Covariate Measurement Error Research Articles

소방관의 실내 측위를 위한 두 발에 장착된 보행항법장치의 입체구적 포인트 기반 위치 영역 융합

The ZUPT (Zero-velocity UPdaTe)-based PDR (Pedestrian Dead Reckoning) mounted on the foot calculates navigation information through the INS (Inertial Navigation System) algorithm, detects the moment when the foot touches the ground through the ZVD (Zero-Velocity Detection) algorithm, and corrects the INS errors through zero-velocity correction filtering. Through this, it is possible to estimate fairly stable position information of a pedestrian. However, the accumulation of errors over time is inevitable. In this paper, we propose a technique to reduce the accumulation of errors through the fusion of PDRs mounted on both feet. After converting the position information of the two PDRs into cubature points, the body position is estimated using the points. The two PDRs are then updated using the body position information as a measurement of the filter. Here, the measurement error covariance matrix is set using the structural constraint of the body and feet to reduce the phenomenon that the position difference between the two PDRs increases over time. The performance of the proposed technique is verified through experiments.

The roles of social economic status and undernutrition in regional disparities of the under‐five mortality rate in Vietnam

From 2005 to 2017, the prevalence of mortality in Vietnamese children under five years old showed large regional disparities. In 2017, mortality in the wealthiest region was 12.6‰, whereas the most disadvantaged region it was three times as high, at 36‰. This study aims to identify factors affecting regional disparities of the under-five mortality rate (U5MR) in Vietnam. We applied Structural Equation Modelling to estimate the degree and the pathway through which undernutrition and socio-economic status (SES) contributed to the under-five mortality disparities. SES is estimated as a common latent factor of three socio-economic measures, that is, education, poverty and income. The direct effect of SES on U5MR is at 2.16 through the underweight pathway, which is 5 times higher than the effect of underweight on U5MR. Through the stunting channel, this direct impact is 1.43, nearly twice as high as the impact of the stunting rate. SES also has an indirect effect on U5MR through these undernutrition pathways. In total, we estimate that an increase in SES index will make the U5MR increase by 2.73‰. Among the three indicators of SES, poverty conveys the strongest signal of a considerable change in SES, thus to a subsequent change in U5MR. Among two types of undernutrition, the effect of stunting on U5MR is dominant, more than 3 times as high as that of underweight. These findings have important implications for socio-economic and health interventions: those that strongly focus on the reduction of regional poverty and stunting rates would be effective in bridging the regional gap in the U5MR in Vietnam.

Small Area Estimation with Measurement Error in t Distributed Covariate Variable

The large need for small area data and limited auxiliary information drive the development of small area estimation methods with auxiliary information comes from survey data. The consequence of the existence of the auxiliary variables from survey data is the development of measurement error models. Survey data is used as auxiliary variables that are taken randomly so that the data is considered to be stochastic. Thus, the measurement error model is assumed to be structural. Meanwhile, auxiliary information or covariates does not always have a normal distribution but sometimes contain outliers so the assumption of the t-distribution is considered to be more appropriate. Therefore, we use the moment-method to estimate the parameters and develop an empirical Bayes-EB predictor in a nested error regression model with measurement errors in the area-level covariates. In addition, the covariate in this model is assumed in the t-distribution which were previously always considered normal. Using simulation studies, we can report the performance of EB predictor under true covariates and measurement errors assumed to be t-distributions based on mean squared prediction errors (EMSPE). The results show that the model we developed leads to a significant increase in efficiency compared to EB predictors previously proposed. Furthermore, this approach is applied in National socio-economic survey (Susenas) data in Malang Regency with the aim of predicting mean years of schooling by districts using monthly per capita household expenditure data as the covariate variables that are considered to have the t-distribution.

Variable selection and estimation for the additive hazards model subject to left-truncation, right-censoring and measurement error in covariates

Variable selection with censored survival data is of great practical importance, and several methods have been proposed for variable selection based on different models. However, the impacts of biased samples caused by left-truncation and covariate measurement error to variable selection are not fully explored. In this paper, we mainly focus on the additive hazards model and analyze variable selection and estimation for survival data subject to left-truncation and measurement error in covariates. We develop the three-stage procedure to correct for error effects, select informative variables, and estimate the parameters of interest simultaneously. Numerical studies are reported to assess the performance of the proposed methods.

Variable selection for ultra-high dimensional quantile regression with missing data and measurement error.

