Statistical methods for dealing with measurement error in covariates : EPIC-InterAct study

This thesis presents a comprehensive exploration of linear mixed models that incorporate measurement errors in specific covariates for longitudinal data with non-ignorable and non-monotone missing responses. The primary objective is to estimate mean response parameters and variance components utilizing a combined methodology of Regression Calibration (RC) and Monte Carlo EM. The investigation begins with an in-depth examination of the RC method applied to linear mixed models, particularly its adaptation to longitudinal data with covariates affected by measurement errors. A thorough simulation study is conducted, involving various mean response functions, revealing that the RC method produces unbiased and efficient estimators in scenarios where the true underlying model includes covariates with measurement errors. Subsequently, linear mixed models are introduced for longitudinal data with non-ignorable missing responses. The thesis proposes a semi-parametric Monte Carlo EM algorithm for the simultaneous estimation of regression parameters and variance components in linear mixed models with non-ignorable and non-monotone missing responses, combining the Monte Carlo EM algorithm of Ibrahim et al. and the RC method. The simulation study demonstrates the effectiveness of the proposed method, even in the presence of a substantial proportion of non-ignorable missing responses. The thesis concludes with an application of the proposed RC-MCEM method to actual longitudinal data from the Canadian Community Health Survey (CCHS), focusing on individuals with alcoholism and exploring how measurement errors in certain covariates can introduce biases in parameter estimation. The complexity of the problem is further elucidated when missingness occurs in the response variable.

It has been well known that ignoring measurement error may result in substantially biased estimates in many contexts including linear and nonlinear regressions. For survival data with measurement error in covariates there has been extensive discussion in the literature with the focus being on the Cox proportional hazards models. However, the impact of measurement error on accelerated failure time (AFT) models has received little attention, though AFT models are very useful in survival data analysis. In this paper, we discuss AFT models with error-prone covariates and study the bias induced by the naive approach of ignoring measurement error in covariates. To adjust for such a bias, we describe a simulation and extrapolation method. This method is appealing because it is simple to implement and it does not require modelling the true but error-prone covariate process that is often not observable. Asymptotic normality for the resulting estimators is established. Simulation studies are carried out to evaluate the performance of the proposed method as well as the impact of ignoring measurement error in covariates. The proposed method is applied to analyse a data set arising from the Busselton Health study (Australian J. Public Health 1994; 18:129-135).

We consider measurement error in covariates in the marginal hazards model for multivariate failure time data. We explore the bias implications of normal additive measurement error without assuming a distribution for the underlying true covariate. To correct measurement-error-induced bias in the regression coefficient of the marginal model, we propose to apply the SIMEX procedure and demonstrate its large and small sample properties for both known and estimated measurement error variance. We illustrate this method using the Lipid Research Clinics Coronary Primary Prevention Trial data with total cholesterol as the covariate measured with error and time until angina and time until nonfatal myocardial infarction as the correlated outcomes of interest.

ABSTRACTOften in data arising out of epidemiologic studies, covariates are subject to measurement error. In addition ordinal responses may be misclassified into a category that does not reflect the true state of the respondents. The goal of the present work is to develop an ordered probit model that corrects for the classification errors in ordinal responses and/or measurement error in covariates. Maximum likelihood method of estimation is used. Simulation study reveals the effect of ignoring measurement error and/or classification errors on the estimates of the regression coefficients. The methodology developed is illustrated through a numerical example.

The incidence of Valley Fever can be predicted using a Poisson regression model, which links the expected incidence count to influential covariates with model coefficients. In real-world practice, the estimated model coefficients are sensitive to the inevitable measurement errors in the covariates, which are usually manifested as classical errors and/or Berkson errors. While conventional methods have separately addressed each type of error, the joint consideration of both, referred to as mixture measurement error in this article, is currently absent from the existing literature, leaving model coefficient estimators with significant biases. This article presents a measurement-error tolerant Poisson regression to mitigate the impacts of the mixture measurement error in covariates of health-care data analysis. An error-structureadapted quasi-likelihood estimation method is proposed to enhance the accuracy of model estimation. The effectiveness of the proposed method is demonstrated through a numerical case study built upon a Valley Fever investigation, validating its improved estimation accuracy and robustness.

