Adjustment For Measurement Error Research Articles

Three methods testing the asymmetry of the leaf blades of the small-leaved lime

Three methods were used to determine the fluctuating asymmetry (FA) of leaf blades and the developmental stability of smallleaved linden (Tilia cordata Mill): the normalizing difference method, the sample normalization method, and the two-factor analysis method (FA10). The collection of leaf blades took place along the latitudinal zonality gradient from north to south in five cities from Murmansk (68°58′ N) to Mozhaisk (55°30′ N), including the cities of Apatity, Petrozavodsk and Saint Petersburg. In all analyses, the highest FA value was obtained in the population of Petrozavodsk, the lowest in the population of Mozhaisk. In other cities, the FA indices differed, except for the populations in Apatity and Petrozavodsk with FA10 indices, respectively, 0.02 (p=0.02) and 0.03 (p=0.01). In the northernmost population (Murmansk), no decrease in developmental stability was noted. The stability of the development of Tilia cordata was more strongly influenced by the climatic and geographical conditions of the area and the technogenic state of the environment than by the geographic latitude. The authors note that a non-parametric sample distribution is advisable to use the two-factor analysis of variance, since normality difference and normalization lead to a non-equivalent deviation of the results. Bonferroni’s adjustments for measurement error were convenient for accurately distributing FA values at significance level.

Is the cholesterol-perfluoroalkyl substance association confounded by dietary fiber intake?: a Bayesian analysis of NHANES data with adjustment for measurement error in fiber intake

BackgroundSerum concentrations of total cholesterol and related lipid measures have been associated with serum concentrations of per- and polyfluoroalkyl substances (PFAS) in humans, even among those with only background-level exposure to PFAS. Fiber is known to decrease serum cholesterol and a recent report based on National Health and Nutrition Examination Survey (NHANES) showed that PFAS and fiber are inversely associated. We hypothesized that confounding by dietary fiber may account for some of the association between cholesterol and PFAS.MethodsWe implemented a Bayesian correction for measurement error in estimated intake of dietary fiber to evaluate whether fiber confounds the cholesterol-PFAS association. The NHANES measure of diet, two 24-h recalls, allowed calculation of an estimate of the “true” long-term fiber intake for each subject. We fit models to the NHANES data on serum cholesterol and serum concentration of perfluorooctanoic acid (PFOA) and two other PFAS for 7,242 participants in NHANES.ResultsThe Bayesian model, after adjustment for soluble fiber intake, suggested a decrease in the size of the coefficient for PFOA by 6.4% compared with the fiber-unadjusted model.ConclusionsThe results indicated that the association of serum cholesterol with PFAS was not substantially confounded by fiber intake.

Bayesian adjustment for measurement error in an offset variable in a Poisson regression model

Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL.

Phantom and big-fish-little-pond-effects on academic self-concept and academic achievement: Evidence from English early primary schools

The Big-Fish-Little-Pond Effect (BFLPE) suggests that school-average achievement has a negative effect on academic self-concept (ASC); some research has also verified a negative effect on students' academic achievement. Our study evaluates the compositional effects of school-average achievement on both outcomes, using a longitudinal sample of English early primary school students in Year 1 and Year 4. We provide evidence for BFLPEs in children as young as six to nine years of age. Further, we show that the BFLPE is a potential mechanism in the negative compositional effect of school average achievement in Year 1 on students' achievement in Year 4. Once adjustments for measurement error are made, the negative effect of school-average achievement on students' self-concept, and on their subsequent achievement, becomes even more negative. Our findings question previous research suggesting that attending a school with higher average achievement necessarily advances students’ outcomes.

Cross-sectional associations between central and general adiposity with albuminuria: observations from 400,000 people in UK Biobank