In this paper, we consider variable selection for ultra-high dimensional quantile regression model with missing data and measurement errors in covariates. Specifically, we correct the bias in the loss function caused by measurement error by applying the orthogonal quantile regression approach and remove the bias caused by missing data using the inverse probability weighting. A nonconvex Atan penalized estimation method is proposed for simultaneous variable selection and estimation. With the proper choice of the regularization parameter and under some relaxed conditions, we show that the proposed estimate enjoys the oracle properties. The choice of smoothing parameters is also discussed. The performance of the proposed variable selection procedure is assessed by Monte Carlo simulation studies. We further demonstrate the proposed procedure with a breast cancer data set.

Heading angle estimation using rotating magnetometer for mobile robots under environmental magnetic disturbances

The heading angle plays a vital role in the localization and mapping of mobile robots. It is generally obtained by fusing measurements from gyroscope and magnetometer. However, ferromagnetic objects in real-world environments will disturb the magnetic field and will, therefore, cause significant errors in the estimated heading angles. This work proposes a novel method that employs a rotating magnetometer to detect ambient spatial magnetic disturbances and corrects the heading angle. The algorithm is based on the extended Kalman filter (EKF). Firstly, a criterion named spatial disturbance index is defined to characterize the disturbance quantitatively. And then the magnetometer measurement error covariance of the EKF is tuned adaptively according to the proposed criterion, so that a relatively reliable heading angle can be obtained even under strong spatial dynamic magnetic disturbances. In addition, the estimated heading angle can quickly restore to the correct value when the spatial disturbances disappear. The proposed algorithm has the benefit of adjusting the fusing degree of gyroscope and magnetometer adaptively to reject spatial disturbances and avoid the adverse impact of inherent gyroscope drift. The algorithm is evaluated under static and dynamic conditions in real-world indoor/outdoor environments. The results show that our algorithm outperforms the conventional EKF with fixed measurement error covariance and also the algorithm using only gyroscope.

A Rapid and Adaptive Alignment under Mooring Condition Using Adaptive EKF and CNN-Based Learning.

Alignment of the inertial navigation system (INS) in the mooring environment should take into account the movements of the waves or wind. The alignment of the INS is performed through an extended Kalman filter (EKF) using zero velocity as a measurement. However, in the mooring condition, this is not perfect stationary, thus the measurement error covariance matrix should be adjusted. In addition, if the measurement error covariance matrix is fixed to one value, the alignment time may take longer or the performance may be reduced depending on the change in mooring conditions. To solve this problem, we propose an alignment method using adaptive Kalman filter and convolution neural network (CNN)-based learning. The proposed method was verified for the superiority of alignment time and accuracy through Monte Carlo simulation in a mooring environment.

Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard.

Observational epidemiological studies often confront the problem of estimating exposure-disease relationships when the exposure is not measured exactly. Regression calibration (RC) is a common approach to correct for bias in regression analysis with covariate measurement error. In survival analysis with covariate measurement error, it is well known that the RC estimator may be biased when the hazard is an exponential function of the covariates. In the paper, we investigate the RC estimator with general hazard functions, including exponential and linear functions of the covariates. When the hazard is a linear function of the covariates, we show that a risk set regression calibration (RRC) is consistent and robust to a working model for the calibration function. Under exponential hazard models, there is a trade-off between bias and efficiency when comparing RC and RRC. However, one surprising finding is that the trade-off between bias and efficiency in measurement error research is not seen under linear hazard when the unobserved covariate is from a uniform or normal distribution. Under this situation, the RRC estimator is in general slightly better than the RC estimator in terms of both bias and efficiency. The methods are applied to the Nutritional Biomarkers Study of the Women's HealthInitiative.

Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error

Many methods have been developed for analyzing survival data which are commonly right-censored. These methods, however, are challenged by complex features pertinent to the data collection as well as the nature of data themselves. Typically, biased samples caused by left-truncation (or length-biased sampling) and measurement error often accompany survival analysis. While such data frequently arise in practice, little work has been available to simultaneously address these features. In this paper, we explore valid inference methods for handling left-truncated and right-censored survival data with measurement error under the widely used Cox model. We first exploit a flexible estimator for the survival model parameters which does not require specification of the baseline hazard function. To improve the efficiency, we further develop an augmented nonparametric maximum likelihood estimator. We establish asymptotic results and examine the efficiency and robustness issues for the proposed estimators. The proposed methods enjoy appealing features that the distributions of the covariates and of the truncation times are left unspecified. Numerical studies are reported to assess the finite sample performance of the proposed methods.

