Imprecise Measurements Research Articles

The Development of the Community Deprivation Index and its Application to Accountable Care Organizations

Abstract There is strong interest among policymakers to adjust for area level deprivation when making payments to providers because such areas have traditionally been underserved. The Medicare Accountable Care Organization Realizing Equity, Access, and Community Health (ACO REACH) model provides higher payments to ACOs serving areas with greater deprivation. The Area Deprivation Index (ADI) is the primary component to measure deprivation for ACO REACH. The ADI is a commonly used deprivation index, but there are concerns about its methodology, primarily its use of non-standardized deprivation factors. Prior research indicates the ADI is mainly determined by home values, which doesn’t allow it to adequately capture deprivation in urban areas. This paper revises and updates the ADI, using American Community Survey data to compute a Census block group deprivation index, the Community Deprivation Index (CDI). The CDI standardizes the deprivation factors to be unit neutral, applies statistical shrinkage to account for the imprecise measurement of the factors, updates several factors, and reweights the factors using the most recently available data. Validation tests suggest the CDI exhibits higher correlations with several health outcome/utilization measures than the ADI. The CDI will better serve policymakers by improving identification of urban areas with higher deprivation.

Quantification of pulmonary edema using automated lung segmentation on computed tomography in mechanically ventilated patients with acute respiratory distress syndrome

BackgroundQuantification of pulmonary edema in patients with acute respiratory distress syndrome (ARDS) by chest computed tomography (CT) scan has not been validated in routine diagnostics due to its complexity and time-consuming nature. Therefore, the single-indicator transpulmonary thermodilution (TPTD) technique to measure extravascular lung water (EVLW) has been used in the clinical setting. Advances in artificial intelligence (AI) have now enabled CT images of inhomogeneous lungs to be segmented automatically by an intensive care physician with no prior radiology training within a relatively short time. Nevertheless, there is a paucity of data validating the quantification of pulmonary edema using automated lung segmentation on CT compared with TPTD.MethodsA retrospective study (January 2016 to December 2021) analyzed patients with ARDS, admitted to the intensive care unit of the Department of Anesthesiology and Critical Care Medicine, University Hospital Mannheim, who underwent a chest CT scan and hemodynamic monitoring using TPTD at the same time. Pulmonary edema was estimated using manually and automated lung segmentation on CT and then compared to the pulmonary edema calculated from EVLW determined using TPTD.Results145 comparative measurements of pulmonary edema with TPTD and CT were included in the study. Estimating pulmonary edema using either automated lung segmentation on CT or TPTD showed a low bias overall (− 104 ml) but wide levels of agreement (upper: 936 ml, lower: − 1144 ml). In 13% of the analyzed CT scans, the agreement between the segmentation of the AI algorithm and a dedicated investigator was poor. Manual segmentation and automated segmentation adjusted for contrast agent did not improve the agreement levels.ConclusionsAutomated lung segmentation on CT can be considered an unbiased but imprecise measurement of pulmonary edema in mechanically ventilated patients with ARDS.

One Question, Many Results—Why Epidemiological Studies Yield Heterogeneous Findings. Part 34 of a Series on Evaluation of Scientific Publications.

Observational epidemiologic studies often yield different results on the same question. In this article, we explain how this comes about. In this review, which is based on publications retrieved by a selective search in PubMed and the Web of Science, we use information from international publications, simulation studies on sampling error, and a quantitative bias analysis on fictitious data to demonstrate why the results of epidemiologic studies are often uncertain, and why it is, therefore, generally necessary to perform more than one study on any particular question. Sampling errors, imprecise measurements, alternative but equally appropriate methods of data analysis, and features of the populations being studied are common reasons why studies on the same question can yield different results. Simulation studies are used to illustrate the fact that effect estimates such as relative risks or odds ratios can deviate markedly from the true value because of sampling error, i.e., by chance alone. Quantitative bias analysis is used to show how strongly effect estimates can be distorted by misclassification of exposures or outcomes. Finally, it is shown through illustrative examples that different but equally appropriate methods of data analysis can lead to divergent study results. The above reasons why epidemiologic study results can be heterogeneous are explained in this review. Quantitative bias analyses and sensitivity analyses with alternative data evaluation strategies can help explain divergent results on one and the same question.

