Nominal Level Research Articles

Type I Error Rates are Not Usually Inflated

The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin by introducing the concept of Type I error rates and distinguishing between statistical errors and theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ misinterpretation of statistical errors and their underestimation of theoretical errors.

Bootstrap Inference for Group Factor Models

Abstract Andreou et al. (2019) have proposed a test for common factors based on canonical correlations between factors estimated separately from each group. We propose a simple bootstrap test that avoids the need to estimate the bias and variance of the canonical correlations explicitly and provide high-level conditions for its validity. We verify these conditions for a wild bootstrap scheme similar to the one proposed in Gonçalves and Perron (2014). Simulation experiments show that this bootstrap approach leads to null rejection rates closer to the nominal level in all of our designs compared to the asymptotic framework.

Confidence interval estimation for reliability of a two parameter Weibull distribution under complete and censored samples

Estimating the reliability function of the two parameter Weibull distribution is a critical task in various fields, providing essential insights into product longevity and optimizing maintenance strategies. Due to its adaptable parameters namely scale parameter α and shape parameter β, the Weibull distribution models diverse failure behaviours, from early-life defects to wear-out periods. By evaluating reliability at key time phases namely early life (t < 0.1α), useful life (0.1α ≤ t ≤ α), and end-of-life (t > α), this estimation process supports quality control, operational forecasting, and end-of-life planning. Such reliability assessments help minimize operational disruptions, improve cost management, and support strategic planning across industries where dependability and lifecycle management are essential, such as in manufacturing, healthcare, and technology sectors. Although it holds practical significance, the estimation of confidence interval (CI) for the reliability function of two parameter Weibull distribution has been relatively underexplored in the literature. This paper presents a new approach for constructing CI for the reliability function of the Weibull distribution using the generalized variable (GV) technique, applicable to both complete samples and type II singly right-censored samples. The empirical evaluation of this method indicates that it provides coverage probabilities that are closely aligned with the nominal level, even when dealing with small uncensored samples (as small as 5) and censored samples where the proportion of censored observations can reach 70%. In comparison, traditional methods for the Weibull distribution tend to yield less reliable or widely varied coverage probabilities for complete samples. The findings are demonstrated through practical examples. Keywords: Reliability, Confidence interval, Generalized Variable approach, Censoring.

Misalignment analysis of WPT level 3/Z2-class of CirPT with DDPR and CirPR for EVs stationary charging.

Future inductive charging ports must possess the capability to charge any electric vehicle (EV), irrespective of the specific coil architecture it is equipped with. This study examines the misalignment scenarios of the global circular pad at transmitter side (CirPT) with circular receiver pad (CirPR) and a double-D receiver pad (DDPR). The CirPT, CirPR, and DDPR configurations for WPT3 (11.1kW) with ground clearance meeting the Z2-class specifications and above ground surface installation are built by utilizing circuit analysis and 3D-finite element simulations, as outlined by the Society of Automotive Engineering (SAE) J2954 standard. The simulated designs are employed to determine the frequency (f) and the compensating network components (CNCs) required to achieve optimal power transfer efficiency while maintaining nominal power levels. The analysis of misalignment scenarios involves examining various performance factors, including coupling coefficient (k), transmission power (Po), efficiency (η), and leakage electromagnetic fields (EMFs). These factors are assessed under conditions of ideal alignment, as well as various linear and angular misalignments within the inductive charging system. The results demonstrate that both the CirPR and DDPR configurations can successfully interface with the CirPT to provide the required Po to the EV battery with commendable efficiency. In perfect alignment, the efficiencies are 95.10% for the CirPT-CirPR model and 91.60% for the CirPT-DDPR model. In maximum misalignment, the efficiencies are 87.10% for the CirPT-CirPR model and 89.50% for the CirPT-DDPR model, all exceeding the acceptable threshold of 80%.

