Estimates Of Model Parameters Research Articles

Population Pharmacokinetic Modeling to Support Trofinetide Dosing for the Treatment of Rett Syndrome.

Oral trofinetide administered using a body weight-banded dosing regimen was approved in the US for the treatment of Rett syndrome (RTT) in patients aged≥2years. This approval was principally based on efficacy and safety findings of the phase 3 LAVENDER study in girls and women aged 5-20years with RTT and extended to younger children aged 2-4years with supporting data from the DAFFODIL study. Weight-banded dosing regimens were selected based on early clinical population pharmacokinetic (popPK) modeling and different scenario simulations. We report the development and application of an updated popPK model to confirm that steady-state trofinetide exposures achieved in individual patients in the LAVENDER study were within target exposure range. A previously developed popPK model using data from nine clinical studies was updated based on 13 clinical studies of trofinetide in healthy volunteers and pediatric and adult patients, including the LAVENDER study. PopPK model and empiric individual Bayesian pharmacokinetic parameter estimates were used to generate trofinetide exposures. Covariate data from the pharmacokinetic dataset from LAVENDER study subjects (n=92) were used to estimate individual steady-state trofinetide exposure (area under concentration-time curve over 0-12 h [AUC0-12]). Steady-state exposures in individual patients in the LAVENDER study were used to confirm that the dosing regimens resulted in exposures within the target range. Among 5- to 20-year-olds receiving the LAVENDER BID dosing regimen [trofinetide 6g(12‒20kg), 8g(>20‒35kg), 10g(>35‒50kg), and 12g(>50kg)], simulated AUC0-12 values overlapped with the target exposure range; median AUC0-12 values were within target exposure range for all weight bands. PopPK model-based simulations confirm that weight-banded trofinetide dosing used in LAVENDER in girls and women aged 5-20years with RTT achieved target exposure. Graphical abstract available for this article.

Population Pharmacokinetics of Trofinetide in a Pediatric Population Aged 2-4Years with Rett Syndrome.

Weight-banded trofinetide dosing improved physician- and caregiver-rated efficacy measures and had acceptable tolerability in patients aged 2‒4years (DAFFODIL study) and 5‒20years (LAVENDER study) with Rett syndrome (RTT). Selection of weight-banded dosing regimens for these studies was based on population pharmacokinetic (popPK) modeling and exposure simulations. This study applied an updated popPK model to confirm steady-state trofinetide exposures achieved in DAFFODIL patients were within target range. A popPK model was developed using data from 14 clinical studies of trofinetide in healthy volunteers and pediatric and adult patients, including the LAVENDER and DAFFODIL studies. Individual exposure measures (area under concentration-time curve over 0-12h [AUC0-12] were generated via integration of the predicted concentration-time profile for each DAFFODIL study participant based on the popPK model and individual empiric Bayesian pharmacokinetic parameter estimates. Distributions of steady-state AUC0-12 values for each body-weight group were compared against target exposure (AUC0-12 = 800‒1200µg·h/mL). Distribution and box plots of simulated steady-state AUC0-12 values achieved with the weight-banded DAFFODIL dosing regimen used in younger individuals aged 2-4years with RTT (twice daily trofinetide 5g[≥ 9 to < 12kg] or 6g [≥ 12 to < 20kg]) indicated good overlap with the target exposure range. Median steady-state AUC0-12 values for both body-weight bands fell within the target exposure range. PopPK model-based simulations confirm that the weight-banded dosing regimen used in DAFFODIL is adequate to achieve target trofinetide exposure in 2- to 4-year-olds with RTT.

Comparing AI versus Optimization Workflows for Simulation-Based Inference of Spatial-Stochastic Systems