Thermal inequality and heat-related adaptive capacity: A systematic review

Abstract Background Extreme heat is an important public health concern. Heat stress exposure and related adaptive capacity are not equally distributed across social groups, generating thermal inequality. We implemented a systematic review to answer the question: In the general population, what is the effect of social disadvantage on exposure to subjective and objective heat stress and adaptive capacity to prevent/reduce exposure to heat stress? Methods We searched for peer-reviewed journal articles published between 2005 and 2024. Screening and data extraction were conducted by one reviewer, with a second screening and extracting 10% for comparison. Synthesis included identification and description of specific social groups unequally exposed to heat stress and with lower adaptive capacity as well as a narrative description of the evidence and identification of research gaps. Results We identified 114 relevant publications. 53% included evidence on objective heat stress, 19% subjective heat stress, and 58% adaptive capacity. Nearly half came from North America (47%), 24% from Asia, and 17% from Europe. Publishing increased over time, from 0 articles in 2005 to 20 articles in 2023. Most studies considered socioeconomic status (SES) (87%), while fewer focused on race/ethnicity or other social factors. Across global regions, lower-SES populations, immigrants, and racial/ethnic minorities are generally more exposed to heat stress and have lower adaptive capacity, and lower-SES and minority neighborhoods are generally hotter and less green. Most studies of objective heat stress use imprecise measures, such as land surface temperature, which are not representative of experienced temperatures. Conclusions This review summarizes the available evidence on inequalities in heat stress exposure and adaptive capacity for the first time and identifies important research gaps related to heat stress measurement and social factors beyond SES. Key messages • Heat stress exposure and related adaptive capacity are not equally distributed across social groups, generating thermal inequality. • Social inequalities must be considered during climate change adaptation planning.

Poverty mapping in the age of machine learning

Recent years have witnessed considerable methodological advances in poverty mapping, much of which has focused on the application of modern machine-learning approaches to remotely-sensed data. Poverty maps produced with these methods generally share a common validation procedure, which assesses model performance by comparing sub-national poverty estimates with survey-based, direct estimates. While unbiased, direct estimates can be imprecise measures of true poverty rates, meaning that it is unclear whether these validation procedures are informative of actual model performance. In this paper, we use a rich dataset from Mexico to provide a more rigorous assessment of the modern approach to poverty mapping by evaluating its performance against a credible ground truth. We find that the modern method under-performs relative to benchmark traditional methods, largely because of the limited predictive capacity of remotely-sensed covariates. For a given covariate set, we also find that machine learning produces more biased poverty estimates than the traditional procedures, particularly for the poorest geographic areas.

The effects of ambient air pollution exposure on Thoroughbred racehorse performance.

Limited research exists on impacts of air pollution on non-human mammals, particularly animal athletes such as Thoroughbred racehorses. Athletes have a greater risk of exposure as heightened exertion and increased airflow carry more pollutants deeper into the respiratory tract. To provide insights into the impact of ambient air pollution, particularly fine particulate matter (PM2.5), on race speed. Retrospective observational study. Data were obtained from The Jockey Club Information Systems, covering 31 407 winning races by Thoroughbred horses in California spanning 10 years (2011-2020) and evaluated the association between air pollution and winning race speeds. For race days, we collected PM2.5 data from the nearest U.S. Environmental Protection Agency (EPA) monitoring site within 100 km of each racetrack (n = 12). We assessed the associations between daily average PM2.5 concentrations and speed of winning horses with linear mixed effects regression. We adjusted for horse characteristics, race-related covariates, temporal indicators (e.g., year), other air pollutants and temperature. We conducted sensitivity analyses by adjusting extreme air pollution days by reassigning values to the 95th percentile value and conducting linear mixed effects regression on series of datasets with incremental cutpoints of PM2.5. In the cutpoint analysis, we found that for PM2.5 between 4 and 23.6 μg/m3, speed decreased 0.0008 m/s (95% CI: -0.0014562 to -0.00018) for every 1 μg/m3 increase of PM2.5. Limitations include the use of offsite monitors leading to imprecise exposure measurements, not using training practice data, and generalisability as the study focuses on California racetracks. This study highlights the need to create advisories to safeguard the performance of horses during periods of poor air quality. Further research is recommended to explore additional factors influencing the relationship between air pollution and equine welfare.