Germanium surface segregation in highly doped Ge:β-Ga2O3 grown by molecular beam epitaxy observed by synchrotron radiation hard x-ray photoelectron spectroscopy

We present a study of Ge segregation at the surface of highly germanium-doped gallium oxide (2.5 × 1020 cm−3 nominal doping level) grown by molecular beam epitaxy. We probed the dopant concentration as a function of depth by hard x-ray photoelectron spectroscopy and standard laboratory photoemission spectroscopy. We notably found that there is germanium segregation within the top 2 nm where its concentration is 3 times the nominal doping level. This increased dopant concentration leads to a threefold enhancement of surface conductivity. The results suggest a reliable method for delta doping for power electronics applications.

Analytic Challenges in Clinical Trials of Early Alzheimer’s Disease

Background: The heavily right-skewed data seen in recently reported Alzheimer’s disease (AD) clinical trials influenced treatment contrasts when data were analyzed via the typical mixed-effects model for repeated measures (MMRM). Methods: An MMRM analysis similar to what is commonly used in AD clinical trials was compared versus robust regression (RR) and the non-parametric Hodges–Lehman estimator (HL). Results: Results in simulated data patterned after AD trials showed that imbalance across treatment arms in the number of patients in the extreme right tail (those with rapid disease progression) frequently occurred. Each analysis method controlled Type I error at or below the nominal level. The RR analysis yielded smaller standard errors and more power than MMRM and HL. In data sets with appreciable imbalance in the number of rapid progressing patients, MMRM results favored the treatment arm with fewer rapid progressors. Results from HL showed the same trend but to a lesser degree. Robust regression yielded similar results regardless of the ratio of rapid progressors. Conclusions: Although more research is needed over a wider range of scenarios, it should not be assumed that MMRM is the optimal approach for trials in early Alzheimer’s disease.

A MR-PheWAS and bidirectional Mendelian randomization study: Exploring for causal relationships of pancreatic cancer.

It is unknown what causes pancreatic cancer. We conducted a phenome-wide Mendelian randomization analysis (MR-pheWAS), a bidirectional Mendelian study, and a systematic review of research in order to thoroughly investigate any causal association between pancreatic cancer and Atlas. We used phenome-wide Mendelian randomization analysis to test for associations between pancreatic cancer and 776 phenotypes (n = 452,264) of Atlas in the UK Biobank. Causality is confirmed by two-sample Mendelian randomization (MR) analysis using correlation found by false discovery rate correction. Simultaneously, a comprehensive evaluation of pancreatic cancer MR studies was conducted in order to complement our findings and harmonize the existing evidence. According to the inverse-variance-weighted model, a total of 41 out of 776 phenotypes had a nominal significance level (P < .05) genetic prediction association with pancreatic cancer. Only genetically predicted pancreatic cancer was shown to be linked with elevated eosinophil counts following false discovery rate correction (P = .031) when several tests were taken into account. Pancreatic cancer and eosinophils were shown to be positively causally associated to one another, establishing a self-loop, according to two-sample MR validation in the IEU database (OR = 1.011, 95% CI: 1.002-1.020, P = .010) (OR = 1.229, 95% CI: 1.037-1.458, P = .017). Although MR-pheWAS found a strong causal relationship between eosinophils and pancreatic cancer, it also found a negative exclusion value for each phenotype and a significant number of suggestive association phenotypes that offered guidance for further research.

The Remarkable X-Ray Spectra and Variability of the Ultraluminous Weak-line Quasar SDSS J1521+5202

We present a focused X-ray and multiwavelength study of the ultraluminous weak-line quasar (WLQ) SDSS J1521+5202, one of the few X-ray weak WLQs that is amenable to basic X-ray spectral and variability investigations. J1521+5202 shows striking X-ray variability during 2006–2023, by up to a factor of ≈32 in 0.5–2 keV flux, and our new 2023 Chandra observation caught it in its brightest X-ray flux state to date. Concurrent infrared/optical observations show only mild variability. The 2023 Chandra spectrum can be acceptably described by a power law with intrinsic X-ray absorption, and it reveals a nominal intrinsic level of X-ray emission relative to its optical/ultraviolet emission. In contrast, an earlier Chandra spectrum from 2013 shows apparent spectral complexity that is not well fit by a variety of models, including ionized absorption or standard Compton-reflection models. Overall, the observations are consistent with the thick-disk plus outflow model previously advanced for WLQs, where a nominal level of underlying X-ray emission plus variable absorption leads to the remarkable observed X-ray variability. In the case of J1521+5202, it appears likely that the outflow, and not the thick disk itself, lies along our line of sight and causes the X-ray absorption.

