Interval Error Research Articles

Estimation of Reliability under Conditional Stress - Strength Setup based on Weibull Distribution

The Weibull distribution has been extensively studied and applied across various fields due to its versatility in modeling a wide range of phenomena, especially in reliability engineering, survival analysis, and lifetime modeling. The concept of Rl a,b , which represents a system's reliability in a conditional stress-strength setup, was proposed by Sabre and Khorshidian (2021). In this research, the problem of estimating reliability of the component is considered when strength variable X and stress variable Y follow independent Weibull distributions with common shapes and different scale parameters under conditional stress-strength setup. The maximum likelihood estimator, asymptotic confidence interval, Bootstrap estimators, Boot-p estimators, and Bayes estimator under-squared error loss function with associated highest posterior density interval are constructed for conditional stress-strength reliability. Simulation study is conducted to estimate mean square error (MSE) of estimator of conditional stress-strength reliability. The real data analysis is also carried out.

Bayesian Inference for Repeated Measures Under Informative Sampling

Survey data are often randomly drawn from an underlying population of inferential interest under a multistage, complex sampling design. A sampling weight proportional to the number of individuals in the population that each sampled individual represents is released. The sampling design is informative with respect to a response variable of interest if the variable correlates with the sampling weights. The distribution for the variables of interest differs in the sample and in the population, requiring correction to the sample distribution to approximate the population. We focus on model-based Bayesian inference for repeated (continuous) measures associated with each sampled individual. We devise a model for the joint estimation of response variable(s) of interest and sampling weights to account for the informative sampling design in a formulation that captures the association of the measures taken on the same individual incorporating individual-specific random-effects. We show that our approach yields correct population inference on the observed sample of units and compare its performance with competing method via simulation. Methods are compared using bias, mean square error, coverage, and length of credible intervals. We demonstrate our approach using a National Health and Nutrition Examination Survey dietary dataset modeling daily protein consumption.

Intelligent reinforcement training optimisation of dispatch strategy for provincial power grids with multi‐agent systems: Considering operational risks and backup availability

AbstractIn order to optimise resource allocation within the province, a two‐stage scheduling model for provincial‐level power grids, encompassing day‐ahead and intra‐day stages is proposed. Firstly, a Conditional Generative Adversarial Network is employed to generate scenarios for load and new energy output. Based on the generated scenario set, the model takes into account the uncertainty and permissible error intervals of new energy and load, utilising conditional value at risk to measure the system scheduling risk. In the day‐ahead stage, an optimisation model is proposed, considering intra‐provincial power purchase demands, with the goal of minimising system operating costs, including risk costs. It optimises day‐ahead scheduling and contingency plans to ensure economic efficiency and robustness of the system based on extreme scenarios. During the training phase, the dataset is enhanced using Conditional Generative Adversarial Network and updated daily, improving the training effectiveness of the multi‐agent proximal policy optimisation intra‐day scheduling model. In the intra‐day stage, the intra‐day scheduling model utilises ultra‐short‐term forecasting data as input to generate contingency plans for dispatching reserve units. Experiments conducted on the IEEE 39‐node system validate the feasibility and effectiveness of the proposed approach.

Is the difference real, is the difference relevant: the minimal detectable and clinically important changes in the Montreal Cognitive Assessment

Background and aimsThe Montreal Cognitive Assessment (MoCA) is a widely used instrument for assessing cognitive function in stroke survivors. To interpret changes in MoCA scores accurately, it is crucial to consider the minimal detectable change (MDC) and minimal clinically important difference (MCID). The aim was to establish the MDC and MCID of the MoCA within 6 months after stroke. MethodsThis cohort study analysed data from the EFFECTS trial. The MoCA was administered at baseline and at 6-month follow-up. The MDC was calculated as the upper limit of the 95 % confidence interval of the standard error of the MoCA mean. The MCID was determined using anchor-based and distribution methods. The visual analogue recovery scale of the Stroke Impact Scale (SIS [primary anchor]) and Euro Quality of Life-5 Dimensions index (EQ-5D [confirmatory anchor]) were used as anchors. The distribution-based method, the Cohen benchmark effect size was chosen. ResultsIn total, 1131 (mean age [SD], 71 [10.6] years) participants were included. The mean (SD) MoCA scores at admission and 6-month follow-up were 22 (5.2) and 25 (4.2), respectively. The MDC of the MoCA was 5.1 points. The anchor method yielded the MCIDs 2 and 1.6 points for SIS and EQ-5D, respectively. Using the distribution method, the MCID for the MoCA was 1 point. ConclusionsEven a small change in MoCA scores can be important for stroke survivors; however, larger differences are required to ensure that any difference in MoCA values is a true change and is not related to the inherent variation in the test. Due to small sample sizes, the results of the anchor analysis need to be interpreted with caution.

