Addressing age measurement errors in fish growth estimation from length-stratified samples.

Fish growth models are crucial for fisheries stock assessments and are commonly estimated using fish length-at-age data. This data is widely collected using length-stratified age sampling (LSAS), a cost-effective two-phase response-selective sampling method. The data may contain age measurement errors (MEs). We propose a methodology that accounts for both LSAS and age MEs to accurately estimate fish growth. The proposed methods use empirical proportion likelihood methodology for LSAS and the structural errors in variables methodology for age MEs. We provide a measure of uncertainty for parameter estimates and standardized residuals for model validation. To model the age distribution, we employ a continuation ratio-logit model that is consistent with the random nature of the true age distribution. We also apply a discretization approach for age and length distributions, which significantly improves computational efficiency and is consistent with the discrete age and length data typically encountered in practice. Our simulation study shows that neglecting age MEs can lead to significant bias in growth estimation, even with small but non-negligible age MEs. However, our new approach performs well regardless of the magnitude of age MEs and accurately estimates SEs of parameter estimators. Real data analysis demonstrates the effectiveness of the proposed model validation device. Computer codes to implement the methodology are provided.

Minimal clinically important change of knee flexion in people with knee osteoarthritis after non-surgical interventions using a meta-analytical approach.

BACKGROUND: Minimal clinically important change (MCIC) represents the minimum patient-perceived improvement in an outcome after treatment, in an individual or within a group over time. This study aimed to determine MCIC of knee flexion in people with knee OA after non-surgical interventions using a meta-analytical approach. METHODS: Four databases (MEDLINE, Cochrane, Web of Science and CINAHL) were searched for studies of randomised clinical trials of non-surgical interventions with intervention duration of ≤ 3 months that reported change in (Δ) (mean change between baseline and immediately after the intervention) knee flexion with Δ pain or Δ function measured using tools that have established MCIC values. The risk of bias in the included studies was assessed using version 2 of the Cochrane risk-of-bias tool for randomised trials (RoB 2). Bayesian meta-analytic models were used to determine relationships between Δ flexion with Δ pain and Δ function after non-surgical interventions and MCIC of knee flexion. RESULTS: Seventy-two studies (k = 72, n = 5174) were eligible. Meta-analyses included 140 intervention arms (k = 61, n = 4516) that reported Δ flexion with Δ pain using the visual analog scale (pain-VAS) and Δ function using the Western Ontario and McMaster Universities Osteoarthritis Index function subscale (function-WOMAC). Linear relationships between Δ pain at rest-VAS (0-100 mm) with Δ flexion were - 0.29 (- 0.44; - 0.15) (ß: posterior median (CrI: credible interval)). Relationships between Δ pain during activity VAS and Δ flexion were - 0.29 (- 0.41, - 0.18), and Δ pain-general VAS and Δ flexion were - 0.33 (- 0.42, - 0.23). The relationship between Δ function-WOMAC (out of 100) and Δ flexion was - 0.15 (- 0.25, - 0.07). Increased Δ flexion was associated with decreased Δ pain-VAS and increased Δ function-WOMAC. The point estimates for MCIC of knee flexion ranged from 3.8 to 6.4°. CONCLUSIONS: The estimated knee flexion MCIC values from this study are the first to be reported using a novel meta-analytical method. The novel meta-analytical method may be useful to estimate MCIC for other measures where anchor questions are problematic. SYSTEMATIC REVIEW REGISTRATION: PROSPERO CRD42022323927.

Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty.

