Total Least Squares Research Articles

Quantifying the relationship between bone and soft tissue measures within the rhesus macaques of Cayo Santiago.

Interpretations of the primate and human fossil record often rely on the estimation of somatic dimensions from bony measures. Both somatic and skeletal variation have been used to assess how primates respond to environmental change. However, it is unclear how well skeletal variation matches and predicts soft tissue. Here, we empirically test the relationship between tissues by comparing somatic and skeletal measures using paired measures of pre- and post-mortem rhesus macaques from Cayo Santiago, Puerto Rico. Somatic measurements were matched with skeletal dimensions from 105 rhesus macaque individuals to investigate paired signals of variation (i.e., coefficients of variation, sexual dimorphism) and bivariate codependence (reduced major axis regression) in measures of: (1) limb length; (2) joint breadth; and (3) limb circumference. Predictive models for the estimation of soft tissue dimensions from skeletons were built from Ordinary Least Squares regressions. Somatic and skeletal measurements showed statistically equivalent coefficients of variation and sexual dimorphism as well as high epiphyses-present ordinary least square (OLS) correlations in limb lengths (R2 >0.78, 0.82), joint breadths (R2 >0.74, 0.83) and, to a lesser extent, limb circumference (R2 >0.53, 0.68). Skeletal measurements are good substitutions for somatic values based on population signals of variation. OLS regressions indicate that skeletal correlates are highly predictive of somatic dimensions. The protocols and regression equations established here provide a basis for reliable reconstruction of somatic dimension from catarrhine fossils and validate our ability to compare or combine results of studies based on population data of either hard or soft tissue proxies.

Disentangling the effect of growth from development in size-related trait scaling relationships.

In plant ecology, the terms growth and development are often used interchangeably. Yet these constitute two distinct processes. Plant architectural traits (e.g. number of successive forks) can estimate development stages. Here, we show the importance of including the effect of development stages to better understand size-related trait scaling relationships (i.e. between height and stem diameter). We focused on one common savanna woody species (Senegalia nigrescens) from the Greater Kruger Area, South Africa. We sampled 406 individuals that experience different exposure to herbivory, from which we collected four traits: plant height, basal stem diameter, number of successive forks (proxy for development stage), and resprouting. We analysed trait relationships (using standardized major axis regression) between height and stem diameter, accounting for the effect of ontogeny, exposure to herbivory, and resprouting. The number of successive forks affects the scaling relationship between height and stem diameter, with the slope and strength of the relationship declining in more developed individuals. Herbivory exposure and resprouting do not affect the overall height-diameter relationship. However, when height and stem diameter were regressed separately against number of successive forks, herbivory exposure and resprouting had an effect. For example, resprouting individuals allocate more biomass to both primary and secondary growth than non-resprouting plants in more disturbed conditions. We stress the need to include traits related to ontogeny so as to disentangle the effect of biomass allocation to primary and secondary growth from that of development in plant functional relationships.

Functional traits are more strongly correlated with biomass than diameter growth

Abstract The functional basis of tree growth is often evaluated based on trunk diameter even though diameter is only one dimension of growth that may not be an integrative measure of resource allocation. We tested the hypothesis that growth—functional trait relationships are stronger when key sources of variation in tree growth are also accounted for, namely tree height and DBH, as well as size‐related variation in wood density and seed production using data from 3881 trees of 24 species in a subtropical forest using ordinary least square regression and standard major axis regression. Wood density varied with tree size for 14 of 24 species, generally increasing with size. For 18 of 24 species, the correlations of leaf mass per area and an index of photosynthetic investment (PI) with biomass growth was stronger than with diameter growth rate. Juveniles did not show stronger relationships than adults but biomass growth adding up with seed production showed stronger relationships with PI than biomass growth alone for three of eight species. Synthesis. Thus, our study helps resolve a paradox of trait‐based ecology, that is, weak growth—trait relationships, as stronger relationships emerged when accounting for more sources of intraspecific, among‐tree variation in resource allocation.