Should a single growth standard be used to judge the nutritional status of children under age 5 years globally? No

Universal growth standards for under-five children, given the worldwide variation in healthy growth and several determinants of anthropometry, are imprecise measures of nutritional status, particularly when used cross-sectionally. In constructing the global-use WHO growth standard, linear growth differences between contributing sites and pooled mean were >0.2 SD in 37% of observations. Systematic reviews confirm even greater variability, notably amplified for weight-for-age and head-circumference-for-age metrics. Unsurprisingly, developed nations had higher, and LMICs lower, growth dimensions. Contextual growth references predict neonatal morbidities, pathological short stature, macrocephaly, cardiometabolic risk factors, and adult noncommunicable diseases better than the WHO standards. Child body composition also varies contextually, with greater adiposity despite comparable weights in South Asian populations. Thus, contextual references, though not the perfect solution, are better suited for everyday practice and nutrition policy. Growth standards should only be used as a screening for clinical judgments aided by precise biomarkers.

Integrating imprecise data in generative models using interval-valued Variational Autoencoders

Variational Autoencoders (VAEs) enable the integration of diverse data sources into a unified latent representation, facilitating the fusion of information from various inputs and the creation of disentangled representations that separate different factors of variation in the data. Traditional VAEs, however, are limited by assuming a single prior distribution for latent variables, which restricts their ability to handle epistemic uncertainty from imprecise measurements and incomplete data. This paper introduces the Interval-Valued Variational Autoencoder (iVAE), which employs a family of prior distributions and incorporates specialized neurons and redefined objective functions for handling interval-valued data. This architecture maintains computational efficiency while extending the model’s applicability to scenarios with pronounced epistemic uncertainty. The iVAE’s efficacy is demonstrated in managing two types of data: intrinsically interval-valued and noisy data preprocessed into interval formats. The first category is exemplified by a graphical analysis of questionnaires, while the second involves case studies focused on estimating the remaining useful life of aviation engines, where the iVAE outperforms traditional methods, thereby providing more accurate diagnostics and robust predictions.

Underwater multizonotope terrain‐aided navigation method with coarse map based on set‐membership filter

AbstractTerrain‐aided navigation (TAN) is a viable method to achieve long‐term underwater navigation for long‐range autonomous underwater vehicles (AUVs). However, the high‐accuracy positioning results of most TAN systems rely on precise a priori seabed terrain maps, which restricts their applicability to a few areas with accurate bathymetric measurements of the seabed terrain. This article introduces a TAN system based on the General Bathymetric Chart of the Oceans (GEBCO) data set for global marine applications. Specifically, to address the low accuracy and poor robustness of the TAN system with imprecise bathymetric measurement and low‐resolution data from the GEBCO data set, this article proposes a multizonotope TAN method based on set‐membership filter (SMF) theory. The SMF theory is employed to handle the unknown distribution of the measurement noise from the GEBCO data set, introducing a multizonotope measurement update model to achieve more precise navigational results while addressing the perceptual ambiguity caused by self‐similar terrain. The smoothness of the terrain is incorporated as a parameter in the generation ranges of multizonotope, enabling adaptive adjustment based on terrain smoothness to reduce costs and enhance navigational performance. The accuracy and robustness of the proposed method are verified through all shipboard experiments, publicly available data sets, and AUV experiments. Compared with state‐of‐the‐art TAN methods, the average and maximum positioning errors have decreased by 64.83% and 48.84%, respectively. Finally, based on the experimental results, a preliminary distribution of suitable areas in the oceans is provided.

Integration of concentration gradient generator with competitive PCR in a droplet for rapid nucleic acid quantification

Competitive PCR is an efficient way for the measurement of nucleic acids without requiring a standard curve. It uses a competitor template mimicking the target sequence for direct comparison and quantification during amplification. However, manually preparing various concentrations for competitive PCR is labor-intensive. Additionally, target and competitor DNA bands are often inadequately separated on gels due to their similar sizes. This leads to inaccurate distinction and imprecise measurement of bandwidths and intensities, resulting in high standard deviations in quantification. Thus, this study presents an alternative way to combine droplet competitive PCR with the concentration gradient generator in a microfluidic device that simplifies competitive PCR preparation and provides precise control over reaction conditions and sample handling. Generating a wide range of competitor-to-target ratios in a single experiment enhances statistical reliability and isolating individual reactions in droplets reduces background noise and increases sensitivity. Additionally, it eliminates gel electrophoresis, improves consistency and reproducibility, requires smaller sample and reagent volumes, and allows direct sample quantification through a calibration curve for fast, simple quantification. We envision that our platform can offer a promising alternative to digital PCR, addressing its challenges and driving progress in molecular biology and diagnostics.