BackgroundWhether measures of central adiposity are more or less strongly associated with risk of albuminuria than body mass index (BMI), and by how much diabetes/levels of glycosylated haemoglobin (HbA1c) explain or modify these associations, is uncertain.MethodsOrdinal logistic regression was used to estimate associations between values of central adiposity (waist-to-hip ratio) and, separately, general adiposity (BMI) with categories of urinary albumin-to-creatinine ratio (uACR) in 408,527 UK Biobank participants. Separate central and general adiposity-based models were initially adjusted for potential confounders and measurement error, then sequentially, models were mutually adjusted (e.g. waist-to-hip ratio adjusted for BMI, and vice versa), and finally they were adjusted for potential mediators.ResultsLevels of albuminuria were generally low: 20,425 (5%) had a uACR ≥3 mg/mmol. After adjustment for confounders and measurement error, each 0.06 higher waist-to-hip ratio was associated with a 55% (95%CI 53–57%) increase in the odds of being in a higher uACR category. After adjustment for baseline BMI, this association was reduced to 32% (30–34%). Each 5 kg/m2 higher BMI was associated with a 47% (46–49%) increase in the odds of being in a higher uACR category. Adjustment for baseline waist-to-hip ratio reduced this association to 35% (33–37%). Those with higher HbA1c were at progressively higher odds of albuminuria, but positive associations between both waist-to-hip ratio and BMI were apparent irrespective of HbA1c. Altogether, about 40% of central adiposity associations appeared to be mediated by diabetes, vascular disease and blood pressure.ConclusionsConventional epidemiological approaches suggest that higher waist-to-hip ratio and BMI are independently positively associated with albuminuria. Adiposity–albuminuria associations appear strong among people with normal HbA1c, as well as people with pre-diabetes or diabetes.

Ex post adjustment for measurement error in stunting calculations: an illustration from Egypt.

The present study provides ranges for the magnitude of bias caused by measurement error in stunting rates, a widely used a proxy for long-term nutritional status. Stunting, which is determined by the number of cases that fall below -2 sd from the mean height-for-age in the population, mechanically increases with higher variance. This variance stems from both natural heterogeneity in the population and measurement error. To isolate the effect of measurement error, we model the true distributions which could give rise to the observed distributions after subtracting a simulated measurement error. We analyse information from three rounds of the Demographic and Health Survey (DHS) in Egypt (2005, 2008 and 2014). Egypt ranks high among developing countries with low-quality anthropometric data collected in the DHS, currently the main source of anthropometry in the country. The study relies on re-analysis of existing DHS data, which record height, weight and age data for children under 5 years old. Under the most conservative assumptions about measurement error, the stunting rate falls by 4 percentage points for the most recent DHS round, while assuming higher levels of measurement error reduces the stunting rate more dramatically. Researchers should be aware of and adjust for data quality concerns in calculating stunting rates for cross-survey comparisons or in communicating to policy makers.

Validation of self-reported occupational noise exposure in participants of a French case-control study on acoustic neuroma.

To validate self-reported occupational loud noise exposure against expert evaluation of noise levels in a French case-control study on acoustic neuroma and to estimate the impact of exposure misclassification on risk estimation. Noise levels were evaluated in 1006 jobs held by 111 cases and 217 population controls by an expert. Case-control differences in self-reporting were analyzed with logistic models. Sensitivity, specificity, positive and negative predictive values, and observed agreement of the self-reports were computed relative to the expert evaluation. They were used to calibrate the odds ratio (OR) between lifetime ever occupational loud noise exposure and the risk of acoustic neuroma, without adjustment for measurement error of the expert assessments. Cases reported noise levels in individual jobs closer to the expert assessment than controls, but the case-control difference was small for lifetime exposures. For expert-rated exposure of 80dB(A), reporting of individual jobs by cases was more sensitive (54% in cases, 37% in controls), whereas specificity (91% in cases, 93% in controls) and observed agreement (82% in cases, 81% in controls) were similar. When lifetime exposure was considered, sensitivity increased (76% in cases, 65% in controls), while cases specificity decreased (84%). When these values were used to calibrate self-reports for exposure misclassification compared to expert evaluation at 80dB(A), the crude OR of 1.7 was reduced to 1.3. Despite the relatively accurate reporting of loud noise, the impact of the calibration on the OR was non-negligible.

Are There Social Returns to Education in Developing Countries? Evidence from Indonesia

Despite growing public-sector investment in education in developing economies, there are few studies that have examined the efficacy of these investments. In this paper, we estimate social returns to education in Indonesia, using individual-level data on wages from five waves of the Indonesia Family Life Surveys (1993–2014) and subdistrict-level data on average education levels from the National Socioeconomic Survey (SUSENAS), a large-scale national-level socioeconomic survey. Our identification strategy rests on the within-sibling variation in average education levels, which is generated because our analysis includes a large sample of siblings who live in different subdistricts. Using sibling fixed effects, we find that a 1-year increase in average education results in a 6%–8% increase in wages. Our results are robust to several robustness checks, including the addition of several controls for labor demand conditions and adjustments for potential measurement error in individual-level education.