Abstract Model parameter inference is a universal problem across science. This challenge is particularly pronounced in developmental biology, where faithful mechanistic descriptions require spatial-stochastic models with numerous parameters, yet quantitative empirical data often lack sufficient granularity due to experimental limitations. Parameterizing such complex models therefore necessitates methods that elaborate on classical Bayesian inference by incorporating notions of optimality and goal-orientation through low-dimensional objective functions that quantitatively encapsulate target system behavior. In this study, we contrast two such inference workflows and apply them to biophysically inspired spatial-stochastic models. Technically, both workflows employ simulation-based inference (SBI) methods: the first leverages a modern deep-learning technique known as sequential neural posterior estimation (SNPE), while the second relies on a classical optimization technique called simulated annealing (SA). We evaluate these workflows by inferring the parameters of two complementary models for the inner cell mass (ICM) lineage differentiation in the blastocyst-stage mouse embryo. This developmental biology system serves as a paradigmatic example of a highly robust and reproducible cell-fate proportioning process that self-organizes under strongly stochastic conditions, such as intrinsic biochemical noise and cell-cell signaling delays. Our results reveal that while both methods provide consistent model parameter estimates, the modern SBI workflow yields significantly richer inferred distributions at an equivalent computational cost. We identify the computational scenarios that favor the modern SBI method over its classical counterpart, and propose a plausible strategy to exploit the complementary strengths of both workflows for enhanced parameter space exploration.

Approximate dynamic programming methods in Bayesian preference elicitation

Bayesian preference elicitation is a statistical framework which can aid in complex decision making processes such as engineering design by offering preference-informed recommendations to a decision maker (DM). In this framework, a DM is asked to answer a sequence of queries, called a questionnaire, where in each query they must select their preferred option among two alternatives. A common method to construct the questionnaire is through the D-optimality criterion, which seeks to select queries which lead to more precise estimates of utility model parameters. Past works have proposed and investigated adaptive methods for questionnaire construction using D-optimality as the query selection criterion. All of these adaptive methods have been based on greedy strategies to the best of our knowledge. In this work, we propose and compare various non-greedy methods for adaptive questionnaire construction in the preference elicitation setting. Our methods utilize a combination of enumeration and mixed integer programming techniques to select queries to present to the DM. Through our simulation studies, we find only a marginal improvement in D-efficiency through the use of non-greedy methods, suggesting that greedy methods are sufficient for this problem.

A Robust ALOHA and Sequential clustering-based mode estimator for low frequency oscillations in power system using synchrophasors

Accurate estimation of low frequency modes in power system are very much important for improving small signal stability. The parametric model parameters estimator known as Total least square estimation of signal parameters via rotational invariance techniques (TLS-ESPRIT) works effectively even in noisy conditions. However, this model parameter estimator requires prior information about numbers of modes of the signal. There are different Model order (MO) estimation techniques discussed in the recent past, which consider the significant eigenvalues of auto-correlation matrix (ACM) for its estimation. As the eigenvalues of ACM highly affected by bad measurements and Outliers, making these techniques inefficient and harder to automate in real time. So, to overcome aforementioned limitations, this paper proposes a robust mode estimation technique that can precisely detect the signal low frequency modes even in the presence of high variance noise and outliers. So, in this proposed work, an annihilating filter-based low-rank Hankel matrix (ALOHA) technique is implemented to obtain the rank deficient Hankel matrix to nullify the existence of noise and outliers in Phasor measurement unit (PMU) signal, thereafter approximated low rank Hankel matrix is considered for estimation of signals dominant modes. Wherein a sequential clustering technique (Sequential K-Mean++) is implemented for detection of numbers of prominent low frequency modes by segregating eigenvalues of ACM into two opponents i.e the signal and noise subspace. Thereafter the estimated MO is considered for estimation of modes through TLS-ESPRIT. The robustness of the proposed technique is validated by scheduling comparative study with recently developed techniques for synthetic signal, two area data, real PMU data of Western Electricity Coordinating Council (WECC) and oscillatory power data obtained from Western System Coordinating Council (WSCC) 9 bus system and IEEE68 bus system simulated through Real Time Digital Simulator (RTDS).

Inference of record failure times from unit generalized Rayleigh distribution

ABSTRACT In this paper, problems of estimation and prediction for record values are discussed for a two-parameter unit generalized Rayleigh distribution. Maximum likelihood estimators of model parameters along with their existence and uniqueness are established, and corresponding approximate confidence intervals are constructed based on asymptotic theory. In addition, alternative generalized inferential approach is provided for comparison based on the proposed pivotal quantities. Further, prediction intervals of remaining useful life are also presented under classical and generalized inferential methods when the unit generalized Rayleigh record values are available. Extensive numerical studies and two real-life examples are conducted to show the performance of the proposed methods. The results indicate that both classical and generalized estimation methods work satisfactorily and the proposed generalized inferential approach performs superior to traditional estimates in general.

Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach

The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study&amp;apos;s findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.