A correction method of magnetic gradient tensor system to improve magnet localization accuracy

The magnetic gradient tensor systems using vector magnetic sensors are easily affected by single sensor error and sensor array misalignment, significantly affecting target localization accuracy. To address this problem, based on the differential measurement theory of magnetic gradient tensor, a vector sensor error model was established, and the single sensor errors were corrected using the total least square (TLS) ellipsoid fitting method. Besides, a misalignment error correction model for the sensor is obtained by constructing a rotation matrix for the magnetic sensor's three-axis orthogonal coordinate system transformation, and the tensor system can be aligned by performing the TLS estimation of the rotation angle. After calibration, the experimental results show that the outputs of each sensor have high coincidence and coaxiality. The root mean square error (RMSE) of the total magnetic intensity (TMI) is reduced to within 100 nT, and the RMSE of the tensor component is reduced to within 85 nT/m. Within a range of 5 m, the magnetic target positioning error is reduced to less than 25.1 cm. This technology can improve the measurement accuracy of the magnetic gradient tensor system with high stability and reliability.

Automated inversion time selection for late gadolinium–enhanced cardiac magnetic resonance imaging

ObjectivesTo develop and share a deep learning method that can accurately identify optimal inversion time (TI) from multi-vendor, multi-institutional and multi-field strength inversion scout (TI scout) sequences for late gadolinium enhancement cardiac MRI.Materials and methodsRetrospective multicentre study conducted on 1136 1.5-T and 3-T cardiac MRI examinations from four centres and three scanner vendors. Deep learning models, comprising a convolutional neural network (CNN) that provides input to a long short-term memory (LSTM) network, were trained on TI scout pixel data from centres 1 to 3 to identify optimal TI, using ground truth annotations by two readers. Accuracy within 50 ms, mean absolute error (MAE), Lin’s concordance coefficient (LCCC) and reduced major axis regression (RMAR) were used to select the best model from validation results, and applied to holdout test data. Robustness of the best-performing model was also tested on imaging data from centre 4.ResultsThe best model (SE-ResNet18-LSTM) produced accuracy of 96.1%, MAE 22.9 ms and LCCC 0.47 compared to ground truth on the holdout test set and accuracy of 97.3%, MAE 15.2 ms and LCCC 0.64 when tested on unseen external (centre 4) data. Differences in vendor performance were observed, with greatest accuracy for the most commonly represented vendor in the training data.ConclusionA deep learning model was developed that can identify optimal inversion time from TI scout images on multi-vendor data with high accuracy, including on previously unseen external data. We make this model available to the scientific community for further assessment or development.Clinical relevance statementA robust automated inversion time selection tool for late gadolinium–enhanced imaging allows for reproducible and efficient cross-vendor inversion time selection.Key Points• A model comprising convolutional and recurrent neural networks was developed to extract optimal TI from TI scout images.• Model accuracy within 50 ms of ground truth on multi-vendor holdout and external data of 96.1% and 97.3% respectively was achieved.• This model could improve workflow efficiency and standardise optimal TI selection for consistent LGE imaging.

An improved solution for total least squares collocation in the EIV-model with random effects

The total least squares (TLS) method within the Errors-In-Variables (EIV) model has been comprehensively investigated in measurement and its relevant fields. However, when prior information is considered, existing solutions in the EIV model with random effects (EIV-REM) have many shortcomings, which limit the application of this approach. We have developed the total least squares collocation (TLSC) solution based on general adjustment, where prior information is added to the functional model in the form of pseudo-observations. The accuracy of the estimated parameters is evaluated, and our TLSC solution is converted into a recursive form. The proposed methodology is applied to a 3D datum transformation and an autoregression model. The results for the datum transformation show that our proposed TLSC solution provides more precise estimates than the traditional least squares (LS) and TLS methods. The results for the autoregression model show that TLSC yields similar performance to the batch solution of TLS, but has advantages in terms of computational complexity.

Robust battery lifetime prediction with noisy measurements via total-least-squares regression

—Machine learning technologies have gained significant popularity in rechargeable battery research in recent years, and have been extensively adopted to construct data-driven solutions to tackle multiple challenges for energy storage in embedded computing systems. An important application in this area is the machine learning-based battery lifetime prediction, which formulates regression models to estimate the remaining lifetimes of batteries given the measurement data collected from the testing process. Due to the non-idealities in practical operations, these measurements are usually impacted by various types of interference, thereby involving noise on both input variables and regression labels. Therefore, existing works that focus solely on minimizing the regression error on the labels cannot adequately adapt to the practical scenarios with noisy variables. To address this issue, this study adopts total least squares (TLS) to construct a regression model that achieves superior regression accuracy by simultaneously optimizing the estimation of both variables and labels. Furthermore, due to the expensive cost for collecting battery cycling data, the number of labeled data samples used for predictive modeling is often limited. It, in turn, can easily lead to overfitting, especially for TLS, which has a relatively larger set of problem unknowns to solve. To tackle this difficulty, the TLS method is investigated conjoined with stepwise feature selection in this work. Our numerical experiments based on public datasets for commercial Lithium-Ion batteries demonstrate that the proposed method can effectively reduce the modeling error by up to 11.95 %, compared against the classic baselines with consideration of noisy measurements.

