitot tube (PT) is related to airspeed indication and flight safety. However, there are few methods to solve the problem of failure prediction and predictive maintenance of PT. This study proposes a method for predicting the remaining useful life (RUL) of the PT based on dynamic operating data. First, an exposure index (EI) characterizing the severity level of operating conditions is proposed based on multiple dynamic operating and environmental parameters, then a cumulative exposure model (CEM) is developed to calculate the cumulative exposure. Dynamic covariate information is incorporated into the time‐to‐failure distribution of PT through the CEM, the RUL distribution of the individual PT is then obtained by Monte Carlo simulation. A case study is carried out based on actual data of a commercial aircraft fleet and shows that the proposed CEM can effectively use historical aircraft environmental information and truncated failure data of the components. The relative error of the remaining life prediction is substantially improved compared to the traditional reliability analysis methods, which means that the proposed model can provide more reliable RUL results based on historical operating conditions, providing better support for PT risk assessment and condition‐based maintenance decisions.

Photovoltaic Module Degradation Forecast Models for Onshore and Offshore Floating Systems

The degradation trend of photovoltaic modules depends on the technology, manufacturing techniques and climatic conditions of the site where they are installed. Longer useful life of the PV modules means that they will be able to produce much more energy than was used to build them; thus, extending the useful life of the modules is beneficial for the environment and increases the cost effectiveness of PVs. The problem of land use has prompted the development of agrivoltaic systems to exploit the same land both for the production of energy and for agriculture, and on water surfaces such as lakes and dams (floating PV). The exploitation of floating PV systems in onshore and offshore areas is currently under study. This constitutes an opportunity for which many factors must be taken into account; a fundamental aspect is the environmental impact, on which some recent studies have focused. Another aspect is the impact of the marine environment on PV system reliability and durability, due to the stress on operating conditions. The aim of this preliminary study is to evaluate the influence of the marine environment on the degradation trend of photovoltaic modules, based on existing models whose inputs are meteorological data from offshore locations. The results obtained from the application of a cumulative exposure model unexpectedly showed a lower degradation value in the offshore environment than on the mainland: −0.95% and −3% values of power decay, respectively. The absolute value of power decay in the onshore case is higher than the typical values because the used model has to be revised, as the empirical coefficients of the model have to be calculated according to the installation environment. The empirical coefficients used in the model were obtained in environmental conditions different from those under study. In the offshore case, the degradation estimated by the model does not take into account some environmental factors typical of the marine environment. Model adaptations calibrated with datasets of plants in environmental conditions similar to those analyzed would allow for greater accuracy in the results.

Robust inference for nondestructive one‐shot device testing under step‐stress model with exponential lifetimes

AbstractOne‐shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one‐shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step‐stress tests allow the experimenter to increase the stress levels at prefixed times gradually during the life‐testing experiment. The cumulative exposure model is commonly assumed for step‐stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z‐type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for nondestructive one‐shot devices under the step‐stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and confidence intervals for different lifetime characteristic such as reliability, distribution quantiles, and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real‐life data sets are analyzed finally for illustrative purpose.

Abstract 12585: Flexible Modeling of the Association Between Cumulative Exposure to Low-Dose Ionizing Radiation From Cardiac Procedures and Risk of Hematopoietic Cancer in Children With Congenital Heart Disease

Background: High-dose ionizing radiation is a well-established risk factor for childhood malignancies, including hematopoietic cancers (HC). However, data on the effect of low-dose ionizing radiation (LDIR) from medical imaging is conflicting and scant, especially in the pediatric population with congenital heart diseases (CHD). This study evaluated the association between cardiac LDIR exposure and hematopoietic cancers among children with CHD. Methods: A nationwide population-based cohort study was conducted using the Canadian Congenital Heart Disease (CanCHD) database. The study population included children born between 1999 and 2017 with at least one CHD diagnosis in their medical records. The cumulative dose of ionizing radiation corresponding to cardiac diagnostic and therapeutic procedures was quantified considering a 6-month exposure lag. The recency-weighted cumulative exposure (WCE) model, a flexible extension of Cox’s proportional hazards model, was used to assess the association. Results: We identified 139,975 children with CHD born between 1999 and 2017 and followed them for 1,388,681 person-years since birth. In this population, 718 hematopoietic cancer cases were observed. Children with HC were exposed to low-dose ionizing radiation earlier in life (median age at first exposure: 6 vs. 10 months; p=0.03) and had more procedures than those without cancer (mean number of procedures: 0.4 vs. 0.2; p<0.001). The cases received higher cumulative LDIR doses than their counterparts (mean dose: 2.3 vs. 1.1 mSv; p<0.001). We observed that cumulative LDIR doses within five years were associated with increased risk of hematopoietic cancer with the maximum association magnitude around 2 years. Conclusion: This is the first large population-based study documenting increased risk of HC associated with increased dose and recency of the LDIR exposure among children with CHD. Along with these findings, future studies focusing on detecting a threshold effect will help physicians decide the exposure point at which increased surveillance on LDIR exposure should be initiated.