Functional projection K-means

A new technique for simultaneous clustering and dimensionality reduction of functional data is proposed. The observations are projected into a low-dimensional subspace and clustered by means of a functional K-means. The subspace and the partition are estimated simultaneously by minimizing the within deviance in the reduced space. This allows us to find new dimensions with a very low within deviance, which should correspond to a high level of discriminant power. However, in some cases, the total deviance explained by the new dimensions is so low as to make the subspace, and therefore the partition identified in it, insignificant. To overcome this drawback, we add to the loss a penalty equal to the negative total deviance in the reduced space. In this way, subspaces with a low deviance are avoided. We show how several existing methods are particular cases of our proposal simply by varying the weight of the penalty. The estimation is improved by adding a regularization term to the loss in order to take into account the functional nature of the data by smoothing the centroids. In contrast to existing literature, which largely considers the smoothing as a pre-processing step, in our proposal regularization is integrated with the identification of both subspace and cluster partition. An alternating least squares algorithm is introduced to compute model parameter estimates. The effectiveness of our proposal is demonstrated through its application to both real and simulated data. Supplementary materials for this article are available online.

Random Effects Meta-Analysis of Contingency Tables with Complete and Partially Complete Data, with Application to COVID-19 Research

We present a random effects meta-analytic approach for analyzing exchangeable 2 × 2 × 2 tables of COVID-19 deaths classified by two comorbidities, for example, diabetes and hypertension. We take the marginal tables of comorbidities as multinomial with table-specific cell probabilities drawn from a Dirichlet distribution. Conditionally hereon, we model the death counts for cell in the 2 × 2 table of possible comorbidity combinations as independent binomial random variables. We allow for a randomly drawn normally distributed frailty to model the correlation of the death counts within the same study. For complete tables, this model can be fitted by standard statistical software. We propose an approximate maximum likelihood (ML) imputation procedure by which tables with missing entries can be completed enabling the use of the same standard procedures and giving a better estimate of model parameters than one would get by leaving partial tables out. The properties of the method are illustrated by simulations.

A note on potential gains in precision of radiation risk estimates from joint analysis.

In estimating radiation-related risk of cancer and other diseases based on the RERF Life Span Study (LSS), joint analyses can be performed where multiple health outcome endpoints are combined in the same model, allowing some parameters to be estimated in common among all endpoints with possible increase in precision of radiation risk and other model parameter estimates. Using as a basis excess relative risk (ERR) and excess absolute risk (EAR) models of the type commonly used in analysis of LSS data at RERF, we use maximum likelihood theory to compute the asymptotic relative standard error of endpoint-specific radiation effect and other parameter estimates using joint analyses as compared to traditional independent analysis. We show that some gains in precision of endpoint-specific radiation risk parameter estimates can be achieved by sharing effect modifier and other model parameters, but only small or negligible gains in precision are achieved for endpoint-specific background modifying or effect modifying parameters when other model parameters are shared. The magnitude of the precision gain for radiation risk estimates depends on the number of endpoints, the baseline incidence rate of the endpoint, and the type of model being used.

A Next Generation of Hierarchical Bayesian Analyses of Hybrid Zones Enables Model-Based Quantification of Variation in Introgression in R.

Hybrid zones, where genetically distinct groups of organisms meet and interbreed, offer valuable insights into the nature of species and speciation. Here, we present a new R package, bgchm, for population genomic analyses of hybrid zones. This R package extends and updates the existing bgc software and combines Bayesian analyses of hierarchical genomic clines with Bayesian methods for estimating hybrid indexes, interpopulation ancestry proportions, and geographic clines. Compared to existing software, bgchm offers enhanced efficiency through Hamiltonian Monte Carlo sampling and the ability to work with genotype likelihoods combined with a hierarchical Bayesian approach, enabling inference for diverse types of genetic data sets. The package also facilitates the quantification of introgression patterns across genomes, which is crucial for understanding reproductive isolation and speciation genetics. We first describe the models underlying bgchm and then provide an overview of the R package and illustrate its use through the analysis of simulated and empirical data sets. We show that bgchm generates accurate estimates of model parameters under a variety of conditions, especially when the genetic loci analyzed are highly ancestry informative. This includes relatively robust estimates of genome-wide variability in clines, which has not been the focus of previous models and methods. We also illustrate how both selection and genetic drift contribute to variability in introgression among loci and how additional information can be used to help distinguish these contributions. We conclude by describing the promises and limitations of bgchm, comparing bgchm to other software for genomic cline analyses, and identifying areas for fruitful future development.