Not all sweetness and light: Non‐structural carbohydrate storage capacity in tree stems is decoupled from leaf but not from root economics

ABSTRACT Non‐structural carbohydrates (NSC) are considered as indicators of the balance between tree carbon sources and sinks and reflect functional strategies throughout different biomes. However, little is known about the contribution of NSC to tree economics, and in particular, whether leaf, stem and coarse root traits co‐ordinate together into a whole‐tree economics spectrum. Twenty‐four functional traits (including NSC content) were measured in leaves, stem and coarse root xylem of up to 90 angiosperm tree species in temperate, Mediterranean and tropical climates. By performing principal component analysis and standardized major axis regression, we explored the relationships between NSC and other functional traits, as well as the effects of climate and phylogeny on these relationships. Our results revealed a covariation between leaf and coarse root NSC content and leaf economic traits, whereas stem NSC content was largely decoupled from the leaf economics spectrum that was mostly driven by leaf nitrogen content and leaf mass per area. Coarse root xylem traits were closely correlated with leaf traits, while most stem xylem traits were independent from the leaf economics spectrum but covaried with coarse root traits. Trade‐offs among traits in tropical species opposed those from other climates. Evolutionary history affected relationships among certain traits but did not change overall patterns. We conclude that due to leaf habit, an extended growing season and heightened defences, tropical species form distinct conservative resource acquisition strategies. Across all climates, as the stem must provide an efficient transport route between roots and leaves, while maintaining the display of branch and leaf organs, stem xylem design and NSC storage capacity lead to a stem economics spectrum that is largely independent from the leaf spectrum, but is coupled with that of coarse roots due to anatomical continuity. Read the free Plain Language Summary for this article on the Journal blog.

Leaf-age and petiole biomass play significant roles in leaf scaling theory.

Foliage leaves are essential for plant survival and growth, and how plants allocate biomass to their leaves reveals their economic and ecological strategies. Prior studies have shown that leaf-age significantly influences leaf biomass allocation patterns. However, unravelling the effects of ontogeny on partitioning biomass remains a challenge because it is confounded by the effects of environmental factors. Here, we aim to elucidate whether leaf-age affects the allocation to the lamina and petiole by examining leaves of known age growing in the same general environmental context. We sampled 2698 Photinia serratifolia leaves developing in the same environment from April to November 2021, representing eight leaf-ages (n > 300 for each leaf-age). Petiole and lamina biomass, and lamina area were measured to evaluate the scaling relationships using reduced major axis regression protocols. The bootstrap percentile method was used to determine the differences in scaling exponents among the different leaf-ages. ANOVA with Tukey's HSD was used to compare the ratios of petiole and lamina biomass to lamina area across the leaf-ages. Correlation tests were used to determine if exponents, intercepts, and ratios differed significantly across the different leaf-ages. The data indicated that (i) the ratio of petiole and lamina biomass to lamina area and the scaling exponent of lamina biomass versus lamina area correlate positively with leaf-age, and (ii) the scaling exponent of petiole biomass versus lamina area correlates negatively with leaf-age. Leaf maturation process involves an inverse proportional allocation between lamina and petiole biomass for expanding photosynthetic area. This phenomenon underscores the effect of leaf-age on biomass allocation and the importance of adopting an ontogenetic perspective when entertaining plant scaling theories and unravelling the principles governing shifts in biomass allocation throughout the leaf lifespan.