Development and comparison of model-integrated evidence approaches for bioequivalence studies with pharmacokinetic end points.

By applying nonlinear mixed-effect (NLME) models, model-integrated evidence (MIE) approaches are able to analyze bioequivalence (BE) data with pharmacokinetic end points that have sparse sampling, which is problematic for non-compartmental analysis (NCA). However, MIE approaches may suffer from inflation of type I error due to underestimation of parameter uncertainty and to the assumption of asymptotic normality. In this study, we developed a MIE BE analysis method that is based on a pre-defined model and consists of several steps including model fitting, uncertainty assessment, simulation, and BE determination. The presented MIE approach has several improvements compared with the previously reported model-integrated methods: (1) treatment, sequence, and period effects are only added to absorption parameters (such as relative bioavailability and rate of absorption) instead of all PK parameters; (2) a simulation step is performed to generate confidence intervals of the pharmacokinetic metrics for BE assessment; and (3) in an effort to maintain type I error, two more advanced parameter uncertainty evaluation approaches are explored, a nonparametric (case resampling) bootstrap, and sampling importance resampling (SIR). To evaluate the developed method and compare the uncertainty assessment methods, simulation experiments were performed for BE studies using a two-way crossover design with different amounts of information (sparse to rich designs) and levels of variability. Based on the simulation results, the method using SIR for parameter uncertainty quantification controls type I error at the nominal level of 0.05 (i.e., the significance level set for BE evaluation) even for studies with small sample size and/or sparse sampling. As expected, our MIE approach for BE assessment exhibited higher power than the NCA-based method, especially as the data becomes sparser and/or more variable.

A Comprehensive Monte Carlo Simulation Study on Multiple Comparison Methods after ANOVA

Multiple comparison methods are applied to control the type I error rate at the nominal level. In this study, we investigate the performance of multiple comparison methods after analysis of variance (ANOVA) is implemented under different conditions. We include Bonferroni, Holm, Hochberg, Hommel, Benjamini-Hochberg (BH), and Benjamini-Yekutieli (BY) correction methods. Monte-Carlo simulation study is applied to assess their performances under different patterns, including sample size and group number combinations. Wide inferences are drawn on considered methods, and suggestions are provided for selecting appropriate methods. Moreover, the methods are implemented on three different types of real-life data sets to emphasize the importance of these correction methods in the research.

Tolerance Intervals Under a Class of Unbalanced Linear Mixed Models

The study of tolerance intervals for linear mixed models under unbalanced data has been mainly focused on one-way random-effects models. In this article, we present a method to compute both one- and two-sided ( β , γ ) -tolerance intervals that is applicable to a more general class of unbalanced linear mixed models. The proposed method is based on the concept of generalized pivotal quantities and thus relies on the derivation of pivotal quantities that are shown to be independent within this particular class of models. The method employs Monte Carlo sampling methods to obtain realizations of the quantities needed to compute the tolerance intervals of interest. Extensive simulation studies confirm that coverage probabilities of the computed tolerance intervals are consistently close to their nominal levels. Furthermore, to showcase the application of our method in real-world scenarios, we provide illustrative examples of case studies that examine models falling within the specified class. Lastly, motivated by the prospective application of our method in drug development, we implement the proposed procedures to estimate shelf life of a drug product through tolerance intervals and unbalanced stability data.

Phenome-Wide Association Study of Latent Autoimmune Diabetes from a Southern Mexican Population Implicates rs7305229 with Plasmatic Anti-Glutamic Acid Decarboxylase Autoantibody (GADA) Levels.