Confidence ellipses for simple regression parameters with Quasi-associated random errors

The work presented in this paper introduces a novel methodology for constructing confidence regions for linear regression parameters using ellipses, particularly in cases where the random errors are quasi-associated. Linear regression is widely employed in statistical analysis to predict a dependent variable using one or more independent variables. Traditionally, it is assumed that random errors in regression models follow a normal distribution. However, this assumption may not hold in many practical applications where errors exhibit dependencies. Thus, this study focuses on quasi-associated random variables, which include both positively and negatively associated variables.We derive exponential inequalities that allow the construction of confidence ellipses for least squares estimates of model parameters. This approach is applied to a Keynesian consumption function, which models the relationship between consumption and national income. Using data on monthly per capita income in Africa over 12 years, we demonstrate the effectiveness of our method in estimating regression parameters when the random errors are quasi-associated. The findings show that this technique can improve the accuracy of statistical models used in fields such as economics and engineering, especially in cases where the traditional assumptions of regression analysis are not met.

Probabilistic reliability model of electrical motors in submersible well pumping units used in the uranium mining by in-situ leaching

Relevance. A submersible electric motor is the most vulnerable component of an electric centrifugal pumping unit used in in-situ leaching uranium mining. The accuracy of calculating the need for new electric motors directly affects the profitability of the uranium production. Aim. Development of a probabilistic reliability model for a submersible electric motor that provides the calculation of its failure probability for the upcoming period of time and allows estimating with sufficient accuracy the number of motors required to replace the failed ones. Methods. Statistical methods, survival analysis, statistical hypothesis testing. Results and conclusions. The authors conducted a study of three probabilistic reliability models for electric motors of submersible well pumping units used in in-situ leaching uranium mining. As a result of the study, the maximum likelihood estimates of model parameters were determined for each model; the adequacy of the models under study was checked based on nonparametric goodness-of-fit tests. Despite the fact that the test results did not allow excluding any of the considered models, a model based on a mixture of two Weibull distributions was selected as a probabilistic reliability model demonstrating higher consistency with real data, compared to the other models. At the same time, the analysis of the components of the mixture distribution indicated the presence of a group of electric motors with an uncharacteristically low time-to-failure value compared to the average value calculated for the entire set of equipment under study, and made it possible to estimate the share of such motors, which amounted to 8% of the total population. Possible reasons explaining such heterogeneity of data, according to the authors, are hidden manufacturing defects or more severe operating conditions in which some submersible electric motors operate.

Thinking beyond the closure assumption: Designing surveys for estimating biological truth with occupancy models

Abstract Occupancy models estimate distributions of imperfectly detected species, but violations of the closure assumption can bias results. However, researchers working with mobile animals may find it impossible to eliminate such violations. Here, we tested the hypothesis that occupancy models fit to realistic sampling data can generate unbiased occupancy estimates for an itinerant Wood Thrush (Hylocichla mustelina) population. In 2013 and 2014, we tracked movements of 41 breeding Wood Thrush males. We modelled territory shift probabilities using logistic exposure models and within‐territory movements using continuous‐time stochastic process models. We then constructed an individual‐based model, simulated (1000 iterations) spatiotemporal locations for individuals and simulated sampling these populations using 162 different point count protocols with variable spatial (sampling radius and point placement method), and temporal (survey length, between‐survey intervals and number of surveys) characteristics. We compared occupancy estimates with true values of instantaneous, daily and seasonal occupancy from the simulations. We parameterized continuous time stochastic process models based on movements within 34 unique territories and estimated a daily territory shift probability of 0.0099 (95% CI: 0.0060, 0.0152). Simulated data indicated that estimates of occupancy ranged from 0.18 (0.06, 1.00) to 0.80 (0.71, 0.89) depending on protocol characteristics. Occupancy estimates increased with increasing survey radius, survey length and between‐survey interval. Protocols using shorter surveys and between‐survey intervals were good estimators for instantaneous occupancy (low bias and mean‐squared error) but poor estimators for daily and seasonal occupancy; longer surveys and intervals generated unbiased estimators of daily occupancy but underestimated seasonal occupancy. Logistic regression models that ignored imperfect detection outperformed occupancy models for estimating instantaneous occupancy but not daily or seasonal occupancy. For mobile animals, occupancy of sampling sites changes in space and time. Consequently, the spatial and temporal aspects of a sampling protocol have strong, but predictable, effects on occupancy model parameter estimates. Our results demonstrate that how these factors interact is critical for designing surveys that produce occupancy estimates representative of the biological process of interest to a researcher.

