Presence Of Covariate Measurement Error Research Articles

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.

Estimation and hypothesis testing with error‐contaminated survival data under possibly misspecified measurement error models

AbstractIn the presence of covariate measurement error, there has been extensive interest in developing estimation methods for parameters associated with various survival models, where the classical additive measurement error model is commonly used to describe the measurement error process. On the contrary, hypothesis testing has been less explored for survival data with error‐contaminated covariates. Furthermore, it is important to study the impact of misspecification of the measurement error process. In this article, we propose a “corrected” score test and a “corrected” Wald test and establish their theoretical properties. Moreover, we exploit the impact of misspecification of measurement error models on parameter estimation and hypothesis testing. Simulation studies are reported to demonstrate the finite‐sample performance of the proposed methods, and a real data example is presented to illustrate the usage of our methods.

Trend-constrained corrected score for proportional hazards model with covariate measurement error.

In many medical research studies, survival time is typically the primary outcome of interest. The Cox proportional hazards model is the most popular method to investigate the relationship between covariates and possibly right-censored survival time. However, in many clinical trials, the true covariates may not always be accurately measured due to natural biological fluctuation or instrument error. It is well know that for regression analysis in general, naively using mismeasured covariates in conventional inference procedures may incur substantial estimation bias. In the presence of covariate measurement error, several functional modeling methods have been proposed under the situation where the distribution of the measurement error is known. Among them are parametric corrected score and conditional score. Although both methods are consistent, each suffers from severe problem of multiple roots or absence of appropriate root when the measurement error is substantial. The problem persists even when the sample size is practically large. We conduct a detailed investigation on the pathological behaviors of parametric corrected score and propose an approach of incorporating additional estimating functions to remedy these pathological behaviors. The estimation and inference are then accomplished by means of quadratic inference function. Extensive simulation studies are conducted to evaluate the performance of proposed method.

On the impact of covariate measurement error on spatial regression modelling.

Spatial regression models have grown in popularity in response to rapid advances in GIS (Geographic Information Systems) technology that allows epidemiologists to incorporate geographically indexed data into their studies. However, it turns out that there are some subtle pitfalls in the use of these models. We show that presence of covariate measurement error can lead to significant sensitivity of parameter estimation to the choice of spatial correlation structure. We quantify the effect of measurement error on parameter estimates, and then suggest two different ways to produce consistent estimates. We evaluate the methods through a simulation study. These methods are then applied to data on Ischemic Heart Disease (IHD).

Simultaneous Inference for HIV Dynamic Models with Skew-t Distribution Incorporating Mismeasured Covariate and Multiple Treatment Factors

It is a common practice to analyze AIDS longitudinal data using nonlinear mixed-effects (NLME) models with normal distribution for HIV dynamics. Normality of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models; some covariates, however, may be often measured with substantial errors. This article, motivated by an AIDS clinical study, discusses a Bayesian NLME joint modeling approach to viral dynamic models with skew-t distribution in the presence of covariate measurement error. In this model, we fully integrate viral load response, time-varying CD4 covariate with measurement error, and time-dependent drug efficacy, which is a function of multiple treatment factors, into the data analysis. Thus, the purpose of this article is to demonstrate our models and methods with application to an AIDS clinical trial study. The results suggest that modeling HIV dynamics and virologic responses with consideration of covariate measurement error and time-varying clinical factors may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment and to help evaluation of clinical trial design in existing therapies.

Using analysis of covariance (ANCOVA) with fallible covariates.

Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but use ANCOVA anyway (and, most likely, report misleading results); (b) attempt to employ 1 of several measurement error models with the understanding that no research has examined their relative performance and with the added practical difficulty that several of these models are not available in commonly used statistical software; or (c) not use ANCOVA at all. First, we discuss analytic evidence to explain why using ANCOVA with fallible covariates produces bias and a systematic inflation of Type I error rates that may lead to the incorrect conclusion that treatment effects exist. Second, to provide a solution for this problem, we conduct 2 Monte Carlo studies to compare 4 existing approaches for adjusting treatment effects in the presence of covariate measurement error: errors-in-variables (EIV; Warren, White, & Fuller, 1974), Lord's (1960) method, Raaijmakers and Pieters's (1987) method (R&P), and structural equation modeling methods proposed by Sörbom (1978) and Hayduk (1996). Results show that EIV models are superior in terms of parameter accuracy, statistical power, and keeping Type I error close to the nominal value. Finally, we offer a program written in R that performs all needed computations for implementing EIV models so that ANCOVA can be used to obtain accurate results even when covariates are measured with error.