Measurement uncertainty has long been a concern in the characterizing and interpreting environmental and toxicological measurements. We compared statistical analysis approaches when there are replicates: a Naïve approach that omits replicates, a Hybrid approach that inappropriately treats replicates as independent samples, and a Measurement Error Model (MEM) approach in a random effects analysis of variance (ANOVA) model that appropriately incorporates replicates. A simulation study assessed the effects of sample size and levels of replication, signal variance, and measurement error on estimates from the three statistical approaches. MEM results were superior overall with confidence intervals for the observed mean narrower on average than those from the Naïve approach, giving improved characterization. The MEM approach also featured an unparalleled advantage in estimating signal and measurement error variance separately, directly addressing measurement uncertainty. These MEM estimates were approximately unbiased on average with more replication and larger sample sizes. Case studies illustrated analyzing normally distributed arsenic and log-normally distributed chromium concentrations in tap water and calculating MEM confidence intervals for the true, latent signal mean and latent signal geometric mean (i.e., with measurement error removed). MEM estimates are valuable for study planning; we used simulation to compare various sample sizes and levels of replication.

Population Size Estimation using Zero-truncated Poisson Regression with Measurement Error.

Population size estimation is an important research field in biological sciences. In practice, covariates are often measured upon capture on individuals sampled from the population. However, some biological measurements, such as body weight may vary over time within a subject's capture history. This can be treated as a population size estimation problem in the presence of covariate measurement error. We show that if the unobserved true covariate and measurement error are both normally distributed, then a naïve estimator without taking into account measurement error will under-estimate the population size. We then develop new methods to correct for the effect of measurement errors. In particular, we present a conditional score and a nonparametric corrected score approach that are both consistent for population size estimation. Importantly, the proposed approaches do not require the distribution assumption on the true covariates, furthermore the latter does not require normality assumptions on the measurement errors. This is highly relevant in biological applications, as the distribution of covariates is often non-normal or unknown. We investigate finite sample performance of the new estimators via extensive simulated studies. The methods are applied to real data from a capture-recapture study.

Minimax Rates of ℓp-Losses for High-Dimensional Linear Errors-in-Variables Models over ℓq-Balls.

In this paper, the high-dimensional linear regression model is considered, where the covariates are measured with additive noise. Different from most of the other methods, which are based on the assumption that the true covariates are fully obtained, results in this paper only require that the corrupted covariate matrix is observed. Then, by the application of information theory, the minimax rates of convergence for estimation are investigated in terms of the ℓp(1≤p<∞)-losses under the general sparsity assumption on the underlying regression parameter and some regularity conditions on the observed covariate matrix. The established lower and upper bounds on minimax risks agree up to constant factors when p=2, which together provide the information-theoretic limits of estimating a sparse vector in the high-dimensional linear errors-in-variables model. An estimator for the underlying parameter is also proposed and shown to be minimax optimal in the ℓ2-loss.

Value and limitations of intracranial recordings for validating electric field modeling for transcranial brain stimulation.

Comparing electric field simulations from individualized head models against in-vivo intra-cranial recordings is considered the gold standard for direct validation of computational field modeling for transcranial brain stimulation and brain mapping techniques such as electro- and magnetoencephalography. The measurements also help to improve simulation accuracy by pinning down the factors having the largest influence on the simulations. Here we compare field simulations from four different automated pipelines against intracranial voltage recordings in an existing dataset of 14 epilepsy patients. We show that modeling differences in the pipelines lead to notable differences in the simulated electric field distributions that are often large enough to change the conclusions regarding the dose distribution and strength in the brain. Specifically, differences in the automatic segmentations of the head anatomy from structural magnetic resonance images are a major factor contributing to the observed field differences. However, the differences in the simulated fields are not reflected in the comparison between the simulations and intra-cranial measurements. This apparent mismatch is partly explained by the noisiness of the intra-cranial measurements, which renders comparisons between the methods inconclusive. We further demonstrate that a standard regression analysis, which ignores uncertainties in the simulations, leads to a strong bias in the estimated linear relationship between simulated and measured fields. Ignoring this bias leads to the incorrect conclusion that the models systematically misestimate the field strength in the brain. We propose a new Bayesian regression analysis of the data that yields unbiased parameter estimates, along with their uncertainties, and gives further insights to the fit between simulations and measurements. Specifically, the unbiased results give only weak support for systematic misestimations of the fields by the models.

Bias correction of bounded location error in binary data.

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.

Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy.