Are We Dosing Correctly? Population Pharmacokinetics of Cefepime in Critically Ill Pediatric Patients

Abstract Background Dosing guidelines of cefepime are well defined in healthy pediatric and adult populations but have not been extensively studied in critically ill pediatric patients. Patients who are critically ill may have significant alterations in antibiotic pharmacokinetics (PK) and pharmacodynamics (PD) due to many factors. Receipt of ECMO or CRRT may further alter PK/PD due to changes in clearance and volume of distribution and the depletion of plasma proteins. Since critically ill pediatric patients are likely to receive multiple courses of antimicrobials, optimization of drug dosing and delivery is critically important for individual patient outcomes. This study will test the hypothesis that the PK of cefepime is substantially altered in critically ill pediatric patients. Methods We prospectively enrolled patients in VUMC pediatric ICUs receiving cefepime, including those receiving ECMO or CRRT. Plasma samples were collected at opportune timepoints enriched for specific PK/PD metrics. Cefepime plasma concentrations were measured by LC-MS/MS. Weight, dose, interval, and administration time were extracted from the medical record. Monolix was used to fit population PK models using one and two-compartment models with a proportional error model. Covariate modeling was performed with a priori selected covariates: ECMO, CRRT, sex, race, ethnicity, gestational age, and creatinine clearance (CrCl). The final covariate model was used to perform probability of target attainment (PTA) analysis using Monte Carlo simulation. 6,000 subjects were simulated for each dosing regimen, with 3 weight categories (≤9 kg, 9-25 kg, and &amp;gt;25 kg) and 2 CrCl categories (≤90 mL/min and &amp;gt;90 mL/min). PTA was calculated over a grid of possible MIC values based on three targets, 65% fT&amp;gt;MIC, 100% fT&amp;gt;MIC, and 100% fT&amp;gt;4×MIC. Results Preliminary data from 84 pediatric participants receiving cefepime were analyzed. Of these, 9 received CRRT and 10 received ECMO. An average of 3 samples were collected per participant. A two compartment with proportional error model was selected as the base model. Population PK parameter estimates for the base model, base model with weight, and final covariate model were calculated. Inclusion of weight and CrCl significantly improved model fit. CRRT, ethnicity, and gestational age did significantly improve model fit, but their inclusion in the model did not provide evidence of being significantly better than the model with only weight and CrCl. The results from the PTA analysis are seen in Figure 1. We observed an overall ordering of PTA by dosing regimen across all three targets, with q8h 3-hour infusion having the highest PTA and q12h 30-minute infusion having the lowest PTA. Increased CrCl led to reduced PTA and as weight increased, PTA also increased. Conclusion This study will be among the first and largest to characterize cefepime PK in the critically ill pediatric population. Clinicians should incorporate local antibiograms with these population PK models to determine optimal dosing in critically ill pediatric patients. The use of extended infusions may be beneficial for PK/PD target achievement, particularly for resistant pathogens. Since clinical covariates affect PK parameters, this population may also benefit from therapeutic drug monitoring. Figure 1. Comparison of PTA among four dosing regimens of cefepime at targets of 65% fT&amp;gt;MIC, 100% fT&amp;gt;MIC, and 100% fT&amp;gt;4×MIC.

Bayesian parameter inference for epithelial mechanics

Cell-based mechanical models, such as the Cell Vertex Model (CVM), have proven useful for studying the mechanical control of epithelial tissue dynamics. We recently developed a statistical method called image-based parameter inference for formulating CVM model functions and estimating their parameters from image data of epithelial tissues. In this study, we employed Bayesian statistics to improve the utility and flexibility of image-based parameter inference. Tests on synthetic data confirmed that both our non-hierarchical and hierarchical Bayesian models provide accurate estimates of model parameters. By applying this method to Drosophila wings, we demonstrated that the reliability of parameter estimation is closely linked to the mechanical anisotropies present in the tissue. Moreover, we revealed that the cortical elasticity term is dispensable for explaining force-shape correlations in vivo. We anticipate that the flexibility of the Bayesian statistical framework will facilitate the integration of various types of information, thereby contributing to the quantitative dissection of the mechanical control of tissue dynamics.