Flood prediction with optimized gated recurrent unit-temporal convolutional network and improved KDE error estimation

<abstract> <p>Flood time series forecasting stands a critical challenge in precise predictive models and reliable error estimation methods. A novel approach utilizing a hybrid deep learning model for both point and interval flood prediction is presented, enhanced by improved kernel density estimation (KDE) for prediction comparison and error simulation. Firstly, an optimized gated recurrent unit-time convolutional network (GRU-TCN) is constructed by tuning the internal structure of the TCN, the activation function, the L2 regularization, and the optimizer. Then, Pearson Correlation is used for feature selection, and the hyperparameters of the improved GRU-TCN are optimized by the subtraction-average-based optimizer (SABO). To further assess the prediction uncertainty, interval predictions are provided via Non-parametric KDE, with an optimized bandwidth setting for accurate error distribution simulation. Experimental comparisons are made on 5-year hydro-meteorological daily data from two stations along the Yangtze River. The proposed model surpasses long short-term memory network (LSTM), TCN, GRU, TCN-LSTM, and GRU-TCN, with a reduction of more than 13% in root mean square error (RMSE) and approximately 15% in mean absolute error (MAE), resulting in better interval estimation and error control. The improved kernel density estimation curves for the errors are closer to the mean value of the confidence intervals, better reflecting the trend of the error distribution. This research enhances the accuracy and reliability of flood predictions and improves the capacity of humans to cope with climate and environmental changes.</p> </abstract>

Malignant neoplasms of the respiratory tract and thoracic organs in the remote period in males of Altai krai affected by first nuclear test at Semipalatinsk test site

BACKGROUND: The study of remote effects of radiation exposure on tumor-related morbidity in population remains a matter of great social significance in Altai Krai.
 AIM: To investigate the incidence rate for malignant neoplasms of respiratory tract and thoracic organs in the remote period in the male population born in 1932–1949 and located in the zone of influence of the first nuclear test.
 METHODS: This retrospective cohort study was based on the analysis of anonymized data and surgical records on morphologically verified cases of primary malignant neoplasms in a male cohort for the period from 2007 to 2016. In this paper, we studied a cohort fixed by the date of the first nuclear test, with a total of 6383 male individuals. The main (exposed) cohort included 2291 men, while the control (non-exposed) cohort included 4092 men who lived in rural communities of the region that were not affected during the first nuclear test. The cohort included 156 cases of morphologically verified diagnosis of primary malignant neoplasms of the respiratory tract and thoracic organs (codes C30–C39 according to the International Classification of Diseases). Person-time incidence rate (PtR), standard error (mPtR) and confidence intervals (95% CI) were calculated. The incidence of respiratory and thoracic malignant neoplasms, structure and relative risk (RR) were assessed. Statistical processing of the data was performed using licensed Microsoft Office 2016 software.
 RESULTS: The number of person-years spent at risk for respiratory and thoracic malignancies in the male population in the main cohort was 16 731 person-years, and in the control cohort — 30 747 person-years. In the main cohort, PtR was 436.32×105 person-years, with an mPtR of 51.07 and 95% CI of 334.18–538.45; in the control cohort the PtR was 269.95×105 person-years with an mPtR of 29.63 and 95% CI of 210.68–329.21. The leading localizations of malignant neoplasms of the respiratory and thoracic organs in men in the main and control cohorts were bronchial and lung malignancies and laryngeal malignancies.
 CONCLUSIONS: An increased relative risk of respiratory and thoracic malignant neoplasms manifesting in the remote period in the male population born and living in rural areas of Altai Krai during the first nuclear test conducted at the Semipalatinsk test site was revealed: RR=1.616, 95% CI 1.180–2.214, with the standard error of relative risk equal to 0.160.