BACKGROUND: Analysis of covariance (ANCOVA) is commonly used to adjust for potential confounders in observational studies of intervention effects. Measurement error in the covariates used in ANCOVA models can lead to inconsistent estimators of intervention effects. While errors-in-variables (EIV) regression can restore consistency, it requires surrogacy assumptions for the error-prone covariates that may be violated in practical settings. OBJECTIVES: The objectives of this article are (1) to derive asymptotic results for ANCOVA using EIV regression when measurement errors may not satisfy the standard surrogacy assumptions and (2) to demonstrate how these results can be used to explore the potential bias from ANCOVA models that either ignore measurement error by using ordinary least squares (OLS) regression or use EIV regression when its required assumptions do not hold. RESULTS: The article derives asymptotic results for ANCOVA with error-prone covariates that cover a variety of cases relevant to applications. It then uses the results in a case study of choosing among ANCOVA model specifications for estimating teacher effects using longitudinal data from a large urban school system. It finds evidence that estimates of teacher effects computed using EIV regression may have smaller bias than estimates computed using OLS regression when the data available for adjusting for students' prior achievement are limited.

On the Sensitivity of Granger Causality to Errors-In-Variables, Linear Transformations and Subsampling.

This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger-causal properties by inducing (spurious) Granger causality, as well as conditions under which it does not. For the errors-in-variables case, we give a continuity result, which implies that: a 'small' noise-to-signal ratio entails 'small' distortions in Granger causality. On filtering, we give general necessary and sufficient conditions under which 'spurious' causal relations between (vector) time series are not induced by linear transformations of the variables involved. This also yields transformations (or filters) which can eliminate Granger causality from one vector to another one. In a number of cases, we clarify results in the existing literature, with a number of calculations streamlining some existing approaches.

Monte Carlo methods for nonparametric regression with heteroscedastic measurement error.

Nonparametric regression is a fundamental problem in statistics but challenging when the independent variable is measured with error. Among the first approaches was an extension of deconvoluting kernel density estimators for homescedastic measurement error. The main contribution of this article is to propose a new simulation-based nonparametric regression estimator for the heteroscedastic measurement error case. Similar to some earlier proposals, our estimator is built on principles underlying deconvoluting kernel density estimators. However, the proposed estimation procedure uses Monte Carlo methods for estimating nonlinear functions of a normal mean, which is different than any previous estimator. We show that the estimator has desirable operating characteristics in both large and small samples and apply the method to a study of benzene exposure in Chinese factory workers.

Locally Efficient Semiparametric Estimators for Proportional Hazards Models with Measurement Error.

We propose a new class of semiparametric estimators for proportional hazards models in the presence of measurement error in the covariates, where the baseline hazard function, the hazard function for the censoring time, and the distribution of the true covariates are considered as unknown infinite dimensional parameters. We estimate the model components by solving estimating equations based on the semiparametric efficient scores under a sequence of restricted models where the logarithm of the hazard functions are approximated by reduced rank regression splines. The proposed estimators are locally efficient in the sense that the estimators are semiparametrically efficient if the distribution of the error-prone covariates is specified correctly, and are still consistent and asymptotically normal if the distribution is misspecified. Our simulation studies show that the proposed estimators have smaller biases and variances than competing methods. We further illustrate the new method with a real application in an HIV clinical trial.

How to regress and predict in a Bland-Altman plot? Review and contribution based on tolerance intervals and correlated-errors-in-variables models.