Sequential unbiased converted measurement non‐linear filter with range rate in ECEF coordinates

Air-to-air target tracking is a challenging task for practical military and civilian applications. In this study, an unbiased converted measurement Kalman filter in Earth-centred Earth-fixed (ECEF) coordinates (E-UCMKF) is proposed for air-to-air target tracking, which takes account for noisy measurements from the airborne radar and the inertial navigation system/global navigation satellite system. The unbiased measurement conversion approach from spherical coordinates to ECEF coordinates is presented, and the Kalman filter is implemented for target state estimation with the unbiased converted measurements and the corresponding measurement error covariances. Besides, when range-rate measurements are available to the processor, a sequential unbiased converted measurement non-linear filter in ECEF coordinates with range-rate measurements (E-SUCMNFwR) is developed, which constructs a pseudo measurement to decorrelate the range-rate measurement noise from the unbiased converted measurement noise, and estimates the state sequentially by the E-UCMKF and a modified cubature Kalman filter. Target tracking scenarios with different sensor accuracies are presented to demonstrate the validity of the proposed algorithms. Simulation results validate the consistency of the proposed unbiased measurement conversion. The results also show that the proposed E-UCMKF and E-SUCMNFwR outperform the conventional algorithms in terms of the position and velocity root-mean-square error, demonstrating their effectiveness and practicality.

Flexible omnibus test in 1:M matched case-crossover study with measurement error in covariate.

The matched case-crossover study design is used in public health, biomedical, and epidemiological research with clustered binary outcomes. Conditional logistic regression is commonly used for analysis because any effects associated with the matching covariates by stratum can be removed. However, some matching covariates often play an important role as effect modifications, causing incorrect statistical testing. The covariates in such studies are often measured with error, so that not accounting for this error can also lead to incorrect inferences for all covariates in the model. However, the methods available for simultaneously evaluating effect modification by matching covariates as well as assessing and characterizing error-in-covariates are limited. In this paper, we propose a flexible omnibus test for testing (1) the significance of a functional association between the clustered binary outcomes and covariates with the measurement error, (2) the existence of effect modifications by matching covariates, and (3) the significance of an interaction effect between the measurement error covariate and other covariates, without specifying the functional forms for these testings. The proposed omnibus test has the flexibility to allow inferences on various hypothesis settings. The advantages of the proposed flexible omnibus test are demonstrated through simulation studies and 1:4 bidirectional matched data analyses from an epidemiology study.

Causal inference for left-truncated and right-censored data with covariate measurement error

Causal inference for left-truncated and right-censored data with covariate measurement error

Uncertainty in Measured Raindrop Size Distributions from Four Types of Collocated Instruments

Four types (2D-video disdrometer: 2DVD; precipitation occurrence sensor system: POSS; micro-rain radar: MRR; and Joss–Waldvogel disdrometer: JWD) of sixteen instruments were collocated within a square area of 400 m2 from 16 April to 8 May 2008 for intercomparison of drop size distribution (DSD) of rain. This unique dataset was used to study the inherent measurement uncertainty due to the diversity of the measuring principles and sampling sizes of the four types of instruments. The DSD intercomparison shows generally good agreement among them, except that the POSS and MRR had higher concentrations of small raindrops (<1.0 mm) and offered a better chance to observe big raindrops (>5.2 mm). The measurement uncertainty ( σ ) was obtained quantitatively after considering the zero or non-zero measurement error covariance between two instruments of the same type. The results indicate the measurement uncertainties were found to be neither independent nor identical among the same type of instruments. The MRR is relatively accurate (lower σ ) due to large sampling volumes and accurate measurement of the Doppler power spectrum. The JWD is the least accurate due to the small sampling volumes. The σ decreases rapidly with increasing time-averaging window. The 2DVD shows the best accuracy of R in longer averaging time, but this is not true for Z due to the small sampling volume. The MRR outperformed other instruments for Z for entire averaging time due to its measuring principle.

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 2-More complex methods of adjustment and advanced topics.

We continue our review of issues related to measurement error and misclassification in epidemiology. We further describe methods of adjusting for biased estimation caused by measurement error in continuous covariates, covering likelihood methods, Bayesian methods, moment reconstruction, moment-adjusted imputation, and multiple imputation. We then describe which methods can also be used with misclassification of categorical covariates. Methods of adjusting estimation of distributions of continuous variables for measurement error are then reviewed. Illustrative examples are provided throughout these sections. We provide lists of available software for implementing these methods and also provide the code for implementing our examples in the Supporting Information. Next, we present several advanced topics, including data subject to both classical and Berkson error, modeling continuous exposures with measurement error, and categorical exposures with misclassification in the same model, variable selection when some of the variables are measured with error, adjusting analyses or design for error in an outcome variable, and categorizing continuous variables measured with error. Finally, we provide some advice for the often met situations where variables are known to be measured with substantial error, but there is only an external reference standard or partial (or no) information about the type or magnitude of the error.