Reliability and validity of the Turkish version of the New Cleveland Clinic Colorectal Cancer Quality of Life Questionnaire.

This study aims to adapt and validate the Cleveland Clinic Colorectal Cancer Quality of Life Questionnaire (CCF-CaQL) in Turkish, addressing the significant need for reliable, language-specific QoL measures for colorectal cancer (CRC) in Turkiye. This effort fills a critical gap in CRC patient care, enhancing both patient-provider communication and disease-specific QoL assessment. The CCF-CaQL was translated into Turkish, verified for accuracy, and reviewed for clarity and relevance. Eligible patients who underwent colorectal surgery for cancer between July 2021 and July 2022 from six hospitals completed the CCF-CaQL and SF-36 questionnaires. For analysis, confirmatory factor analysis using Smart PLS 4 and descriptive statistics were employed. The questionnaire's reliability and validity were assessed using Cronbach alpha, composite reliability, and the heterotrait-monotrait (HTMT) ratio, along with multicollinearity checks and factor loadings. Nonparametric resampling was used for precise error and confidence interval calculations, and the Spearman coefficient and split-half method were applied for reliability testing. In the study involving 244 colorectal cancer patients, confirmatory factor analysis of the CCF-CaQL indicated effective item performance, with one item removed due to lower factor loading. The questionnaire exhibited high internal consistency, evidenced by a Cronbach alpha value of 0.909. Convergent validity was strong, with all average variance extracted (AVE) values exceeding 0.4. Discriminant validity was confirmed with HTMT coefficients below 0.9, and no significant multicollinearity issues were observed (VIF values < 10). Parallel testing with the SF-36 scale demonstrated moderate to very strong correlations, affirming the CCF-CaQL's comparability in measuring quality of life. The Turkish version of the CCF-CaQL was validated for assessing quality of life in colorectal cancer patients. This validation confirms its reliability and cultural appropriateness for use in Turkiye. The disease-specific nature of the CCF-CaQL makes it a useful tool in clinical and research settings, enhancing patient care by accurately monitoring treatment effects and interventions in the Turkish colorectal cancer patient population.

Сценарии за развитие на сектор „Биологично земеделие“ в светлината на ОСП 2023 – 2027 година

The research aims to make a scenario analysis that will show what changes, perspectives and trends would be expected in the development of organic farming (OF) in our country, related to the change of main factors, mechanisms and means of support in the policy and with the objectives of the EU Green Deal. The study of the scenarios in the organic farming sector, their evaluation and the measurement of the probability that each of the options will happen is indicative of the future development of this sector, of the opportunities and prospects for it. It follows a quantitative approach to measure the possible changes in the organic farming sector. It is based on and is part of the work on the research project “Perspectives for Bulgarian agriculture and rural areas in the context of the CAP 2021 – 2027 and the EU Recovery Plan”, developed by a team led by associate professor Dr. B. Ivanov, IAI, Agricultural Academy – Sofia in 2021 – 2022. The research is based on the methodology developed for the purposes of the above-mentioned project, using the relevant algorithm, and the main applied methods are comparative assessment, probabilistic study with covariances, descriptive analysis, indicator method, expert assessment and statistical methods for determining trends (Ivanov et al., 2023). When developing the forecast scenarios, to track the possible consequences and effects of assuming different options for the development of OF in our country, two groups of indicators have been used – result and derivative ones. The average scenario score was used as an indicator of how likely the different scenarios were to occur. The specific scenarios and the average scores are determined within limits, according to the standard error and confidence interval according to the methodology of the above-mentioned project. Although the overall probability of the proposed three scenarios (pessimistic, normal and optimistic), measured by the probability coefficient, is unsatisfactory – 0.43, as well as the average scores for the pessimistic and moderate scenarios, the average score for the optimistic scenario is considered satisfactory. From the presented assumptions, estimates and probability scenarios, it can be concluded that the assumed changes in the indicators for the development of organic agriculture lead to relatively close probabilities for the occurrence of the optimistic and moderate scenarios. However, the optimistic scenario has the highest percentage – 18%, followed by the moderate scenario – 16%. I.e. the probability that organic agriculture will develop by 2027 according to the optimistic scenario is the highest. The realization of such a scenario by 2027 would be positive for Bulgarian agriculture in general and for OF in particular. This coincides with the trends that have been noticed recently – there is an increased interest of society in consuming organic products; at the same time, a number of EC- documents set goals for increasing the areas managed by organic farming methods. The increased public interest and concern for the protection of the environment and the health of people and animals has provoked a number of measures in both EU and national policy related to the support of the sector of OF.