Bayesian analysis for multiple step-stress accelerated life test model under gamma lifetime distribution and type-II censoring

PurposeThe step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.Design/methodology/approachA Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.FindingsThe authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.Originality/valueMost of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

Statistical Inference in the Cumulative Exposure Lognormal Model with Hybrid Censoring

This research aims to analyze data coming from step stress life testing experiments where the stress level is incremented at a preset time to obtain failure data faster. To analyze step stress data, a model that extrapolates the information attained from the accelerated tests to normal conditions needs to be fit to the life test data. We used the Cumulative Exposure Model (CEM) to model simple step stress lognormal life test data where hybrid censoring is present and applied the maximum likelihood estimation method to find the point and interval estimates of the parameters. Bootstrap intervals (bootstrap-t intervals and percentile intervals) were also constructed. We then performed a simulation study to assess the proposed methods of estimation under different hybrid censoring schemes. The Bias and MSE of the maximum likelihood estimators (MLEs) along with the coverage probability and average lengths of the corresponding confidence intervals were investigated. Finally, an illustrative example has been used to demonstrate the application of the methods discussed in this paper.

E-Bayesian and H-Bayesian Inferences for a Simple Step-Stress Model with Competing Failure Model under Progressively Type-II Censoring

In this paper, we discuss the statistical analysis of a simple step-stress accelerated competing failure model under progressively Type-II censoring. It is assumed that there is more than one cause of failure, and the lifetime of the experimental units at each stress level follows exponential distribution. The distribution functions under different stress levels are connected through the cumulative exposure model. The maximum likelihood, Bayesian, Expected Bayesian, and Hierarchical Bayesian estimations of the model parameters are derived based on the different loss function. Based on Monte Carlo Simulations. We also get the average length and the coverage probability of the 95% confidence intervals and highest posterior density credible intervals of the parameters. From the numerical studies, it can be seen that the proposed Expected Bayesian estimations and Hierarchical Bayesian estimations have better performance in terms of the average estimates and mean squared errors, respectively. Finally, the methods of statistical inference discussed here are illustrated with a numerical example.

Optimal Test Plan of Step-Stress Model of Alpha Power Weibull Lifetimes under Progressively Type-II Censored Samples

In this study, the estimation of the unknown parameters of an alpha power Weibull (APW) distribution using the concept of an optimal strategy for the step-stress accelerated life testing (SSALT) is investigated from both classical and Bayesian viewpoints. We used progressive type-II censoring and accelerated life testing to reduce testing time and costs, and we used a cumulative exposure model to examine the impact of various stress levels. A log-linear relation between the scale parameter of the APW distribution and the stress model has been proposed. Maximum likelihood estimators for model parameters, as well as approximation and bootstrap confidence intervals (CIs), were calculated. Bayesian estimation of the parameter model was obtained under symmetric and asymmetric loss functions. An optimal test plan was created under typical operating conditions by minimizing the asymptotic variance (AV) of the percentile life. The simulation study is discussed to demonstrate the model’s optimality. In addition, real-world data are evaluated to demonstrate the model’s versatility.

Optimal design of cyclic-stress accelerated life tests for lognormal lifetime distribution

ABSTRACT Accelerated life tests (ALTs) have frequently been used in industry to assess the reliability of products within an affordable amount of time and cost. Most of the previous works on designing ALT plans have dealt with the case of constant-, step- or progressive-stress loading, which may not be adequate for products operating under cyclic-stress loading at the use condition. In this paper, optimal and compromise ALT plans are developed under the assumptions of cyclic-stress loading, lognormal lifetime distribution, log-linear relationship between the scale parameter of the lifetime distribution and stress variable and the cumulative exposure model for the effect of changing stress levels. In particular, the common floor level and the proportion of units assigned to two (for optimal plans) or three (for compromise plans) cyclic-stress conditions are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized. In addition, a sample size determination method is developed, and sensitivity analysis procedures are presented to evaluate the robustness of the proposed ALT plans in the face of uncertainty in the pre-estimation of a model parameter. The whole process is illustrated with an example.