Student well-being: In search of definitions, measures, and research designs

BackgroundLittle is known about the role of teachers in promoting student well-being. In part, this is due to varied definitions of well-being, imprecise measurement, and unclear theoretical models that specify social influences. To address these concerns, the authors of this special issue focus on student well-being and teacher-related antecedents. MethodIn this commentary, I evaluate the various definitions of well-being offered by each author and their implications for understanding links between well-being and contextual factors. I also examine the theoretical foundations of each paper and consider the impact of the teacher characteristics and instructional strategies on student well-being. Finally, I consider the measurement and design strategies utilized in the special issue studies and how they might lead the field forward. ResultsDifferent approaches to defining and measuring well-being highlight its multi-dimensional nature. A number of antecedents of well-being also are identified, ranging from autonomy-supportive teaching and teacher-student relationships to teachers’ attitudes towards cultural phenomenon and immigration. Finally, studies utilize multi-informant and multi-level assessments and longitudinal and mediational designs. ConclusionThe authors identify teacher-related, instructional, and climate factors that contribute to students’ subjective well-being, highlighting the notion that well-being can be manifest along multiple dimensions and multiple levels of functioning. In addition, the authors examine a number of factors that contribute to student well-being, identifying important antecedents. The use of multi-informant and multi-level assessments along with longitudinal designs also strengthened this work. Overall, the papers in this SI offer clear pathways for future research in this area.

Simulation of time-crystal-like behavior for a few-boson chiral soliton model in a ring

We present numerical simulations for a chiral soliton model with N=2,3 bosons in a ring, which is a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS found spontaneous formation of a soliton due to the position measurement, but quantum fluctuations cause the soliton to subsequently decay before it has a chance to perform even one revolution of the ring. Based on this, they concluded that time-crystal dynamics are impossible for Wilczek's model of a bright soliton in a ring. In contrast, for our few-boson chiral soliton model, allowing for imprecise (weak) measurements of the particle position, we show that time-crystal-like behavior is possible, allowing for several revolutions of the spontaneously formed soliton around the ring. Published by the American Physical Society 2024

Shuffled multi-channel sparse signal recovery

Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To address this issue systematically, we frame it as a signal reconstruction problem where correspondences between samples and channels are lost. Assuming a sensing matrix for the signals, we show the problem’s equivalence to a highly structured unlabeled sensing problem and establish conditions for unique recovery. This is crucial since existing unlabeled sensing theory is inapplicable and results for reconstructing shuffled multi-channel signals do not yet exist. Our results extend to continuous-time sparse signals, and we derive conditions for reconstructing shuffled sparse signals. For the two-channel case, we provide a first reconstruction method, which combines sparse signal recovery with robust linear regression, outperforming existing unlabeled sensing methods in numerical experiments. Additionally, we showcase its effectiveness in a real-world application involving calcium imaging traces. Our theory marks a significant initial step in addressing this challenging signal reconstruction problem, with potential extensions to diverse signal representations encountered in real-world problems with imprecise measurement or channel assignment.

Applying motion compensation to offshore wind lidar reconstructed wind measurements

Floating lidar systems present an effective and advantageous solution for offshore wind speed measurements, providing wind speed and direction data at multiple heights with easy deployment to provide widespread wind information around an area. One of the causes of apprehension, however, concerns buoy motion which induces overestimations of turbulence intensity and potentially imprecise measurements of horizontal wind speed. This research aims to reduce this uncertainty by applying motion compensation to three wind field reconstruction techniques (scalar, vector, and hybrid) to assess the amelioration on horizontal wind speed and turbulence intensity; especially how motion compensation can improve scalar and hybrid outputs. A three-month dataset of a floating lidar system (FLS) was compared to a nearby fixed lidar. The results demonstrate that motion compensation provides an improvement for horizontal wind speed measurement but inflates the overestimation of turbulence intensity from the floating lidar system. Though scalar reconstruction measurements provide slightly more accurate data compared to hybrid reconstructed measurements, motion compensation helps limit the bias disparity; ergo, applying motion compensation reduces the differences in bias for scalar and hybrid reconstructed measurements. This study results in two conclusions. Basic motion compensation provides a notable amelioration for horizontal wind speed FLS measurements, yet further research must be conducted to find a suitable method to improve turbulence intensity. Additionally, the scalar reconstruction method still slightly outperforms hybrid reconstruction in offshore measurement results, but motion compensation aids in limiting the differences between the two.