Research on the Design and Practice of Civics Teaching in College Physical Education Courses Based on VAR Modeling

Abstract In this paper, a penalty function is added in the construction of the VAR model to control the accuracy of the model prediction, and considering the nature of the correlation between the variables, a weight fusion with Laplace penalty is introduced to generate a sparse solution to complete the construction of the vector autoregressive model. The basic types of vector autoregressive models under panel data are divided, the number of parameters to be estimated is determined, the parameters of the vector autoregressive model are estimated by the generalized method of moments estimation, and the parameter fitting effect of the model is improved by the great likelihood parameter estimation method, and the vector autoregressive model for panel data is constructed. Based on the VAR model, we propose a design scheme for the teaching of Civics in college sports courses and analyze the development of sports + Civics and the teaching effect of the courses through simulation and empirical analysis. The results of the study showed that OSI and OPCI rejected the original hypothesis at the significance level of 5% after second-order differencing, at which time both p-values were less than 0.1, and the series was smooth. The elasticity coefficient of the starting value of the sports response path is 0.0342, and the error interval is [0.0564, 0.06], indicating that the future development of the scale of “Sports + Civics” is stable.

Clock synchronizing radio access networks to picosecond precision using optical clock distribution and clock phase caching

Performing positioning of future mobile devices using trilateration through radio access networks would provide a robust alternative to currently used global navigation satellite systems. However, the positioning accuracy is strongly dependent on the time synchronization accuracy of the antennas used as location reference points. Consequently, achieving sub-30 cm positioning accuracies requires the synchronization of radio access network antennas to sub-nanosecond accuracy. Here we show a clock phase synchronization and optical clock signal distribution approach to clock synchronization in radio access networks that achieves 0.98-ps root-mean-square precision clock synchronization, in a real-time field-trial demonstration on 37.6-km dark fiber, with optical clock frequency synchronization and clock phase caching operating using 25.6-Gb/s commercial transceivers. We quantify the clock synchronization performance of our approach using standard metrics, including time deviation (TDEV) and mean time interval error (MTIE). Furthermore, we estimate the impact of varying the phase update rate used in clock phase caching on the clock synchronization performance of our approach. Through our two combined approaches, we explore a route towards achieving sub-nanosecond clock synchronization in radio access networks.

Indirect measurement method for high frequency response of complex structure based on statistical energy analysis

The harsh working environments often make it difficult to measure high frequency responses of complex structures in the fields such as aerospace and aeronautic, which severely hinders the evaluation of structural performance and safety. An indirect measurement method is proposed to estimate the high frequency responses of non-measurable subsystems using a statistical energy analysis (SEA) framework. Whether or not the non-measurable subsystem includes input load, two indirect measurement approaches are developed by constructing an overdetermined problem and a well-posed problem respectively. Both utilize only the power flow balance equations of unexcited subsystems to solve the problems and thus do not require solving for input loads. The approaches are validated numerically and experimentally through case study of a rocket engine structure. Furthermore, the interval error analyses indicate that the approaches are robust against SEA modeling errors and response measuring errors.