Total least squares bias in climate fingerprinting regressions with heterogeneous noise variances and correlated explanatory variables

AbstractRegression‐based “fingerprinting” methods in climate science employ total least squares (TLS) or orthogonal regression to remedy attenuation bias arising from measurement error due to reliance on climate model‐generated explanatory variables. Proving the consistency of multivariate TLS requires assuming noise variances are equal across all variables in the model. This assumption has been challenged empirically in the climate context but little is known about TLS biases when the assumption is violated. Monte Carlo analysis is used herein to examine coefficient biases when the noise variances are not equal. The analysis allows the explanatory variables to be negatively correlated which is typical in climate applications. Ordinary least squares (OLS) exhibits the expected attenuation bias which vanishes as the noise variances on the explanatory variables disappear. In some cases, TLS corrects attenuation bias but more typically imparts large and generally positive biases. OLS performs well when the true value of whereas TLS performs quite poorly. This implies that TLS is not well suited for tests of the null. When TLS tends to exhibit opposite biases to OLS. Diagnostic information specific to each data sample should be consulted before using TLS to avoid spurious inferences and replacing OLS attenuation bias with other, potentially larger biases.

Effects of the ABCC8 R1420H loss-of-function variant on beta-cell function, diabetes incidence, and retinopathy

IntroductionThe ABCC8 gene regulates insulin secretion and plays a critical role in glucose homeostasis. The effects of an ABCC8 R1420H loss-of-function variant on beta-cell function, incidence of type 2 diabetes,...

Direction of Arrival Estimation With Gain-Phase Uncertainties in Unknown Nonuniform Noise

This paper considers the problem of direction-of-arrival (DOA) estimation for narrowband source signals under the coexistence of gain-phase uncertainties and nonuniform noise. Firstly, by exploiting the low-rank property of the covariance of signal components, and the diagonal property of noise covariance, an optimization problem with low-rank constraints is formulated to estimate the nonuniform noise covariance matrix, which is then solved efficiently by the alternating direction method of multipliers (ADMM). Secondly, a linear transformation operator is employed to construct a rank reduction (RARE) estimator, and subsequently an initial DOA and gain-phase uncertainties are obtained via one-dimensional (1-D) spectral search. With initial estimates, an augmented DOA estimation is finally achieved by constructing a weighted and structured sparse total least-squares (WSS-TLS) optimization problem, which is solved using the block coordinate descent algorithm. Simulation results show the superior performance of the proposed method, and it achieves better tradeoff between computational complexity and performance, compared to existing methods.

Improving accuracy in state of health estimation for lithium batteries using gradient-based optimization: Case study in electric vehicle applications.

Significant improvements in battery performance, cost reduction, and energy density have been made since the advancements of lithium-ion batteries. These advancements have accelerated the development of electric vehicles (EVs). The safety and effectiveness of EVs depend on accurate measurement and prediction of the state of health (SOH) of lithium-ion batteries; however, this process is uncertain. In this study, our primary goal is to enhance the accuracy of SOH estimation by reducing uncertainties in state of charge (SOC) estimation and measurements. To achieve this, we propose a novel method that utilizes the gradient-based optimizer (GBO) to evaluate the SOH of lithium batteries. The GBO minimizes a cost with the aim of selecting the optimal candidate for updating the SOH through a memory-fading forgetting factor. We evaluated our method against four robust algorithms, namely particle swarm optimization-least square support vector regression (PSO-LSSV), BCRLS-multiple weighted dual extended Kalman filtering (BCRLS-MWDEKF), Total least square (TLS), and approximate weighted total least squares (AWTLS) in hybrid electric vehicle (HEV) and electric vehicle (EV) applications. Our method consistently outperformed the alternatives, with the GBO achieving the lowest maximum error. In EV scenarios, GBO exhibited maximum errors ranging from 0.65% to 1.57% and mean errors ranging from 0.21% to 0.57%. Similarly, in HEV scenarios, GBO demonstrated maximum errors ranging from 0.81% to 3.21% and mean errors ranging from 0.39% to 1.03%. Furthermore, our method showcased superior predictive performance, with low values for mean squared error (MSE) (<1.8130e-04), root mean squared error (RMSE) (<1.35%), and mean absolute percentage error (MAPE) (<1.4).