Does Acinetobacter calcoaceticus glucose dehydrogenase produce self-damaging H2O2?

The soluble glucose dehydrogenase (sGDH) from Acinetobacter calcoaceticus has been widely studied and is used, in biosensors, to detect the presence of glucose, taking advantage of its high turnover and insensitivity to molecular oxygen. This approach, however, presents two drawbacks: the enzyme has broad substrate specificity (leading to imprecise blood glucose measurements) and shows instability over time (inferior to other oxidizing glucose enzymes). We report the characterization of two sGDH mutants: the single mutant Y343F and the double mutant D143E/Y343F. The mutants present enzyme selectivity and specificity of 1.2 (Y343F) and 5.7 (D143E/Y343F) times higher for glucose compared with that of the wild-type. Crystallographic experiments, designed to characterize these mutants, surprisingly revealed that the prosthetic group PQQ (pyrroloquinoline quinone), essential for the enzymatic activity, is in a cleaved form for both wild-type and mutant structures. We provide evidence suggesting that the sGDH produces H2O2, the level of production depending on the mutation. In addition, spectroscopic experiments allowed us to follow the self-degradation of the prosthetic group and the disappearance of sGDH's glucose oxidation activity. These studies suggest that the enzyme is sensitive to its self-production of H2O2. We show that the premature aging of sGDH can be slowed down by adding catalase to consume the H2O2 produced, allowing the design of a more stable biosensor over time. Our research opens questions about the mechanism of H2O2 production and the physiological role of this activity by sGDH.

CdTe@ZnS quantum dots for rapid detection of organophosphorus pesticide in agricultural products

Organophosphorus pesticides (OPPs) constitute the most widely employed class of pesticides. However, the prevalent use of OPPs, while advantageous, raises concerns due to their toxicity, posing serious threats to food safety. Chemical sensors utilizing quantum dots (QDs) demonstrate promising applications in rapidly detecting OPPs residues, thereby facilitating efficient inspection of agricultural products. In this study, we employ an aqueous synthesis approach to prepare low toxic CdTe@ZnS QDs with stable fluorescence properties. To mitigate the risk of imprecise measurements stemming from the inherent susceptibility of fluorescence to quenching, we have adopted the principle of fluorescence resonance energy transfer (FRET) for the construction of the turn-on quantum dot sensor. With a detection limit for chlorpyrifos as low as 10 ppb (10 μg/L), the QDs sensor exhibits notable resistance to interference from various pesticides. Application of this system to detect organophosphorothioate pesticides in apples produced results consistent with those obtained from high-performance liquid chromatography (HPLC) detection, affirming the promising application prospects of this sensing system for the rapid detection of OPPs residues.

Measuring Body Composition and Functional Strength: Implications for the Clinical Assessment of Skeletal Muscle