Relative evaluation of probabilistic methods for spatio-temporal wind forecasting

Short-term wind power forecasting has become a de facto tool to better facilitate the integration of such renewable energy resources into modern power grids. Instead of point predictors, which produce single-value predictions for the expected power, probabilistic forecasts predict probability distributions over the expected power output or associated confidence intervals. In this study, three different parametric and non-parametric methods for uncertainty modelling in wind power forecasting were studied, namely quantile regression (QR), variational inference and a maximum likelihood estimation (MLE) method. Johnson’s SU distribution was studied as a novel candidate for modelling wind power, which is a transformed normal distribution that exhibits both skew and heavy tails. This was one of the first studies to provide a thorough investigation of Johnson’s SU distribution for uncertainty modelling in a complex deep learning framework for wind forecasting. It was found that Johsnon’s SU likelihood and QR-based models significantly outperformed models using Gaussian likelihoods, based on a range of quantitative metrics to evaluate probability distributions and qualitative investigation of produced forecasts. Variational inference models using Johnson’s SU likelihoods performed remarkably well, with near-perfect calibration and higher precision than models using any of the other methods for uncertainty modelling, as evaluated through the pinball loss, Average Coverage Error (ACE) and Prediction Interval Coverage Percentage (PICP) metric. With the superior performance of Johnson’s SU likelihood models, the study mainly contributes to the literature by introducing another candidate distribution for probabilistic wind forecasting, which is analytical, unbounded and easy to integrate into modern deep learning frameworks.

Seasonal autoregressive integrated moving average (SARIMA) time-series model for milk production forecasting in pasture-based dairy cows in the Andean highlands.

Milk production in the Andean highlands is variable over space and time. This variability is related to fluctuating environmental factors such as rainfall season which directly influence the availability of livestock feeding resources. The main aim of this study was to develop a time-series model to forecast milk production in a mountainous geographical area by analysing the dynamics of milk records thorough the year. The study was carried out in the Andean highlands, using time-series models of monthly milk records collected routinely from dairy cows maintained in a controlled experimental farm over a 9-year period (2008-2016). Several statistical forecasting models were compared. The Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percent Error (MAPE) were used as selection criteria to compare models. A relation between monthly milk records and the season of the year was modelled using seasonal autoregressive integrated moving average (SARIMA) methods to explore temporal redundancy (trends and periodicity). According to white noise residual test (Q = 13.951 and p = 0.052), Akaike Information Criterion and MAE, MAPE, and RMSE values, the SARIMA (1, 0, 0) x (2, 0, 0)12 time-series model resulted slightly better forecasting model compared to others. In conclusion, time-series models were promising, simple and useful tools for producing reasonably reliable forecasts of milk production thorough the year in the Andean highlands. The forecasting potential of the different models were similar and they could be used indistinctly to forecast the milk production seasonal fluctuations. However, the SARIMA model performed the best good predictive capacity minimizing the prediction interval error. Thus, a useful effective strategy has been developed by using time-series models to monitor milk production and alleviate production drops due to seasonal factors in the Andean highlands.

Statistics for quantifying aging in time transfer system delays

Residual time delays in time transfer systems such as two-way satellite time and frequency transfer (TWSTFT), or GPS carrier phase (GPSCP) change over time. A double difference such as TWSTFT—GPSCP provides information on the changes in the relative time delays of the two systems. These changes are referred to as aging or time dispersion. A first difference statistic, RMS time interval error, TIERMS, provides the RMS time dispersion. The time deviation statistic (TDEV) or a variation on the Allan deviation (ADEV), referred to here as ADEVS, provide information on the nature of the random fluctuations in aging. This paper describes analytical and Monte Carlo techniques used to estimate the aging (time dispersion) from TDEV or ADEVS statistics, and finds that the aging can be more than a factor of four larger than TDEV or ADEVS. The use of ADEVS is recommended over TDEV since it is sensitive to time drift.