Scaling relationships between leaf petiole and lamina size of two Photinia species

ABSTRACT Exploring the morphometric scaling relationships between lamina and petiole functional traits is important to our understanding of foliage and plant ecosystem dynamics. For this purpose, we examined the leaves of two evergreen species, i.e. Photinia × fraseri “Red Robin”, which has relatively small leaves, and Photinia serratifolia, which has relatively larger leaves. Approximately > 320 leaves from each species were collected monthly from April to August during the growing season, and the t-test was used to determine the significance of interspecific differences in lamina and petiole traits. Reduced major axis regression protocols were used to fit the scaling relationships of petiole fresh mass (PFM) vs. lamina fresh mass (LFM), PFM vs. lamina area (A), petiole dry mass (PDM) vs. lamina dry mass (LDM), and PDM vs. A. The increase in PDM was positively correlated with increasing LDM. However, there was a temporal variation in PDM/LDM. Both PDM/LDM and PFM/LFM for P. serratifolia were significantly higher than those of P. × fraseri. There was a strong positive correlation between petiole size (as measured by PFM and PDM) and lamina size (as measured by LFM, LDM and A). These relationships reveal statistically robust scaling relationships between petiole size and lamina size for each of the two species, and provide additional support for the hypothesis called “diminishing returns”, i.e. a disproportionate increase in one leaf trait (e.g. LDM) with respect to increasing another leaf trait (e.g. PDM).

Optimal Fingerprinting with Estimating Equations

Abstract Climate change detection and attribution have played a central role in establishing the influence of human activities on climate. Optimal fingerprinting, a linear regression with errors in variables (EIVs), has been widely used in detection and attribution analyses of climate change. The method regresses observed climate variables on the expected climate responses to the external forcings, which are measured with EIVs. The reliability of the method depends critically on proper point and interval estimations of the regression coefficients. The confidence intervals constructed from the prevailing method, total least squares (TLS), have been reported to be too narrow to match their nominal confidence levels. We propose a novel framework to estimate the regression coefficients based on an efficient, bias-corrected estimating equations approach. The confidence intervals are constructed with a pseudo residual bootstrap variance estimator that takes advantage of the available control runs. Our regression coefficient estimator is unbiased, with a smaller variance than the TLS estimator. Our estimation of the sampling variability of the estimator has a low bias compared to that from TLS, which is substantially negatively biased. The resulting confidence intervals for the regression coefficients have coverage rates close to the nominal level, which ensures valid inferences in detection and attribution analyses. In applications to the annual mean near-surface air temperature at the global, continental, and subcontinental scales during 1951–2020, the proposed method led to shorter confidence intervals than those based on TLS in most of the analyses. Significance Statement Optimal fingerprinting is an important statistical tool for estimating human influences on the climate and for quantifying the associated uncertainty. Nonetheless, the estimators from the prevailing practice are not as optimal as believed, and their uncertainties are underestimated, both owing to the unreliable estimation of the optimal weight matrix that is critical to the method. Here we propose an estimation method based on the theory of estimating equations; to assess the uncertainty of the resulting estimator, we propose a pseudo bootstrap procedure. Through extensive numerical studies commonly used in statistical investigations, we demonstrate that the new estimator has a smaller mean-square error, and its uncertainty is estimated much closer to the true uncertainty than the prevailing total least squares method.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares (WTLS) have been regarded as the standard tool for the errors-in-variables (EIV) model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors. However, in many geodetic applications, some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix. It is called the linear structured EIV (LSEIV) model. Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications. On the one hand, the functional part of the LSEIV model is modified into the errors-in-observations (EIO) model. On the other hand, the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix. The algorithms are derived through the Lagrange multipliers method and linear approximation. The estimation principles and iterative formula of the parameters are proven to be consistent. The first-order approximate variance-covariance matrix (VCM) of the parameters is also derived. A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach. Afterwards, the least squares (LS), total least squares (TLS) and linear structured weighted total least squares (LSWTLS) solutions are compared and the accuracy evaluation formula is proven to be feasible and effective. Finally, the LSWTLS is applied to the field of deformation analysis, which yields a better result than the traditional LS and TLS estimations.