Two main methodologies for assessing equivalence in method-comparison studies are presented separately in the literature. The first one is the well-known and widely applied Bland-Altman approach with its agreement intervals, where two methods are considered interchangeable if their differences are not clinically significant. The second approach is based on errors-in-variables regression in a classical (X,Y) plot and focuses on confidence intervals, whereby two methods are considered equivalent when providing similar measures notwithstanding the random measurement errors. This paper reconciles these two methodologies and shows their similarities and differences using both real data and simulations. A new consistent correlated-errors-in-variables regression is introduced as the errors are shown to be correlated in the Bland-Altman plot. Indeed, the coverage probabilities collapse and the biases soar when this correlation is ignored. Novel tolerance intervals are compared with agreement intervals with or without replicated data, and novel predictive intervals are introduced to predict a single measure in an (X,Y) plot or in a Bland-Atman plot with excellent coverage probabilities. We conclude that the (correlated)-errors-in-variables regressions should not be avoided in method comparison studies, although the Bland-Altman approach is usually applied to avert their complexity. We argue that tolerance or predictive intervals are better alternatives than agreement intervals, and we provide guidelines for practitioners regarding method comparison studies. Copyright © 2016 John Wiley & Sons, Ltd.

Estimating and testing interactions when explanatory variables are subject to non-classical measurement error.

Assessing interactions in linear regression models when covariates have measurement error (ME) is complex.We previously described regression calibration (RC) methods that yield consistent estimators and standard errors for interaction coefficients of normally distributed covariates having classical ME. Here we extend normal based RC (NBRC) and linear RC (LRC) methods to a non-classical ME model, and describe more efficient versions that combine estimates from the main study and internal sub-study. We apply these methods to data from the Observing Protein and Energy Nutrition (OPEN) study. Using simulations we show that (i) for normally distributed covariates efficient NBRC and LRC were nearly unbiased and performed well with sub-study size ≥200; (ii) efficient NBRC had lower MSE than efficient LRC; (iii) the naïve test for a single interaction had type I error probability close to the nominal significance level, whereas efficient NBRC and LRC were slightly anti-conservative but more powerful; (iv) for markedly non-normal covariates, efficient LRC yielded less biased estimators with smaller variance than efficient NBRC. Our simulations suggest that it is preferable to use: (i) efficient NBRC for estimating and testing interaction effects of normally distributed covariates and (ii) efficient LRC for estimating and testing interactions for markedly non-normal covariates.

Non-Gaussian Berkson errors in bioassay.

The experimental design plays an important role in every experimental study. However, if errors in the settings of the studied factors cannot be avoided, i.e. Berkson errors occur, the estimates of the model parameters may be biased and the variability in the study increased. Correction methods for the effect of Berkson errors are compared. The emphasis is on the study of correlated Berkson errors which follow non-Gaussian distribution as this appears to have been a neglected, yet important, area. It is shown that the regression calibration approach bias correction methods are useful when the Berkson errors are independent. However, when these errors are dependent, the newly proposed method B-SIMEX clearly outperforms the other methods.

Regression calibration with instrumental variables for longitudinal models with interaction terms, and application to air pollution studies.

In this paper, we derive forms of estimators and associated variances for regression calibration with instrumental variables in longitudinal models that include interaction terms between two unobservable predictors and interactions between these predictors and covariates not measured with error; the inclusion of the latter interactions generalize results we previously reported. The methods are applied to air pollution and health data collected on children with asthma. The new methods allow for the examination of how the relationship between health outcome leukotriene E4 (LTE4, a biomarker of inflammation) and two unobservable pollutant exposures and their interaction are modified by the presence or absence of upper respiratory infections. The pollutant variables include secondhand smoke and ambient (outdoor) fine particulate matter. Simulations verify the accuracy of the proposed methods under various conditions.

A Discriminant Function Approach to Adjust for Processing and Measurement Error When a Biomarker is Assayed in Pooled Samples.