Latent autoimmune diabetes in adults (LADA) is characterized by the presence of glutamate decarboxylase autoantibodies (GADA). LADA has intermediate features between type 1 diabetes and type 2 diabetes. In addition, genetic risk factors for both types of diabetes are present in LADA. Nonetheless, evidence about the genetics of LADA in non-European populations is scarce. This study aims to perform a genome-wide association study with a phenome-wide association study of LADA in a southeastern Mexican population. We included 59 patients diagnosed with LADA from a previous study and 3121 individuals without diabetes from the MxGDAR/ENCODAT database. We utilized the GENESIS package in R to perform the genome-wide association study (GWAS) of LADA and PLINK for the phenome-wide association study (PheWAS) of LADA features. Nine polymorphisms reach the nominal association level (1 × 10-5) in the GWAS. The PheWAS showed that rs7305229 is genome-wide and associated with serum GADA levels in our sample (p = 1.84 × 10-8). rs7305229 is located downstream of the FAIM2 gene; previous reports associate FAIM2 variants with childhood obesity, body mass index, body adiposity measures, lymphocyte CD8+ activity, and anti-thyroid peroxidase antibodies. Our findings reveal that rs7305229 affects the GADA levels in patients with LADA from southeastern Mexico. More studies are needed to determine if this risk genotype exists in other populations with LADA.

Robust Control Scheme for Optimal Power Sharing and Selective Harmonic Compensation in Islanded Microgrids

In power systems, nonlinear loads cause harmonic distortion, adversely affecting sensitive equipment such as induction motors, power electronics, and variable-speed drives. This paper presents a novel control strategy that integrates with existing hierarchical control systems to mitigate voltage imbalances and harmonic disturbances in AC-islanded microgrids. The proposed method utilizes selective harmonic order filtering through multiple second-order generalized integrators (MSOGI) to extract negative, positive, and harmonic order components. The distributed generation (DG) unit control mechanism is designed to immediately correct voltage imbalances and harmonic disruptions, distributing the compensatory load evenly to rectify real and reactive power imbalances and harmonic disturbances. The microgrid’s control architecture primarily includes droop controllers for real and reactive power of positive sequences, voltage and current regulation inner control loops, an additional loop for correcting imbalances and harmonics, and secondary controllers to maintain voltage magnitude and frequency at nominal levels, ensuring high-quality voltage at the point of common coupling (PCC). The effectiveness of this approach is demonstrated through simulation results on the MATLAB/Simulink platform, proving its ability to effectively mitigate voltage imbalances and harmonic issues with the total harmonic of voltage reduced to approximately THDv = 0.5% and voltage unbalance factor (VUF) within approximately 0.1%.

Rank-transformed subsampling: inference for multiple data splitting and exchangeable p-values

Abstract Many testing problems are readily amenable to randomized tests, such as those employing data splitting. However, despite their usefulness in principle, randomized tests have obvious drawbacks. Firstly, two analyses of the same dataset may lead to different results. Secondly, the test typically loses power because it does not fully utilize the entire sample. As a remedy to these drawbacks, we study how to combine the test statistics or p-values resulting from multiple random realizations, such as through random data splits. We develop rank-transformed subsampling as a general method for delivering large-sample inference about the combined statistic or p-value under mild assumptions. We apply our methodology to a wide range of problems, including testing unimodality in high-dimensional data, testing goodness-of-fit of parametric quantile regression models, testing no direct effect in a sequentially randomized trial and calibrating cross-fit double machine learning confidence intervals. In contrast to existing p-value aggregation schemes that can be highly conservative, our method enjoys Type I error control that asymptotically approaches the nominal level. Moreover, compared to using the ordinary subsampling, we show that our rank transform can remove the first-order bias in approximating the null under alternatives and greatly improve power.