Detection of Structural Damage in a Shaking Table Test Based on an Auto-Regressive Model with Additive Noise

Damage identification plays an important role in enhancing resilience by facilitating precise detection and assessment of structural impairments, thereby strengthening the resilience of critical infrastructure. A current challenge of vibration-based damage detection methods is the difficulty of enhancing the precision of the detection results. This problem can be approached through improving the noise reduction performance of algorithms. A novel method based partially on the errors-in-variables (EIV) model and its total least-squares (LS) algorithm is proposed in this study. Compared with a classical damage detection approach involving adoption of auto-regressive (AR) models and the least-squares (LS) method, the proposed method accounts for all the observation errors as well as the relationships between them, especially in an elevated level of noise, which leads to a better accuracy. Accordingly, a shaking table test and its corresponding finite element simulation of a full-scale web steel structure were conducted. The acceleration time-series output data of the model after suffering from different seismic intensities were used to identify damage using the presented detection method. The response and identification results of the experiment and the finite element analysis are consistent. The finding of this paper indicated that the presented approach is capable of detecting damage with a higher accuracy, especially when the signal noise is high.

Binocular measurement method for a continuous casting slab based on the one-dimensional probabilistic Hough transform and local sub-pixel sifting.

Due to the low measurement accuracy of the continuous casting slab model caused by difficulty in detecting ideal corners, a binocular measurement method based on the one-dimensional probabilistic Hough transform and local sub-pixel sifting is proposed. First, the one-dimensional probabilistic Hough transform based on inclination angle voting and the Freeman chain code is used to detect the line segments of the exterior outline. Next, sub-pixel points are extracted in each region of interest (ROI) by using Zernike moments, and sifted in the overlapping area of adjacent ROIs. Then the orthogonal total least squares (TLS) method is applied to fitting sub-pixel edges. Finally, after the key points are matched, three-dimensional localization and measurement are completed according to the binocular vision measurement principle. The experimental results show that the minimum relative error and average relative error of length reach 0.3401% and 0.3945%, respectively, satisfying the measurement requirement. Compared with scale-invariant feature transform (SIFT) and the oriented FAST and rotated BRIEF (ORB), the measurement error of the proposed algorithm is reduced by 80.01% and 74.63%, respectively. Compared with another edge fitting method based on k-means clustering and least squares fitting, its measurement error is reduced by 34.11%, and the time consumption is shortened by 39.07%, verifying its excellent performance in accuracy and efficiency.

Morphometrics, Growth and Condition of the Invasive Bivalve Rangia cuneata during Colonisation of the Oder Estuary (North-Western Poland)

The aim of this study was to determine the biological, morphometric, and shape characteristics of the bivalve Rangia cuneata in the initial phase of colonisation. A total of 504 specimens were caught for the study. Their average length was 31.06 mm (range 12.7–43.2 mm) and weight 6.0 g (0.5–15.3 g). The population was dominated by individuals of 25–30 mm and 30–35 mm in length and the age of 3+ and 4+. The standard major axis regression for measurable traits describing shell cross-section indicate the allometric nature of growth for most parameters. Elongation and convexity indices by age group indicate a change in the shell shape as it becomes more elongated and convex in individuals that have already reached sexual maturity. The collected specimens were of larger sizes compared to other Baltic populations of the species, and similar in size to populations found in the neighboring Pomeranian Bay. The increase in length of R. cuneata in the Oder estuary is smaller compared to the species native sites, probably due to the lower water temperature in the study area. Considering the invasive potential of R. cuneata, it seems necessary to monitor closely its population and distribution in the estuary of Western Baltic.

Establishment of a reference interval for glycated albumin based on medical check-up data from multiple medical institutions

Objectives: Data were collected to establish a reference interval for glycated albumin (GA), as well as to calculate a cutoff value for diagnosing diabetes mellitus and the GA level corresponding to a 75-g oral glucose tolerance test (OGTT) 2 h plasma glucose (2h-PG) level of 200 mg/dL. Methods: This study involved 1,843 subjects who were undergoing medical check-ups at several medical institutions and whose HbA1c and GA levels had been measured by OGTT. Results: The GA reference interval that was calculated based on the data obtained from study subjects with normal glucose tolerance was 12.1–17.1%. Using standardized major axis regression, the levels that corresponded to an OGTT 2h-PG level of 11.1 mmol/L were a GA level of 17.5% and an HbA1c level of 47.5 mmol/mol. A receiver-operating characteristic curve analysis was used to calculate the points at which sensitivity and specificity matched as the cutoff values, and the results yielded a GA level of 15.0% (sensitivity 69.3%). Conclusions: The GA reference interval was calculated to be 12.1–17.1%. We propose a GA level of 17.4% as a cutoff value to diagnose diabetes mellitus and a GA level of 15.0% as a screening cutoff value for diabetes mellitus, taking previous reports into account.