Pooling biological specimens prior to performing expensive laboratory assays has been shown to be a cost effective approach for estimating parameters of interest. In addition to requiring specialized statistical techniques, however, the pooling of samples can introduce assay errors due to processing, possibly in addition to measurement error that may be present when the assay is applied to individual samples. Failure to account for these sources of error can result in biased parameter estimates and ultimately faulty inference. Prior research addressing biomarker mean and variance estimation advocates hybrid designs consisting of individual as well as pooled samples to account for measurement and processing (or pooling) error. We consider adapting this approach to the problem of estimating a covariate-adjusted odds ratio (OR) relating a binary outcome to a continuous exposure or biomarker level assessed in pools. In particular, we explore the applicability of a discriminant function-based analysis that assumes normal residual, processing, and measurement errors. A potential advantage of this method is that maximum likelihood estimation of the desired adjusted log OR is straightforward and computationally convenient. Moreover, in the absence of measurement and processing error, the method yields an efficient unbiased estimator for the parameter of interest assuming normal residual errors. We illustrate the approach using real data from an ancillary study of the Collaborative Perinatal Project, and we use simulations to demonstrate the ability of the proposed estimators to alleviate bias due to measurement and processing error.

Instrument Assisted Regression for Errors in Variables Models with Binary Response.

We study errors-in-variables problems when the response is binary and instrumental variables are available. We construct consistent estimators through taking advantage of the prediction relation between the unobservable variables and the instruments. The asymptotic properties of the new estimator are established, and illustrated through simulation studies. We also demonstrate that the method can be readily generalized to generalized linear models and beyond. The usefulness of the method is illustrated through a real data example.

Model selection for marginal regression analysis of longitudinal data with missing observations and covariate measurement error.

Missing observations and covariate measurement error commonly arise in longitudinal data. However, existing methods for model selection in marginal regression analysis of longitudinal data fail to address the potential bias resulting from these issues. To tackle this problem, we propose a new model selection criterion, the Generalized Longitudinal Information Criterion, which is based on an approximately unbiased estimator for the expected quadratic error of a considered marginal model accounting for both data missingness and covariate measurement error. The simulation results reveal that the proposed method performs quite well in the presence of missing data and covariate measurement error. On the contrary, the naive procedures without taking care of such complexity in data may perform quite poorly. The proposed method is applied to data from the Taiwan Longitudinal Study on Aging to assess the relationship of depression with health and social status in the elderly, accommodating measurement error in the covariate as well as missing observations.

Linear time-dependent reference intervals where there is measurement error in the time variable-a parametric approach.

This article re-examines parametric methods for the calculation of time specific reference intervals where there is measurement error present in the time covariate. Previous published work has commonly been based on the standard ordinary least squares approach, weighted where appropriate. In fact, this is an incorrect method when there are measurement errors present, and in this article, we show that the use of this approach may, in certain cases, lead to referral patterns that may vary with different values of the covariate. Thus, it would not be the case that all patients are treated equally; some subjects would be more likely to be referred than others, hence violating the principle of equal treatment required by the International Federation for Clinical Chemistry. We show, by using measurement error models, that reference intervals are produced that satisfy the requirement for equal treatment for all subjects.

Regression calibration for models with two predictor variables measured with error and their interaction, using instrumental variables and longitudinal data.

Regression calibration provides a way to obtain unbiased estimators of fixed effects in regression models when one or more predictors are measured with error. Recent development of measurement error methods has focused on models that include interaction terms between measured-with-error predictors, and separately, methods for estimation in models that account for correlated data. In this work, we derive explicit and novel forms of regression calibration estimators and associated asymptotic variances for longitudinal models that include interaction terms, when data from instrumental and unbiased surrogate variables are available but not the actual predictors of interest. The longitudinal data are fit using linear mixed models that contain random intercepts and account for serial correlation and unequally spaced observations. The motivating application involves a longitudinal study of exposure to two pollutants (predictors) - outdoor fine particulate matter and cigarette smoke - and their association in interactive form with levels of a biomarker of inflammation, leukotriene E4 (LTE 4 , outcome) in asthmatic children. Because the exposure concentrations could not be directly observed, we used measurements from a fixed outdoor monitor and urinary cotinine concentrations as instrumental variables, and we used concentrations of fine ambient particulate matter and cigarette smoke measured with error by personal monitors as unbiased surrogate variables. We applied the derived regression calibration methods to estimate coefficients of the unobserved predictors and their interaction, allowing for direct comparison of toxicity of the different pollutants. We used simulations to verify accuracy of inferential methods based on asymptotic theory.