A metabolomic profile of biological aging in 250,341 individuals from the UK Biobank

The metabolomic profile of aging is complex. Here, we analyse 325 nuclear magnetic resonance (NMR) biomarkers from 250,341 UK Biobank participants, identifying 54 representative aging-related biomarkers associated with all-cause mortality. We conduct genome-wide association studies (GWAS) for these 325 biomarkers using whole-genome sequencing (WGS) data from 95,372 individuals and perform multivariable Mendelian randomization (MVMR) analyses, discovering 439 candidate “biomarker - disease” causal pairs at the nominal significance level. We develop a metabolomic aging score that outperforms other aging metrics in predicting short-term mortality risk and exhibits strong potential for discriminating aging-accelerated populations and improving disease risk prediction. A longitudinal analysis of 13,263 individuals enables us to calculate a metabolomic aging rate which provides more refined aging assessments and to identify candidate anti-aging and pro-aging NMR biomarkers. Taken together, our study has presented a comprehensive aging-related metabolomic profile and highlighted its potential for personalized aging monitoring and early disease intervention.

Impact of wind turbine nominal power limitation over wind turbine blade remaining useful life and its economic consequences

The present paper investigates the effects of wind turbine nominal power limitation on the remaining useful life of turbine blades. It also looks at the economic impact of this limitation. In this context, the paper provides wind turbine owners and operators with an overview of how to potentially extend the remaining useful life of wind turbine blades and lays out the economic benefits that can be achieved via the modulation of nominal power. In investigating wind turbine blade damage, prior studies focused mainly on predictive models based on the 10 minutes SCADA data wind speed history, without however, trying to protract the remaining useful life of the blades. Only a handful of papers have explored the possibility of increasing the remaining useful life by adjusting the start-up and shutdown procedures with poor results. It would appear that wind turbine blade fatigue damage mainly increases when the wind turbine is in a power production regime, and the mechanical stresses associated with this regime are a function of the nominal power of the wind turbine. The present work therefore investigates the impacts of nominal power changes on both the remaining useful life of wind turbine blades and the economic value of the wind turbine in a bid to identify an optimal control mode. The wind turbine blade damage evaluation is based on 10 minutes SCADA data and the FAST simulation tool with the ultimate goal of providing wind turbine operators with an easy application. The damage evaluation is then applied considering different nominal power levels for the same wind turbine model in order to see the resulting impact on the remaining useful life. This project therefore takes a pioneering approach by proposing a remaining useful life optimization tool to wind turbine operators, in effect, a decision-making tool regarding which exploitation strategy to adopt.

Covariate-constrained randomization in cluster randomized 2 × 2 factorial trials: application to a diabetes prevention study

BackgroundCluster randomized trials (CRTs) are randomized trials where randomization takes place at an administrative level (e.g., hospitals, clinics, or schools) rather than at the individual level. When the number of available clusters is small, researchers may not be able to rely on simple randomization to achieve balance on cluster-level covariates across treatment conditions. If these cluster-level covariates are predictive of the outcome, covariate imbalance may distort treatment effects, threaten internal validity, lead to a loss of power, and increase the variability of treatment effects. Covariate-constrained randomization (CR) is a randomization strategy designed to reduce the risk of imbalance in cluster-level covariates when performing a CRT. Existing methods for CR have been developed and evaluated for two- and multi-arm CRTs but not for factorial CRTs.MethodsMotivated by the BEGIN study—a CRT for weight loss among patients with pre-diabetes—we develop methods for performing CR in 2 × 2 factorial cluster randomized trials with a continuous outcome and continuous cluster-level covariates. We apply our methods to the BEGIN study and use simulation to assess the performance of CR versus simple randomization for estimating treatment effects by varying the number of clusters, the degree to which clusters are associated with the outcome, the distribution of cluster level covariates, the size of the constrained randomization space, and analysis strategies.ResultsCompared to simple randomization of clusters, CR in the factorial setting is effective at achieving balance across cluster-level covariates between treatment conditions and provides more precise inferences. When cluster-level covariates are included in the analyses model, CR also results in greater power to detect treatment effects, but power is low compared to unadjusted analyses when the number of clusters is small.ConclusionsCR should be used instead of simple randomization when performing factorial CRTs to avoid highly imbalanced designs and to obtain more precise inferences. Except when there are a small number of clusters, cluster-level covariates should be included in the analysis model to increase power and maintain coverage and type 1 error rates at their nominal levels.