Longitudinal plasmode algorithms to evaluate statistical methods in realistic scenarios: an illustration applied to occupational epidemiology

IntroductionPlasmode simulations are a type of simulations that use real data to determine the synthetic data-generating equations. Such simulations thus allow evaluating statistical methods under realistic conditions. As far as we know, no plasmode algorithm has been proposed for simulating longitudinal data. In this paper, we propose a longitudinal plasmode framework to generate realistic data with both a time-varying exposure and time-varying covariates. This work was motivated by the objective of comparing different methods for estimating the causal effect of a cumulative exposure to psychosocial stressors at work over time.MethodsWe developed two longitudinal plasmode algorithms: a parametric and a nonparametric algorithms. Data from the PROspective Québec (PROQ) Study on Work and Health were used as an input to generate data with the proposed plasmode algorithms. We evaluated the performance of multiple estimators of the parameters of marginal structural models (MSMs): inverse probability of treatment weighting, g-computation and targeted maximum likelihood estimation. These estimators were also compared to standard regression approaches with either adjustment for baseline covariates only or with adjustment for both baseline and time-varying covariates.ResultsStandard regression methods were susceptible to yield biased estimates with confidence intervals having coverage probability lower than their nominal level. The bias was much lower and coverage of confidence intervals was much closer to the nominal level when considering MSMs. Among MSM estimators, g-computation overall produced the best results relative to bias, root mean squared error and coverage of confidence intervals. No method produced unbiased estimates with adequate coverage for all parameters in the more realistic nonparametric plasmode simulation.ConclusionThe proposed longitudinal plasmode algorithms can be important methodological tools for evaluating and comparing analytical methods in realistic simulation scenarios. To facilitate the use of these algorithms, we provide R functions on GitHub. We also recommend using MSMs when estimating the effect of cumulative exposure to psychosocial stressors at work.

A 62 ppm MDR Deviation and Sub-250 ns MTIE Railway Balise

A balise is a specialized device utilized for train communication and control. However, existing balises are composed of separate components, resulting in high production costs, low integration, and significant room for improvement in stability. We propose an integrated solution, to enhance the integration of balises, reducing the number of discrete components. Additionally, we propose a feedback-enabled energy extraction circuit with a limiter-based startup circuit, to enhance the stability of the balise system. The prototype was fabricated using 180 nm high voltage(HV) complementary metal oxide semiconductor(CMOS) technology. Once implemented in the balise, the number of discrete components in the system is reduced by 25%, and the system can start up within 20 ms and operate stably. The mean data rate (MDR) deviation of the balise is only 62 ppm, which is 69% lower than that specified in the test specification for the Eurobalise form–fit–function interface specification (FFFIS), and the maximum time interval error (MTIE) is less than 250 ns.

A-090 Impact of Changing Total Calcium Methodology on Observed Hypercalcemia Prevalence at an Academic Health System

Abstract Background The UC Davis Health clinical chemistry laboratory implemented a new total laboratory automation (Roche Diagnostics, Indianapolis, IN) system in February 2022—replacing a prior system (Beckman Coulter, Brea, CA) that was in place since 2007. In August 2022, primary care and endocrinology providers contacted laboratory leadership to report an increase in patients with calcium values flagged as abnormally elevated, resulting in increased communications from patients to primary care providers and increased referrals to endocrinology. This change in testing methodology produced a shift in the upper reference interval limit from 10.5 mg/dL to 10.0 mg/dL. The new testing methodology determined total calcium photometrically vs by indirect potentiometry via the outgoing method. We hypothesize photometric-based total calcium measurements to be more sensitive. Methods We conducted a retrospective study to investigate the reported increase in hypercalcemic values—our electronic health system’s (EHR) EPIC’s self-service reporting tool (“SlicerDicer”) was utilized for data acquisition and visualization. Although the reference interval had already been verified prior to implementation, a “normal study” study was conducted to re-confirm manufacturer derived intervals. One hundred thirty-six samples from apparently healthy adults (age ≥ 18 years) were banked for this study. Parathyroid hormone (PTH) values were then measured to confirm levels were within normal limits. Additional observational data was also collected for PTH levels pre- and post-new automation line implementation. Quality control (QC) and proficiency testing (PT) data was also reviewed during this time. Results In the four months preceding implementation of the new automation line, 1211 patients had total calcium values flagged as elevated, compared to 5146 patients during a similar post implementation time period (302.8/month vs 1286.5/month), or an increase of 324.9%. During these same time periods, patients with abnormal PTH were observed at 270.8/month pre-implementation compared to 393/month post (45.2% increase). An increase in patients with concurrently performed calcium and PTH was also observed (30.3%; 583.8/month vs 760.8/month), though a greater increase was seen in patients with concurrently elevated calcium and abnormal PTH (294.5%; 22.8/month vs 89.8/month). One hundred twenty samples with normal PTH values were included in the total calcium normal study, which reported a mean (SD) value of 9.3 (0.33) mg/dL, confirming the manufacturer-derived intervals of 8.7–10 mg/dL. No biases, shifts, or trends were observed in PT or QC data in the four months preceding and post analyzer change. Conclusion Increased hypercalcemic events post-automation line implementation is likely not due to analytical error or inappropriate reference intervals, but rather due to increased sensitivity of methodology. Hypercalcemic cases determined by our new methodology were corroborated by corresponding abnormal PTH values. The perceived increased sensitivity could be due to known limitations of indirect potentiometry (i.e., lack of selectivity, difficulty detecting all forms of calcium, etc.). Further investigation is warranted to determine the overall impact of changing this one assay on the health system.