Statistical Considerations for Planning Clinical Trials with Quantitative Imaging Biomarkers.

As imaging technologies and treatment options continue to advance, imaging outcome measures are becoming increasingly utilized as the basis of making major decisions in new drug development and clinical practice. Quantitative imaging biomarkers (QIBs) are now commonly used for subject selection, response assessment, and safety monitoring. Although quantitative measurements can have many advantages compared with subjective, qualitative endpoints, it is important to recognize that QIBs are measured with error. This study uses Monte Carlo simulation to examine the impact of measurement error on a variety of clinical trial designs as well as to test proposed adjustments for measurement error. The focus is on some of the QIBs currently being studied by the Quantitative Imaging Biomarkers Alliance. The results show that the ability of QIBs to discriminate between health states and predict patient outcome is attenuated by measurement error; however, the known technical performance characteristics of QIBs can be used to adjust study sample size, control the misinterpretation rate of imaging findings, and establish statistically valid decision thresholds. We conclude that estimates of the precision and bias of a QIB are important for properly designing clinical trials and establishing the level of imaging standardization required.

A bayesian way to correct for measurement error in drug risk estimates from EHR data.

IntroductionData from electronic medical records is now readily available and records information needed in pharmacoepidemiological studies not usually found in administrative data such as risk factors and biometrics. Yet, EMR data leads to measurement error due to primary non-adherence. Bayesian bias correction could provide corrected estimates from administrative data.
 Objectives and ApproachWe present a method for correcting risk estimates from EMR data using linked data. In our example, we estimate the risk of cardiovascular events from oral-hypoglycemics in patients with type-2 diabetes in Boston, Quebec, and the UK between 2009 and 2012. Using linked EMR and administrative data in Quebec, we compute a positive and negative predicting value of prescription on dispensation for each class of oral-hypoglycemics. The cardiovascular risk is then analysed using a bayesian Weibull survival model adjusted for potential confounders. A similar model is then computed that accounts for exposure measurement error using the PPV and NPV.
 ResultsThe Quebec and Boston cohorts have similar sizes with 1197 and 2346 patients, but the UK was bigger at 41370 patients. In Quebec's data, there were important differences in PPV and NPV by class of oral-hypoglycemics with PPVs for Biguanides at 0.81, Sulphonylureas at 0.65, and others at 0.50. The pattern for NPV differed with the same classes having respectively values of 0.56, 0.97, and 0.99. Estimates from the naïve model are typical of similar analysis but compared to their correction, they were generally overprecise and biased towards the null. The adjusted estimated were adequately representing the increased uncertainty with hazard ratios for Sulphonylureas going from 1.72 (1.22, 2.41) to 3.19 (1.36, 5.93), and from 1.09 (0.86, 1.39) to 1.05 (0.45, 2.16) for no drugs
 Conclusion/ImplicationsBayesian adjustment for measurement error allowed us to use linked data to regenerate uncertainty and to correct the bias in our risk estimates. Our approach was impacted by the observed low predictive value of prescribing, by reduced transportability of our PPV and NPV estimates, and other sources of bias.

Nonparametric Adjustment for Measurement Error in Time-to-Event Data: Application to Risk Prediction Models

ABSTRACTMismeasured time-to-event data used as a predictor in risk prediction models will lead to inaccurate predictions. This arises in the context of self-reported family history, a time-to-event predictor often measured with error, used in Mendelian risk prediction models. Using validation data, we propose a method to adjust for this type of error. We estimate the measurement error process using a nonparametric smoothed Kaplan–Meier estimator, and use Monte Carlo integration to implement the adjustment. We apply our method to simulated data in the context of both Mendelian and multivariate survival prediction models. Simulations are evaluated using measures of mean squared error of prediction (MSEP), area under the response operating characteristics curve (ROC-AUC), and the ratio of observed to expected number of events. These results show that our method mitigates the effects of measurement error mainly by improving calibration and total accuracy. We illustrate our method in the context of Mendelian risk prediction models focusing on misreporting of breast cancer, fitting the measurement error model on data from the University of California at Irvine, and applying our method to counselees from the Cancer Genetics Network. We show that our method improves overall calibration, especially in low risk deciles. Supplementary materials for this article are available online.

Invited Commentary: The Contribution to the Field of Nutritional Epidemiology of the Landmark 1985 Publication by Willett et al.