Multivariate normality tests with two-step monotone missing data: a critical review with emphasis on the different methods of handling missing values

Two-step monotone missing data is a special case of missing data that attracted the attention of researchers since it not only appears frequently in applications but also since under the hypothesis of multivariate normality a unique and explicit solution to the likelihood equations exists. This importance prompted Yamada et al. [Kurtosis tests for multivariate normality with monotone incomplete data. Test. 2015;24:532–557. doi: 10.1007/s11749-014-0423-1] and Kurita and Seo [Multivariate normality test based on kurtosis with two-step monotone missing data. J Multivar Anal. 2022;188:104–824. doi: 10.1016/j.jmva.2021.104824] to propose four procedures in total for testing multivariate normality with two-step monotone missing data. The aim of this paper is twofold. On the one, to compare, for the first time, the performance of the four aforementioned multivariate normality tests via a Monte Carlo study. The second aim of the paper is to compare the performance of the four existing testing procedures with the respective procedures derived as a combination of 12 popular methods for handling incomplete data and 6 multivariate normality tests for complete data. We show that in several cases the tests proposed by Yamada et al. [Kurtosis tests for multivariate normality with monotone incomplete data. Test. 2015;24:532–557. doi: 10.1007/s11749-014-0423-1] and Kurita and Seo [Multivariate normality test based on kurtosis with two-step monotone missing data. J Multivar Anal. 2022;188:104–824. doi: 10.1016/j.jmva.2021.104824] are unable to achieve the nominal significance level. At the same time, no single procedure was found to be the most powerful in all situations of multivariate alternatives considered. As a consequence, the use of specific combinations of methods of handling missing data and testing multivariate normality with complete data is recommended.

Uncertainty quantification and confidence intervals for naive rare-event estimators

Abstract We consider the estimation of rare-event probabilities using sample proportions output by naive Monte Carlo or collected data. Unlike using variance reduction techniques, this naive estimator does not have an a priori relative efficiency guarantee. On the other hand, due to the recent surge of sophisticated rare-event problems arising in safety evaluations of intelligent systems, efficiency-guaranteed variance reduction may face implementation challenges which, coupled with the availability of computation or data collection power, motivate the use of such a naive estimator. In this paper we study the uncertainty quantification, namely the construction, coverage validity, and tightness of confidence intervals, for rare-event probabilities using only sample proportions. In addition to the known normality, Wilson, and exact intervals, we investigate and compare them with two new intervals derived from Chernoff’s inequality and the Berry–Esseen theorem. Moreover, we generalize our results to the natural situation where sampling stops by reaching a target number of rare-event hits. Our findings show that the normality and Wilson intervals are not always valid, but they are close to the newly developed valid intervals in terms of half-width. In contrast, the exact interval is conservative, but safely guarantees the attainment of the nominal confidence level. Our new intervals, while being more conservative than the exact interval, provide useful insights into understanding the tightness of the considered intervals.

Methods of increasing the efficiency of energy supply to oil and gas industry enterprises

Realization of high-tech designs in gas and oil industry contributes to more efficient functioning of production. Development of quality minerals is not a scientific and technical progress, but a stable level indicator based on the general economic aspect.Therefore, the introduction of high quality updated technologies and additions to production functioning systems always leads to a greater need for their use. To maximize energy efficiency in gas and oil production, it is recommended to use high-quality autonomous power sources. The sets of optimization possibilities on algorithms of systems of distribution of power loads of electric transformer substations taking into account large productivity of producing wells at oil fields are developed. Recommendations on quality utilization, developed on the basis of long algorithms, allow to increase step-by-step nominal level of power loads at pumping units operation. It is proved that to maximize energy efficiency enterprises need to use their own high-quality autonomous power sources. The article considers the efficiency and cost-effective possibilities of production energyconsuming and quality functioning equipment in the oil and gas industry. In addition, taking into account the benefits on the basis of the study was carried out a largescale analysis of data on the characteristics of relative efficiency and reliability to the technical condition of gas turbine and gas piston power plants.