A Bayesian hybrid method for the analysis of generalized linear models with missing-not-at-random covariates

Missing data handling is one of the main problems in modelling, particularly if the missingness is of type missing-not-at-random (MNAR) where missingness occurs due to the actual value of the observation. The focus of the current article is generalized linear modelling of fully observed binary response variables depending on at least one MNAR covariate. For the traditional analysis of such models, an individual model for the probability of missingness is assumed and incorporated in the model framework. However, this probability model is untestable, as the missingness of MNAR data depend on their actual values that would have been observed otherwise. In this article, we consider creating a model space that consist of all possible and plausible models for probability of missingness and develop a hybrid method in which a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is combined with Bayesian Model Averaging (BMA). RJMCMC is adopted to obtain posterior estimates of model parameters as well as probability of each model in the model space. BMA is used to synthesize coefficient estimates from all models in the model space while accounting for model uncertainties. Through a validation study with a simulated data set and a real data application, the performance of the proposed methodology is found to be satisfactory in accuracy and efficiency of estimates.

Reliability estimation and statistical inference under joint progressively Type-II right-censored sampling for certain lifetime distributions

In this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum–Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton–Raphson method, the stochastic expectation–maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request.

Reliability inference for dual constant-stress accelerated life test with exponential distribution and progressively Type-II censoring

Accelerated life test provides a feasible and effective way to rapidly derive lifetime information by exposing products to higher-than-normal operating conditions. However, most of the previous research on accelerated life test has focused on the application of a single stress factor and a traditional censoring scheme. This article considers the reliability inference for a dual constant-stress accelerated life test model with exponential distribution and progressively Type-II censoring. Point estimates for model parameters are provided using maximum likelihood estimation and the weighted least squares method based on random variable transformation. In addition, we construct asymptotic confidence intervals, approximate confidence intervals, and bootstrap confidence intervals for the parameters of interest. Finally, extensive simulation studies and an illustrative example are presented to investigate the performance of the proposed methods.

Determinants influencing alcohol-related two-vehicle crash severity: A multivariate Bayesian hierarchical random parameters correlated outcomes logit model

Alcohol-related driving remains a significant concern due to its profound association with the likelihood of traffic crashes and the severity of resulting injuries, especially between two vehicles. To investigate the determinants influencing the alcohol-related two-vehicle crash severity, a foundational framework employed was a multinomial logit model. Meanwhile, by incorporating random intercept from individual case and vehicle levels to accommodate unobserved heterogeneity, and covariance matrices to underscore correlated outcomes, a multivariate hierarchical random parameters correlated outcomes logit model was proposed. Additionally, to further explore the potential temporal instability of explanatory variables, a random slope from a per-year indicator was introduced into the model. Crash data from the US Statewide Integrated Traffic Records System (SWITRS) database spanning from January 1, 2016, to December 31, 2021, was used. Three crash injury severity categories were examined, encompassing severe injury, minor injury, and no injury, with characteristics related to the driver, vehicle, road, environment, crash, and time serving as explanatory variables. The model results highlighted significant heterogeneity, with each case and vehicle accounting for 56.9% of the total variance for minor injuries and 50.8% for severe injuries. Furthermore, a significant negative correlation was explicitly exhibited between minor injury and severe injury outcomes at the case level. In terms of potential temporal instability, we provided per-year (2016–2019) parameter estimates and identified significant instability for indicators such as non-intersection, broadside and head-on collisions, cloudy weather conditions, and drivers who had been drinking but were not under the influence. Considering the impact of the COVID-19 pandemic, we divided the accident time into pre-COVID and during-COVID periods, modeling parameter estimates for both periods. This analysis revealed significant instability in several factors influenced by the pandemic. Additionally, noteworthy disparities in the estimated results of explanatory variables emerged in comparison to those general two-vehicle crashes or alcohol-related crashes, providing valuable insights. For instance, drivers who had been drinking but were not under the influence were less likely to sustain severe injuries, but the probability of minor injuries increased. These findings underscore the significance of thorough investigations into the determinants of injury severity in alcohol-impaired two-vehicle crash severity, along with the temporal instability of such factors. They hold important implications for effective traffic safety management and the formulation of prohibitive countermeasures.