Single and Multiple Ramp Progressive Stress with Binomial Removal: Practical Application for Industry

The objective of this article is to conduct a full study on the failure times of items when subjected to a progressive-stress accelerated life test. These failure times follow the Modified Kies exponential distribution. We performed the experiments under a type-II censoring scheme with binomial removal. The stress design has two ways to be applied either the simple ramp-stress test or the multiple ramp-stress level design of acceleration. We made a comparison between these two designs to decide which design is better. When the lifetime of test units follows the Modified Kies distributions, the cumulative exposure model has been used to apply the acceleration on the failure times to produce early failures. The simulation study was done to compare two types of progressive-stress designs. Different estimation techniques such as maximum likelihood estimation and Bayes estimation are employed to estimate the model parameters. The Metropolis Hasting method is used to derive the Bayesian estimates under symmetric and asymmetric loss functions. We also developed interval estimation as well as point estimation, and we estimated the asymptotic confidence intervals, bootstrap, and credible for the distribution parameters. We made a comparison between different estimation methods. We used real data from a practical experiment as a real data set example to assess the performance of the estimations methods. These data are analyzed to demonstrate the adequacy and superiority of the distribution to fit accelerated failure times. Also, we studied the existence and uniqueness of the roots and we used graphs to assure that the estimates used are unique and global maximum. Finally, some noteworthy conclusions are reached.

Optimal Design for a Bivariate Step-Stress Accelerated Life Test with Alpha Power Exponential Distribution Based on Type-I Progressive Censored Samples

We consider an optimization design for the alpha power exponential (APE) distribution as asymmetrical probability distributions under progressive type-I censoring for a step-stress accelerated life test. In this study, two stress variables are taken into account. To save the time and cost of lifetime testing, progressive censoring and accelerated life testing are utilized. The test units’ lifespans are supposed to follow an APE distribution. A cumulative exposure model is used to study the impact of varying stress levels. A log-linear relationship between the APE distribution’s scale parameter and stress is postulated. The maximum likelihood estimators, Bayesian estimators of the model parameters based on the symmetric loss function, approximate confidence intervals (CIs) and credible intervals are provided. Under normal operating conditions, an ideal test plan is designed by minimizing the asymptotic variance of the percentile life.

엔진 유지점검과 정지능력을 고려한 액체로켓 추진시스템의 신뢰도 모형

Purpose: In this paper, we present a reliability model for a liquid rocket propulsion system with the engine out capability.<BR>Methods: Previously, researchers have developed such a reliability model, in which a failure decay function is used to modify time-independent reliability to time-dependent reliability for each engine. In that model, engine reliability at different thrust values was estimated independently, and the check-up time and mission time were fixed. Such a model is not useful for determining the check-up time necessary to achieve the system reliability target. In this paper, we present a system reliability model in terms of the engine check-up time and mission time. We use the cumulative exposure model to relate the lifetime of an engine operating at different thrust values, assuming that the lifetime of each engine follows a general distribution. By using a mixed exponential distribution, we obtain a closed form expression of system reliability and explain how time-independent engine reliability can be transformed to time-dependent engine reliability.<BR>Result: The proposed model is useful for determining the check-up time that provides the target mission reliability.<BR>Conclusion: The reliability of a liquid rocket propulsion system must be expressed explicitly in terms of the engine reliability depending on the check-up time and the mission time if the check-up time must be determined to achieve the system reliability requirement.

Prediction of Future Lifetimes for a Simple Step-Stress Model with Type-II Censoring and Rayleigh Distribution

In this paper, we discuss the prediction problem of the lifetimes to failure of units from Rayleigh distribution with Type-II censoring for a simple step-stress setup under cumulative exposure model. We consider several methods of point prediction, including maximum likelihood predictor, conditional median predictor, and best unbiased predictor. In addition, we discuss the prediction intervals for future lifetimes of the censored units using pivotal quantity, highest conditional density, and shortest-length based methods. Monte Carlo simulation is conducted to compare the proposed prediction methods. Further, a real data set is analyzed for illustrative purposes.