The semiquantitative food frequency questionnaire (FFQ) has been the primary source of dietary exposure data in epidemiology for decades. Although frequency instruments had been evaluated before the 1985 publication "Reproducibility and Validity of a Semiquantitative Food Frequency Questionnaire" by Willett et al. (Am J Epidemiol. 1985;122(1):51-65), that paper was the prototype for the development and validation of what was then a highly innovative method for collecting dietary data. This approach was adopted in nearly all subsequent cohort studies of diet and disease. The paper also catalyzed an extended scientific discourse regarding methods for validation, energy adjustment, and measurement error. It is now well established that data from FFQs and other self-reported dietary assessment instruments have both value and error and that this error should be considered in the analysis and interpretation of findings, including sensitivity analyses in which adjustment for measurement error is explored. Advances in technology make it feasible to consider collecting multiple granular short-term instruments such as recalls or records over time in addition to FFQs among all participants in large cohort studies; both provide valuable information. Without a doubt, the 1985 publication by Willett et al. provided the foundation that propelled the field of nutritional epidemiology forward, and it continues to be relevant today.

Sugar-sweetened beverage intake and cardiovascular risk factor profile in youth with type 1 diabetes: application of measurement error methodology in the SEARCH Nutrition Ancillary Study.

The SEARCH Nutrition Ancillary Study aims to investigate the role of dietary intake on the development of long-term complications of type 1 diabetes in youth, and capitalise on measurement error (ME) adjustment methodology. Using the National Cancer Institute (NCI) method for episodically consumed foods, we evaluated the relationship between sugar-sweetened beverage (SSB) intake and cardiovascular risk factor profile, with the application of ME adjustment methodology. The calibration sample included 166 youth with two FFQ and three 24 h dietary recall data within 1 month. The full sample included 2286 youth with type 1 diabetes. SSB intake was significantly associated with higher TAG, total and LDL-cholesterol concentrations, after adjusting for energy, age, diabetes duration, race/ethnicity, sex and education. The estimated effect size was larger (model coefficients increased approximately 3-fold) after the application of the NCI method than without adjustment for ME. Compared with individuals consuming one serving of SSB every 2 weeks, those who consumed one serving of SSB every 2 d had 3.7 mg/dl (0.04 mmol/l) higher TAG concentrations and 4.0 mg/dl (0.10 mmol/l) higher total cholesterol and LDL-cholesterol concentrations, after adjusting for ME and covariates. SSB intake was not associated with measures of adiposity and blood pressure. Our findings suggest that SSB intake is significantly related to increased lipid levels in youth with type 1 diabetes, and that estimates of the effect size of SSB on lipid levels are severely attenuated in the presence of ME. Future studies in youth with diabetes should consider a design that will allow for the adjustment for ME when studying the influence of diet on health status.

The association of long-term exposure to PM2.5 on all-cause mortality in the Nurses' Health Study and the impact of measurement-error correction.

BackgroundLong-term exposure to particulate matter less than 2.5 μm in diameter (PM2.5) has been consistently associated with risk of all-cause mortality. The methods used to assess exposure, such as area averages, nearest monitor values, land use regressions, and spatio-temporal models in these studies are subject to measurement error. However, to date, no study has attempted to incorporate adjustment for measurement error into a long-term study of the effects of air pollution on mortality.MethodsWe followed 108,767 members of the Nurses’ Health Study (NHS) 2000–2006 and identified all deaths. Biennial mailed questionnaires provided a detailed residential address history and updated information on potential confounders. Time-varying average PM2.5 in the previous 12-months was assigned based on residential address and was predicted from either spatio-temporal prediction models or as concentrations measured at the nearest USEPA monitor. Information on the relationships of personal exposure to PM2.5 of ambient origin with spatio-temporal predicted and nearest monitor PM2.5 was available from five previous validation studies. Time-varying Cox proportional hazards models were used to estimate hazard ratios (HRs) and 95 percent confidence intervals (95%CI) for each 10 μg/m3 increase in PM2.5. Risk-set regression calibration was used to adjust estimates for measurement error.ResultsIncreasing exposure to PM2.5 was associated with an increased risk of mortality, and results were similar regardless of the method chosen for exposure assessment. Specifically, the multivariable adjusted HRs for each 10 μg/m3 increase in 12-month average PM2.5 from spatio-temporal prediction models were 1.13 (95%CI:1.05, 1.22) and 1.12 (95%CI:1.05, 1.21) for concentrations at the nearest EPA monitoring location. Adjustment for measurement error increased the magnitude of the HRs 4-10% and led to wider CIs (HR = 1.18; 95%CI: 1.02, 1.36 for each 10 μg/m3 increase in PM2.5 from the spatio-temporal models and HR = 1.22; 95%CI: 1.02, 1.45 from the nearest monitor estimates).ConclusionsThese findings support the large body of literature on the adverse effects of PM2.5, and suggest that adjustment for measurement error be considered in future studies where possible.