Covariate Measurement Error: Bias Reduction under Response-Based Sampling

In this paper we propose a general framework to deal with the presence of covariate measurement error (CME) in response-based (RB) samples. Using Chesher’s (1991) methodology, we obtain a small error variance approximation for the contaminated sampling distributions that characterise RB samples with CME. Then, following Chesher (2000), we develop generalised method of moments (GMM) estimators that reduce the bias of the most well known likelihood-based estimators for RB samples which ignore the existence of CME and derive a score test to detect the presence of this type of measurement error. Our approach only requires the specification of the conditional distribution of the response variable given the latent covariates and the classical additive measurement error model assumption, the availability of information on both the marginal probability of the strata in the population and the variance of the measurement error not being essential. Monte Carlo evidence is presented which suggests that, in RB samples of moderate sizes, the bias-reduced GMM estimators perform well. JEL: C51, C52.

Quantile Regression With Measurement Error

Regression quantiles can be substantially biased when the covariates are measured with error. In this paper we propose a new method that produces consistent linear quantile estimation in the presence of covariate measurement error. The method corrects the measurement error induced bias by constructing joint estimating equations that simultaneously hold for all the quantile levels. An iterative EM-type estimation algorithm to obtain the solutions to such joint estimation equations is provided. The finite sample performance of the proposed method is investigated in a simulation study, and compared to the standard regression calibration approach. Finally, we apply our methodology to part of the National Collaborative Perinatal Project growth data, a longitudinal study with an unusual measurement error structure.

On Corrected Score Approach for Proportional Hazards Model with Covariate Measurement Error

In the presence of covariate measurement error with the proportional hazards model, several functional modeling methods have been proposed. These include the conditional score estimator (Tsiatis and Davidian, 2001, Biometrika 88, 447-458), the parametric correction estimator (Nakamura, 1992, Biometrics 48, 829-838), and the nonparametric correction estimator (Huang and Wang, 2000, Journal of the American Statistical Association 95, 1209-1219) in the order of weaker assumptions on the error. Although they are all consistent, each suffers from potential difficulties with small samples and substantial measurement error. In this article, upon noting that the conditional score and parametric correction estimators are asymptotically equivalent in the case of normal error, we investigate their relative finite sample performance and discover that the former is superior. This finding motivates a general refinement approach to parametric and nonparametric correction methods. The refined correction estimators are asymptotically equivalent to their standard counterparts, but have improved numerical properties and perform better when the standard estimates do not exist or are outliers. Simulation results and application to an HIV clinical trial are presented.

Local Polynomial Regression and Simulation–Extrapolation

SummaryThe paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski's simulation–extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses SIMEX's particular estimation method and considers higher degree local polynomial estimators. We illustrate the accuracy of our asymptotic expressions with a Monte Carlo study, compare our method with other estimators with a second set of Monte Carlo simulations and apply our method to a data set from nutritional epidemiology. SIMEX was originally developed for parametric models. Although SIMEX is, in principle, applicable to nonparametric models, a serious problem arises with SIMEX in nonparametric situations. The problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing. We believe that this is the first paper to address this difficulty.

Estimation of Dependence Between Paired Correlated Failure Times in the Presence of Covariate Measurement Error

SummaryIn many biomedical studies, covariates are subject to measurement error. Although it is well known that the regression coefficients estimators can be substantially biased if the measurement error is not accommodated, there has been little study of the effect of covariate measurement error on the estimation of the dependence between bivariate failure times. We show that the dependence parameter estimator in the Clayton–Oakes model can be considerably biased if the measurement error in the covariate is not accommodated. In contrast with the typical bias towards the null for marginal regression coefficients, the dependence parameter can be biased in either direction. We introduce a bias reduction technique for the bivariate survival function in copula models while assuming an additive measurement error model and replicated measurement for the covariates, and we study the large and small sample properties of the dependence parameter estimator proposed.

Segmented regression in the presence of covariate measurement error in main study/validation study designs.

This article considers the problem of segmented regression in the presence of covariate measurement error in main study/validation study designs. First, we derive a closed and interpretable form for the full likelihood. After that, we use the likelihood results to compute the bias of the estimated changepoint in the case when the measurement error is ignored. We find the direction of the bias in the estimated changepoint to be determined by the design distribution of the observed covariates, and the bias can be in either direction. We apply the methodology to data from a nutritional study that investigates the relation between dietary folate and blood serum homocysteine levels and find that the analysis that ignores covariate measurement error would have indicated a much higher minimum daily dietary folate intake requirement than is obtained in the analysis that takes covariate measurement error into account.

Bayesian Smoothing and Regression Splines for Measurement Error Problems

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and regression P-splines. Two methods are described for exploration of the posterior. The first, called the iterative conditional modes (ICM), is only partially Bayesian. ICM uses a componentwise maximization routine to find the mode of the posterior. It also serves to create starting values for the second method, which is fully Bayesian and uses Markov chain Monte Carlo (MCMC) techniques to generate observations from the joint posterior distribution. Use of the MCMC approach has the advantage that interval estimates that directly model and adjust for the measurement error are easily calculated. We provide simulations with several nonlinear regression functions and provide an illustrative example. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method are better than those of ICM and also of previously proposed frequentist methods, at least in the examples that we have studied.

Linear Transformation Models for Failure Time Data With Covariate Measurement Error

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.