Skeletal muscle represents the largest single component of the body, comprising up to 50% of total mass in healthy individuals. Body composition assessment has largely focused on overweight and obese individuals, but healthy skeletal muscle is also an important indicator of health and wellbeing. We hypothesized that estimates of lean body mass and empirical measures of functional strength should be directly correlated with one another. In the current study, we estimated body composition using two different field methods. Bioimpedance spectroscopy (BIS) employs 256 frequencies of low energy electrical current to estimate body composition. We used BIS (Impedimed SFB7) to determine percent body fat and fat free mass in physically active volunteers, ranging in age from 18 – 62 years. In addition, we used the Jackson and Pollock 3-site skin fold method to estimate these parameters from the same individuals. We also measured functional strength with a whole body dynamometer to determine mid-thigh pull strength, and a grip dynamometer to assess grip strength (Baseline Evaluation Instruments). Data collected from more than 75 men and women revealed significant correlations between fat-free mass (FFM) and both measures of functional strength. Interestingly, men and women fell along the same trend line, with women exhibiting similar strength for a given FFM. Moreover, functional strength standardized to FFM provides an objective measure of relative strength that was not different between men and women. The American Medical Association released a new policy statement about body mass index (BMI) in June of 2023, highlighting that BMI is an imprecise measure of body composition and recommending that alternative measures, such as more precise measurement of body composition, also be used. Indeed, we found that for individuals with a BMI of less than 30, there was direct relationship between FFM and functional strength. By contrast, percent body fat was not correlated with BMI within this range. We suggest that FFM and functional strength could be used to assess healthy weight, in conjunction with BMI. These measures could also be used to screen for sarcopenia, cachexia, and other conditions associated with significant muscle loss. Skeletal muscle represents an often underappreciated component of health and a more precise assessment of muscle mass and strength should be used as a measure of overall health. This work was supported by a Keenan Award at St. Bonaventure University. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Calculating Potential Energy Surfaces with Quantum Computers by Measuring Only the Density Along Adiabatic Transitions.

We show that chemically accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring only the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted real-space time-dependent density functional theory Kohn-Sham (KS) potential obtained from the geometry-varying densities of the full wave function. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas the total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet states in first quantization, as well as the ground state of three- and four-electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with a shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using a few shots) along the time evolution and smoothing the resulting density evolution. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent KS calculation using the inverted potential with the measured density. This can be used to determine whether longer adiabatic evolution times are required to satisfy the adiabatic theorem.

Model Predictive Control for Speed-Dependent Active Suspension System with Road Preview Information.

This paper proposes a model predictive control (MPC) scheme based on linear parameter variation to enhance the damping control of speed-dependent active suspensions. The controller is developed by introducing a speed-dependent term, specifically front- and rear-wheel time delays, to the half-car model using the Padé approximation. Subsequently, the model is augmented with time-varying parameter dependence. An adaptive Kalman filter based on variance matching is employed to estimate system states affected by imprecise sensor measurement noise. Finally, a set of explicit control laws incorporating road preview information and available vehicle speed are determined offline using multi-parameter linear programming (mp-LP), simplifying online implementation to searching for optimal solutions in a lookup table. Simulation results demonstrate a significant improvement in active suspension control under changing vehicle speeds compared to passive control.

Novel Adaptive Control for Flexible-Joint Robots With Unknown Measurement Sensitivity

For the existing tracking control schemes of flexible-joint robots, precise sensor measurement is an implicit premise. However, idealized sensors are difficult to achieve due to manufacturing technology or other external factors. To this end, this paper further investigates the tracking control problem for flexible-joint robots with unknown measurement sensitivity. Specifically, for such multi-input multi-output Euler-Lagrange systems with completely unknown system dynamics, a novel measurement values-based adaptive control method is proposed by fusing sensitivity information and system variables into Lyapunov function candidates, where the restriction on system states in other the approximation lemma-based results is removed, since unknown nonlinearities are scaled by the structural characteristics of system variables. Above all, even if there are measurement errors, satisfactory tracking performance can be obtained by adjusting the design parameters, which is proved by rigorous theoretical analysis. Finally, hardware experiments further verify the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the trajectory tracking control problem for flexible-joint robots under imprecise sensor measurements. Due to manufacturing technology limitations and component aging, there is inevitably a deviation between the measured values of sensors and real values, and this problem may become more prominent as the working environment of flexible-joint robots tends to become more complex. To our knowledge, most of the existing solutions for flexible-joint robots are developed based on precise sensor measurements, and they may fail to achieve satisfactory performance when real state information is not available. Moreover, the prior knowledge about model parameters and measurement sensitivity is difficult or impossible to exactly obtain in practice, which seriously hinders the further application of control methods that are dependent on system dynamics. To this end, this paper proposes a novel tracking control scheme based on measurement information for flexible-joint robots with unknown measurement sensitivity, where the dependence on model information is eliminated with the elaborately constructed Lyapunov function candidates, and the real tracking error is still adjusted to an acceptable range even if there are measurement errors. Preliminary experiments on a flexible-joint robot developed by Quanser company demonstrate the feasibility and effectiveness of the proposed method. In future studies, designing an effective scheme to achieve direct preset tracking control is the focus of the work.