Long-Term Ambient Residential Traffic-Related Exposures and Measurement Error-Adjusted Risk of Incident Lung Cancer in the Netherlands Cohort Study on Diet and Cancer.

BackgroundThe International Agency for Research on Cancer (IARC) recently declared air pollution carcinogenic to humans. However, no study of air pollution and lung cancer to date has incorporated adjustment for exposure measurement error, and few have examined specific histological subtypes.ObjectivesOur aim was to assess the association of air pollution and incident lung cancer in the Netherlands Cohort Study on Diet and Cancer and the impact of measurement error on these associations.MethodsThe cohort was followed from 1986 through 2003, and 3,355 incident cases were identified. Cox proportional hazards models were used to estimate hazard ratios and 95% confidence intervals, for long-term exposures to nitrogen dioxide (NO2), black smoke (BS), PM2.5 (particulate matter with diameter ≤ 2.5 μm), and measures of roadway proximity and traffic volume, adjusted for potential confounders. Information from a previous validation study was used to correct the effect estimates for measurement error.ResultsWe observed elevated risks of incident lung cancer with exposure to BS [hazard ratio (HR) = 1.16; 95% CI: 1.02, 1.32, per 10 μg/m3], NO2 (HR = 1.29; 95% CI: 1.08, 1.54, per 30 μg/m3), PM2.5 (HR = 1.17; 95% CI: 0.93, 1.47, per 10 μg/m3), and with measures of traffic at the baseline address. The exposures were positively associated with all lung cancer subtypes. After adjustment for measurement error, the HRs increased and the 95% CIs widened [HR = 1.19 (95% CI: 1.02, 1.39) for BS and HR = 1.37 (95% CI: 0.86, 2.17) for PM2.5].ConclusionsThese findings add support to a growing body of literature on the effects of air pollution on lung cancer. In addition, they highlight variation in measurement error by pollutant and support the implementation of measurement error corrections when possible.CitationHart JE, Spiegelman D, Beelen R, Hoek G, Brunekreef B, Schouten LJ, van den Brandt P. 2015. Long-term ambient residential traffic–related exposures and measurement error–adjusted risk of incident lung cancer in the Netherlands Cohort Study on Diet and Cancer. Environ Health Perspect 123:860–866; http://dx.doi.org/10.1289/ehp.1408762

Computer-aided variables sampling inspection plans for compositional proportions and measurement error adjustment

Many quality characteristics encountered in the food industry are compositional proportions, e.g. protein percentage in milk powder. The distributions of these quality characteristics are intrinsically not normal as well as cannot be well-approximated by it. Moreover the shape of underlying distribution of the quality characteristic in each lot is likely to change in a short-run production process due to process adjustment actions and heterogeneity in raw materials. As a result, the standard variables sampling plans based on the normal distribution are not appropriate. The impact of measurement error, which is often strongly present in analytical testing, has not yet been well-addressed in the non-normal variables sampling inspection procedures. This paper proposes a computer-aided procedure for the identification of the underlying distribution, adjustment for the measurement error, and then the design of the sampling inspection plan. The weighted kernel deconvolution approach is employed for measurement error adjustment and a new procedure for designing a variables plan allowing for uncertainty in the shape parameters of the underlying distribution is developed.

Relative validity and reliability of an FFQ in youth with type 1 diabetes.