This chapter focuses on measurement error in covariates in regression analyses in which the aim is to estimate the association between one or more covariates and an outcome, adjusting for confounding. Error in covariate measurements, if ignored, results in biased estimates of parameters representing the associations of interest. Studies with variables measured with error can be considered as studies in which the true variable is missing, for either some or all study participants. We make the link between measurement error and missing data and describe methods for correcting for bias due to covariate measurement error with reference to this link, including regression calibration (conditional mean imputation), maximum likelihood and Bayesian methods, and multiple imputation. The methods are illustrated using data from the Third National Health and Nutrition Examination Survey (NHANES III) to investigate the association between the error-prone covariate systolic blood pressure and the hazard of death due to cardiovascular disease, adjusted for several other variables including those subject to missing data. We use multiple imputation and Bayesian approaches that can address both measurement error and missing data simultaneously. Example data and R code are provided in online materials.

On choice and effect of weight matrix for response sensitivity-based damage identification with measurement and model errors

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.

In some clinical trials and epidemiologic studies, investigators are interested in knowing whether the variability of a biomarker is independently predictive of clinical outcomes. This question is often addressed via a naïve approach where a sample-based estimate (e.g., standard deviation) is calculated as a surrogate for the "true" variability and then used in regression models as a covariate assumed to be free of measurement error. However, it is well known that the measurement error in covariates causes underestimation of the true association. The issue of underestimation can be substantial when the precision is low because of limited number of measures per subject. The joint analysis of survival data and longitudinal data enables one to account for the measurement error in longitudinal data and has received substantial attention in recent years. In this paper we propose a joint model to assess the predictive effect of biomarker variability. The joint model consists of two linked sub-models, a linear mixed model with patient-specific variance for longitudinal data and a full parametric Weibull distribution for survival data, and the association between two models is induced by a latent Gaussian process. Parameters in the joint model are estimated under Bayesian framework and implemented using Markov chain Monte Carlo (MCMC) methods with WinBUGS software. The method is illustrated in the Ocular Hypertension Treatment Study to assess whether the variability of intraocular pressure is an independent risk of primary open-angle glaucoma. The performance of the method is also assessed by simulation studies.

Instrumental variable (IV) analysis has been widely used in economics, epidemiology, and other fields to estimate the causal effects of covariates on outcomes, in the presence of unobserved confounders and/or measurement errors in covariates. However, IV methods for time-to-event outcome with censored data remain underdeveloped. This paper proposes a Bayesian approach for IV analysis with censored time-to-event outcome by using a two-stage linear model. A Markov chain Monte Carlo sampling method is developed for parameter estimation for both normal and non-normal linear models with elliptically contoured error distributions. The performance of our method is examined by simulation studies. Our method largely reduces bias and greatly improves coverage probability of the estimated causal effect, compared with the method that ignores the unobserved confounders and measurement errors. We illustrate our method on the Women's Health Initiative Observational Study and the Atherosclerosis Risk in Communities Study.

Methods of analyzing survival data with high‐dimensional covariates are often challenged by the presence of measurement error in covariates, a common issue arising from various applications. Conducting naive analysis with measurement‐error effects ignored usually gives biased results. However, relatively little research has been focused on this topic. In this article, we consider this important problem and discuss variable selection for proportional hazards models with high‐dimensional covariates subject to measurement error. We propose a penalized “corrected” likelihood‐based method to simultaneously address the measurement‐error effects and perform variable selection. We establish theoretical results including the consistency, the oracle property and the asymptotic distribution of the proposed estimator. Simulation studies are conducted to assess the finite sample performance of the proposed method. To illustrate the use of our method, we apply the proposed method to analyze a dataset arising from the breast cancer study.

Several methods have been proposed in the literature for computing unbiased and efficient estimates of the parameters of generalized linear models when the covariates are measured with error. However, to our knowledge, no documented research on computational techniques for parameter estimation currently exist in the literature when the data is a longitudinal count data influenced by an unobservable latent variable and observable covariates that are measured with error. In this paper, we propose a nonstationary conditionally Poisson mixed model for such data and develop unbiased estimating equations with iterative methods for computing estimates of the effect of the covariates, variance of the latent variable, and the correlation index parameter. The performance of the iterative methods is examined through extensive simulation studies. The results show that the methods performed well when the magnitude of the measurement error is not so large as to dominate or mask the effect of the true covariates. Using observed longitudinal count data on the number of patents awarded to 168 firms in the United States from 1974 to 1979 along with associated covariate information on the type of firm, log of the book value of capital in 1972 and research and development (R & D) expenditures we have demonstrated how the methods proposed in this paper can be applied to a real data. In addition, we derive the influence function of the estimator of the covariate effect and discuss the asymptotic properties of the estimator. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 151-180.

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.

Small Area Estimation under Square Root Transformed Fay-Herriot Model with Functional Measurement Error in Covariates

A resampling approach for adjustment in prediction models for covariate measurement error