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1-Basic theory and simple methods of adjustment.

Measurement error and misclassification of variables frequently occur in epidemiology and involve variables important to public health. Their presence can impact strongly on results of statistical analyses involving such variables. However, investigators commonly fail to pay attention to biases resulting from such mismeasurement. We provide, in two parts, an overview of the types of error that occur, their impacts on analytic results, and statistical methods to mitigate the biases that they cause. In this first part, we review different types of measurement error and misclassification, emphasizing the classical, linear, and Berkson models, and on the concepts of nondifferential and differential error. We describe the impacts of these types of error in covariates and in outcome variables on various analyses, including estimation and testing in regression models and estimating distributions. We outline types of ancillary studies required to provide information about such errors and discuss the implications of covariate measurement error for study design. Methods for ascertaining sample size requirements are outlined, both for ancillary studies designed to provide information about measurement error and for main studies where the exposure of interest is measured with error. We describe two of the simpler methods, regression calibration and simulation extrapolation (SIMEX), that adjust for bias in regression coefficients caused by measurement error in continuous covariates, and illustrate their use through examples drawn from the Observing Protein and Energy (OPEN) dietary validation study. Finally, we review software available for implementing these methods. The second part of the article deals with more advanced topics.

Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables

In many applications involving regression analysis, explanatory variables (or covariates) may be imprecisely measured or may contain missing values. Although there exists a vast literature on measurement error modeling to account for errors-in-variables, and on missing data methodology to handle missingness, very few methods have been developed to simultaneously address both. In this paper, we consider likelihood-based multiple imputation to handle missing data, and combine this with two well-known functional measurement error methods: simulation-extrapolation and corrected score. This unified approach has several appealing characteristics: the model fitting procedure is easy to understand and off-the-shelf software can be incorporated into the modeling framework; no calibration data or a validation subset is required in the model fitting procedure; and the missing data component of the proposed approach is likelihood-based which allows standard likelihood machinery. We demonstrate our methods on simulated datasets and apply them to daily ozone pollution measurements in Los Angeles where observed covariates consist of missing data and imprecise measurements. We conclude that the proposed methods substantially reduce bias and mean squared errors in regression coefficients, in comparison to methods that ignore either measurement error or missingness in covariates.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system, such as projectile's trajectory estimation and control. While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined, which may result in filtering divergence. As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model, we improve the weighted least squares method (WLSM) with minimum model error principle. Invariant embedding method is adopted to solve the cost function including the model error. With the knowledge of measurement data and measurement error covariance matrix, we use gradient descent algorithm to determine the weighting matrix of model error. The uncertainty and linearization error of model are recursively estimated by the proposed method, thus achieving an online filtering estimation of the observations. Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

Estimation in the Cox survival regression model with covariate measurement error and a changepoint.

The Cox regression model is a popular model for analyzing the relationship between a covariate vector and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulation-extrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM10 and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 andMPPLE.

Model selection and model averaging for analysis of truncated and censored data with measurement error

Model selection plays a critical role in statistical inference and a large literature has been devoted to this topic. Despite extensive research attention on model selection, research gaps still remain. An important but relatively unexplored problem concerns truncated and censored data with measurement error. Although analysis of left-truncated and right-censored (LTRC) data has received extensive interests in survival analysis, there has been no research on model selection for LTRC data with measurement error. In this paper, we take up this important problem and develop inferential procedures to handle model selection for LTRC data with measurement error in covariates. Our development employs the local model misspecification framework ([6]; [10]) and emphasizes the use of the focus information criterion (FIC). We develop valid estimators using the model averaging scheme and establish theoretical results to justify the validity of our methods. Numerical studies are conducted to assess the performance of the proposed methods.

Conditional density estimation with covariate measurement error

We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing estimators for measurement error. Asymptotic properties of the resultant estimators under different types of measurement error distributions are derived. Moreover, we adjust bandwidths readily available from existing bandwidth selection methods developed for error-free data to obtain bandwidths for the new estimators. Extensive simulation studies are carried out to compare the proposed estimators with naive estimators that ignore measurement error, which also provide empirical evidence for the effectiveness of the proposed bandwidth selection methods. A real-life data example is used to illustrate implementation of these methods under practical scenarios. An R package, lpme, is developed for implementing all considered methods, which we demonstrate via an R code example in Appendix B.2.