To evaluate the relative validity and reliability of the SEARCH FFQ that was modified from the Block Kids Questionnaire. Study participants completed the eighty-five-item FFQ twice plus three 24 h dietary recalls within one month. We estimated correlations between frequencies obtained from participants with the true usual intake for food groups and nutrients, using a two-part model for episodically consumed foods and measurement error adjustment. The multi-centre SEARCH for Diabetes in Youth Nutrition Ancillary Study. A subgroup of 172 participants aged 10-24 years with type 1 diabetes. The mean correlations, adjusted for measurement error, of food groups and nutrients between the FFQ and true usual intake were 0·41 and 0·38, respectively, with 57 % of food groups and 70 % of nutrients exhibiting correlations >0·35. Correlations were high for low-fat dairy (0·80), sugar-sweetened beverages (0·54), cholesterol (0·59) and saturated fat (0·51), while correlations were poor for high-fibre bread and cereal (0·16) and folate (0·11). Reliability of FFQ intake based on two FFQ administrations was also reasonable, with 54 % of Pearson correlation coefficients ≥0·5. Reliability was high for low-fat dairy (0·7), vegetables (0·6), carbohydrates, fibre, folate and vitamin C (all 0·5), but less than desirable for low-fat poultry and high-fibre bread, cereal, rice and pasta (0·2-0·3). While there is some room for improvement, our findings suggest that the SEARCH FFQ performs quite well for the assessment of many nutrients and food groups in a sample of youth with type 1 diabetes.

Trait anxiety and trait anger measured by ecological momentary assessment and their correspondence with traditional trait questionnaires

Ecological momentary assessments (EMA) of anxiety and anger/hostility were obtained every 25–30min over two 24-h periods, separated by a median of 6months, from 165 employees at a university in the Northeast. We used a multilevel trait-state-error structural equation model to estimate: (1) the proportion of variance in EMA anxiety and anger/hostility attributable to stable trait-like individual differences; (2) the correspondence between these trait-like components of EMA anxiety and anger/hostility and traditional questionnaire measures of each construct; and (3) the test–retest correlation between two 24-h averages obtained several months apart. After adjustment for measurement error, more than half the total variance in EMA reports of anxiety and anger/hostility is attributable to stable trait-like individual differences; however, the trait-like component of each construct is only modestly correlated with questionnaire measures of that construct. The 6-month “test–retest” correlations of latent variables representing the true 24-h EMA average anxiety and average anger are quite high (r⩾0.83). This study represents the longest follow-up period over which EMA-based estimates of traits have been examined. The results suggest that although the trait component (individual differences) of EMA momentary ratings of anxiety and anger is larger than the state component, traditional self-report questionnaires of trait anxiety and anger correspond only weakly with EMA-defined traits.

Adjustment for measurement error in evaluating diagnostic biomarkers by using an internal reliability sample

Biomarkers are often measured with error due to imperfect lab conditions or temporal variability within subjects. Using an internal reliability sample of the biomarker, we develop a parametric bias-correction approach for estimating a variety of diagnostic performance measures including sensitivity, specificity, the Youden index with its associated optimal cut-point, positive and negative predictive values, and positive and negative diagnostic likelihood ratios when the biomarker is subject to measurement error. We derive the asymptotic properties of the proposed likelihood-based estimators and show that they are consistent and asymptotically normally distributed. We propose confidence intervals for these estimators and confidence bands for the receiver operating characteristic curve. We demonstrate through extensive simulations that the proposed approach removes the bias due to measurement error and outperforms the naïve approach (which ignores the measurement error) in both point and interval estimation. We also derive the asymptotic bias of naïve estimates and discuss conditions in which naïve estimates of the diagnostic measures are biased toward estimates produced when the biomarker is ineffective (i.e., when sensitivity equals 1 - specificity) or are anticonservatively biased. The proposed method has broad biomedical applications and is illustrated using a biomarker study in Alzheimer's disease. We recommend collecting an internal reliability sample during the biomarker discovery phase in order to adequately evaluate the performance of biomarkers with careful adjustment for measurement error.

Measurement Error Adjustment Using the SIMEX Method: An Application to Student Growth Percentiles

Growth models are used extensively in the context of educational accountability to evaluate student-, class-, and school-level growth. However, when error-prone test scores are used as independent variables or right-hand-side controls, the estimation of such growth models can be substantially biased. This article introduces a simulation-extrapolation (SIMEX) method that corrects measurement error induced bias. The SIMEX method is applied to quantile regression, which is the basis of Student Growth Percentile, a descriptive growth model adopted in a number of states to diagnose and project student growth. A simulation study is conducted to demonstrate the performance of the SIMEX method in reducing bias and mean squared error in quantile regression with a mismeasured predictor. One of the simulation cases is based on longitudinal state assessment data. The analysis shows that measurement error differentially biases growth percentile results for students at different achievement levels and that the SIMEX method corrects such biases and closely reproduces conditional distributions of current test scores given past true scores. The potential applications and limitations of the method are discussed at the end of this paper with suggestions for further studies.