Fully Parametric and Semi-Parametric Regression Models for Common Events with Covariate Measurement Error in Main Study/Validation Study Designs

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.

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.

The impact of covariate measurement errors on the estimation of relative risk regression parameters is discussed. First the dependence of the induced relative risk process on the cumulative baseline failure rate function is noted. Next induced relative risk models under some specific failure time and measurement error models are described, including the much simplified models that are appropriate under a 'rare disease' assumption. The presentation then turns to the joint estimation of relative risk parameters of primary interest along with measurement error parameters. A partial likelihood product is proposed for such estimation and asymptotic properties are indicated. Guidance is also presented as to the appropriate size of a 'validation' sample relative to the full cohort size. Finally some more general considerations are presented as to the usefulness and interpretation of deattenuated regression coefficients.

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

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).

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.

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

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.

Preterm birth, defined as delivery before 37 completed weeks' gestation, is a leading cause of infant morbidity and mortality. Identifying factors related to preterm delivery is an important goal of public health professionals who wish to identify etiologic pathways to target for prevention. Validation studies are often conducted in nutritional epidemiology in order to study measurement error in instruments that are generally less invasive or less expensive than “gold standard” instruments. Data from such studies are then used in adjusting estimates based on the full study sample. However, measurement error in nutritional epidemiology has recently been shown to be complicated by correlated error structures in the study-wide and validation instruments. Investigators of a study of preterm birth and dietary intake designed a validation study to assess measurement error in a food frequency questionnaire (FFQ) administered during pregnancy and with the secondary goal of assessing whether a single administration of the FFQ could be used to describe intake over the relatively short pregnancy period, in which energy intake typically increases. Here, we describe a likelihood-based method via Markov chain Monte Carlo to estimate the regression coefficients in a generalized linear model relating preterm birth to covariates, where one of the covariates is measured with error and the multivariate measurement error model has correlated errors among contemporaneous instruments (i.e., FFQs, 24-hour recalls, and biomarkers). Because of constraints on the covariance parameters in our likelihood, identifiability for all the variance and covariance parameters is not guaranteed, and, therefore, we derive the necessary and sufficient conditions to identify the variance and covariance parameters under our measurement error model and assumptions. We investigate the sensitivity of our likelihood-based model to distributional assumptions placed on the true folate intake by employing semiparametric Bayesian methods through the mixture of Dirichlet process priors framework. We exemplify our methods in a recent prospective cohort study of risk factors for preterm birth. We use long-term folate as our error-prone predictor of interest, the FFQ and 24-hour recall as two biased instruments, and the serum folate biomarker as the unbiased instrument. We found that folate intake, as measured by the FFQ, led to a conservative estimate of the estimated odds ratio of preterm birth (.76) when compared to the odds ratio estimate from our likelihood-based approach, which adjusts for the measurement error (.63). We found that our parametric model led to similar conclusions to the semiparametric Bayesian model.

A measurement error model proposed previously allows for correlations between subject-specific biases and between random within-subject errors in the surrogates obtained from two modes of measurement. However, most of these model parameters are not identifiable from the standard validation study design, including, importantly, the attenuation factor needed to correct for bias in relative risk estimates due to measurement error. We propose validation study designs that permit estimation and inference for the attenuation factor and other parameters of interest when these correlations are present. We use an estimating equations framework to develop semi-parametric estimators for these parameters, exploiting instrumental variables techniques. The methods are illustrated through application to data from the Nurses' Health Study and Health Professionals' Follow-up Study, and comparisons are made to more restrictive models.

In medical studies, patients' biological parameters are often imprecisely measured due to the measuring mechanism or the biological variability. In the presence of covariate measurement error, survival analysis using the Cox model with the observed covariate may yield a biased estimate for the regression parameter. Existing research on this topic has focused on adapting the Cox model to covariates with measurement errors. In this article we generalize linear transformation models to accommodate covariate measurement error. We derive inference procedures for the regression coefficients of examining the covariate effects on survival times under a generalized estimating equation framework. Our method relaxes the normality assumption on the unobserved true covariates and the measurement errors and can be easily adopted to conduct sensitivity analyses when the magnitude of the measurement error variance is unknown. The extra variation owing to the measurement error corrections is accounted for through an asymptotic U statistic expression of the estimator for the measurement error model parameter. We illustrate the numerical performance of our estimator with an example, and investigate it through simulation studies.

Survey designs for producing population prevalence estimates, such as abortion rates, need to consider multiple sources of error. Abortion prevalence has been found to suffer from underreporting. Abortion rates can also be underestimated due to unit nonresponse. However, it is when these two phenomena are linked that it becomes a particularly critical problem for both researchers interested in studying abortion rates and survey research practitioners. For substantive researchers, results may depend on the mix of these survey errors, in unexpected ways. For survey methodologists, decreasing one source of error may lead to greater bias in estimates by increasing the influence of another source. Identifying common causes can inform when to expect differences in rates due to the mix of nonresponse and measurement error, while helping practitioners design surveys that reduce both sources of error. This article addresses both nonresponse and measurement error in abortion estimates. We found that those with a lower likelihood to participate in the survey were also more likely to underreport such experiences. We interpret both nonresponse and measurement error as stemming from a common cause: the likely social stigma that reporting of these experiences poses to individuals. Although these results show that naive increasing of response rates may lead to greater bias in survey estimates, we also find limited evidence that some survey design changes can reduce the link between nonresponse and measurement error. This finding is worthy of replication for practitioners in order to break the link between these sources of error.

We investigated the conditions under which the information matrix, conditional on covariates, and the unconditional version, integrated over marginal distribution of covariates, are increasing functions of the measurement error variance, and when the conditional and unconditional asymptotic variances of the maximum likelihood estimate are decreasing functions of the measurement error variance. We say that a paradox occurs when one can decrease the variance of the maximum likelihood estimate by increasing measurement error. Two covariate measurement error models were considered: the Berk-son and the classical measurement error models, with continuous and binary dependent variables, The measurement error variance was assumed known. We found that in the linear model with Berkson eovariate measurement error, the paradox can occur when the model variance is known and quite large. With binary data and the Berkson eovariate measurement error, the paradox is likely to occur for rare events. The paradox based upon the unconditional variance, calculated as the inverse of the unconditional information matrix, does not occur with the classical measurement error model. However, if does occur for the conditional variance, as calculated by the inverse of the observed information matrix, in some circumstances. Empirical evidence for this is illustrated using data from the Nurses' Health Study.

Recognition that measurement error in the independent (predictor) variable of data used for regression modeling necessitates special methods of model fitting dates back to the late 1800s. In the ensuing 100 years attention was devoted almost entirely to measurement error in linear regression models, at which time advances in computing opened the door to the nonlinear statistical modeling generally, and to the study of measurement error in nonlinear regression modeling in particular. This article contains an introduction to the problem of measurement error in regression using linear regression measurement error models to illustrate key ideas. It includes a discussion of the types of measurement error commonly studied (classical and Berkson, differential and nondifferential) and how those types arise in practice. A summary of the consequences of ignoring measurement error when analyzing data measured with error is presented, with detailed results given for simple and multiple linear measurement error models. Pointers to the literature on both linear and nonlinear measurement error models are provided.

991012735768003412 HKUST Electronic Theses Statistical methods for dealing with measurement error in covariates : EPIC-InterAct study by Cao Zhiqiang thesis 2019 xv, 155 pages : illustrations ; 30 cm In Statistics, most theories are developed to deal with statistical modeling…Read more ›