A Generalized Bootstrap Procedure of the Standard Error and Confidence Interval Estimation for Inverse Probability of Treatment Weighting

The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient resampling scheme and untreated oversized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error and confidence intervals of the IPTW approach. Compared with the OB procedure and other three procedures in comparison, the GB procedure has the highest precision and yields conservative standard error estimates. As a result, the GB procedure produces short confidence intervals with highest coverage rates. We demonstrate the effectiveness of the GB procedure via two simulation studies and a dataset from the National Educational Longitudinal Study-1988 (NELS-88).

Including supramaximal verification reduced uncertainty in VO2peak response rate.

Many reports describe using a supramaximal verification phase-exercising at a power output higher than the highest power output recorded during an incremental cardiopulmonary test-to validate VO2max. The impact of verification phases on estimating the proportion of individuals who increased VO2peak in response to high-intensity interval training (HIIT) remains an underexplored area in the individual response literature. This analysis investigated the influence of same-day and separate-day verification phases during repeated measurements (incremental tests-INCR1 and INCR2; incremental tests+supramaximal verification phases-INCR1+and INCR2+) of VO2peak on typical error (TE) and the proportion of individuals classified as responders (i.e., the response rate) following 4 weeks of HIIT (n=25) or a no-exercise control period (n=9). Incorporation of supramaximal verification consistently reduced the standard deviation of individual response, TE, and confidence interval (CI) widths. However, variances were statistically similar across all groups (p>0.05). Response rates increased when incorporating either one (INCR1 to INCR1+; 24%-48%, p=0.07) or two (INCR2 to INCR2+; 28%-48%, p=0.063) supramaximal verification phases. However, response rates remained unchanged when either zero-based thresholds or smallest worthwhile difference response thresholds were used (50% and 90% CIs, all p>0.05). Supramaximal verification phases reduced random variability in VO2peak response to HIIT. Compared with separate-day testing (INCR2 and INCR2+), the incorporation of a same-day verification (INCR1+) reduced CI widths the most. Researchers should consider using a same-day verification phase to reduce uncertainty and better estimate VO2peak response rate to HIIT.

Load-independent multi-objective sensor placement method for localization and reconstruction of external excitations under interval uncertainties

The direct measurement of external excitations under operation conditions remains challenging in many engineering applications. This study proposes a method of optimal sensor placement for the best localization and reconstruction of external excitations when considering multi-source uncertainties. The excitation inversion is achieved in the framework of minimizing the discrepancy between the forward and inversed modal loads. To accurately obtain the modal force in the time-domain excitation reconstruction algorithm, three combined indicators of the interested modal matrix are defined, which integrate measures of effectiveness, stability, orthogonality, and robustness of inverse modal transformation. The optimal sensor placement is determined by multi-objective particle swarm optimization and Pareto optimal solution. In addition, to alleviate the computational burden of loading localization, a surrogate model based on an interval kriging interpolation model and sequential sampling strategies is established for the forward modal forces. And a time-dependent interval error of modal forces inspired by the theory of second-order narrow bounds in system reliability is developed to guide the inversion process. Notably, the developed sensor selection and excitation inversion methods are independent of the type, location, and time evolution of external excitations. Eventually, two numerical examples and an experimental case are discussed to demonstrate the validity and feasibility of the developed approach.