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PubMed2004

Assessment of salivary flow rate: biologic variation and measure error.

OBJECTIVE: To investigate the applicability of the swab method in the measurement of salivary flow rate in multiple-handicap drooling children. To quantify the measurement error of the procedure and the biologic variation in the population. STUDY DESIGN: Cohort study. METHODS: In a repeated measurements design, a baseline series of salivary flow rates were obtained from 45 children. The within-subject SD (SW) was calculated to express the measurements error according to a procedure introduced by Bland and Altman. RESULTS: Two hundred twenty-four samples (mean 0.40 mL/min, SD 0.19 mL/min) were obtained and analyzed. The results of this study indicate that consistent scores were obtained at subsequent measurements, and good parity existed between the two measurements of salivary flow rate at each session. The SW could be estimated (0.11 mL/min), which was applied to quantify the specific variation of the salivary flow rate in our population. CONCLUSION: According to Bland and Altman, the SW, which is a quantification of the measurement error and biologic variation, was found to be a useful tool to evaluate the obtained baseline salivary flow rate measurements. The swab method can be used to evaluate salivary flow rates in drooling children with cerebral palsy during interventional studies that aim to reduce saliva production.

Adolescent↗

PubMed2000

A measurement error model for time-series studies of air pollution and mortality.

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.

Journal Article↗

PubMed1992

Correction of logistic regression relative risk estimates and confidence intervals for random within-person measurement error.

Frequently, covariates used in a logistic regression are measured with error. The authors previously described the correction of logistic regression relative risk estimates for measurement error in one or more covariates when a "gold standard" is available for exposure assessment. For some exposures (e.g., serum cholesterol), no gold standard exists, and one must assess measurement error via a reproducibility substudy. In this paper, the authors present measurement error methods for logistic regression when there is error (possibly correlated) in one or more covariates and one has data from both a main study and a reproducibility substudy. Confidence intervals from this procedure reflect error in parameter estimates from both studies. These methods are applied to the Framingham Heart Study, where the 10-year incidence of coronary heart disease is related to several coronary risk factors among 1,731 men disease-free at examination 4. Reproducibility data are obtained from the subgroup of 1,346 men seen at examinations 2 and 3. Estimated odds ratios comparing extreme quintiles for risk factors with substantial error were increased after correction for measurement error (serum cholesterol, 2.2 vs. 2.9; serum glucose, 1.3 vs. 1.5; systolic blood pressure, 2.8 vs. 3.8), but were generally decreased or unchanged for risk factors with little or no error (body mass index, 1.6 vs. 1.6; age 65-69 years vs. 35-44 years, 4.3 vs. 3.8; smoking, 1.7 vs. 1.7).

Adult↗

PubMed1991

Identification of insulin receptor systems: assessing the impact of model selection and measurement error on precision of parameter estimates using Monte Carlo study.

An extensive Monte Carlo study has been carried out in order to study the effect of measurement error on the precision of parameter estimates of an insulin binding system. Hypothetical radioimmunoassay experiments were generated for insulin binding to erythrocytes. The design of experiments followed strictly the protocol of real experiments. Randomly generated error was added to the synthetic data. The standard technique, a weighted non-linear regression analysis, was employed to re-estimate parameters of a model of two receptor sites and a model of negative co-operativity. As the original parameter values were known, the differences between original and estimated values was studied for (a) measurement error in the range from 0-17%, (b) random initial estimates and (c) error-free non-specific binding. In addition, analytical estimates of parameter precision were compared with the true between-experiment variation of parameter estimates. At the measurement error of 12%, a one site model is recommended to estimate the high affinity population of the two sites model. Plausible results can be expected in 90% of experiments, the between-experiment variation being approximately 30%. The model of two receptor sites gives approximately two thirds of plausible results. The high affinity population can be estimated with the between-experiment variation of 40%, the low affinity population is virtually unidentifiable with the between-experiment variation of approximately 100% and parameter estimates biased to higher values. Only half of the results obtained from the model of negative co-operativity are plausible, the variation in parameter estimates ranges from 90-150% and estimates are biased to higher values. At the level of 12% measurement error, random initial estimates do not significantly affect the estimation process, provided initial estimates are selected from a feasible range. At the same measurement error, the error-free non-specific binding does not improve the results, indicating that the mean of six replicates may be taken as a reliable estimate of non-specific binding. The analytical estimates of the coefficient of variation systematically underestimates the true between-experiments coefficient of variation, the difference has been found to be about 50%.

Erythrocytes↗

PubMed2006

Addressing measurement error bias in nurse staffing research.

OBJECTIVE: To assess the extent of measurement error bias due to methods used to allocate nursing staff to the acute care inpatient setting and to recommend estimation methods designed to overcome this bias. DATA SOURCES/STUDY SETTING: Secondary data obtained from the California Office of Statewide Health Planning and Development (OSHPD) and the Centers for Medicare and Medicaid Services' Healthcare Cost Report Information System for 279 general acute care hospitals from 1996 to 2001. STUDY DESIGN: California OSHPD provides detailed nurse staffing data for acute care inpatients. We estimate the measurement error and the resulting bias from applying different staffing allocation methods. Estimates of the measurement errors also allow insights into the best choices for alternate estimation strategies. PRINCIPAL FINDINGS: The bias induced by the adjusted patient days method (and its modification) is smaller than for other methods, but the bias is still substantial: in the benchmark simple regression model, the estimated coefficient for staffing level on quality of care is expected to be one-third smaller than its true value (and the bias is larger in a multiple regression model). Instrumental variable estimation, using one staffing allocation measure as an instrument for another, addresses this bias, but only particular choices of staffing allocation measures and instruments are suitable. CONCLUSIONS: Staffing allocation methods induce substantial attenuation bias, but there are easily implemented estimation methods that overcome this bias.

Bias↗

PubMed1998

Covariate measurement error and the estimation of random effect parameters in a mixed model for longitudinal data.

We explore the effects of measurement error in a time-varying covariate for a mixed model applied to a longitudinal study of plasma levels and dietary intake of beta-carotene. We derive a simple expression for the bias of large sample estimates of the variance of random effects in a longitudinal model for plasma levels when dietary intake is treated as a time-varying covariate subject to measurement error. In general, estimates for these variances made without consideration of measurement error are biased positively, unlike estimates for the slope coefficients which tend to be 'attenuated'. If we can assume that the residuals from a longitudinal fit for the time-varying covariate behave like measurement errors, we can estimate the original parameters without the need for additional validation or reliability studies. We propose a method to test this assumption and show that the assumption is reasonable for the example data. We then use a likelihood-based method of estimation that involves a simple extension of existing methods for fitting mixed models. Simulations illustrate the properties estimators.

Analysis of Variance↗

PubMed2002

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.

Bias↗

PubMed1997

Measurement error correction for logistic regression models with an "alloyed gold standard".

Recently, some authors have questioned the validity of methods which correct relative risk estimates for measurement error and misclassification when the "gold standard" used to obtain information about the measurement error process is itself imperfect. When such an "alloyed" gold standard is used to validate the usual exposure measurement, the bias in the "regression calibration" (Rosner et al., Stat Med 1989; 8:1051-69) measurement-error correction factor for relative risks estimated from logistic regression models is derived. This quantity is a function of the correlations of the "alloyed" gold standard (X) and the usual exposure assessment method (Z) with the truth, of the ratio of the variances of X and Z, and of the correlation between the errors in the "alloyed" gold standard and the errors in the usual exposure assessment method. In this paper, it is proven that if the errors between Z and X are uncorrelated, the regression calibration method has no bias even when the gold standard is "alloyed." When a third method of exposure assessment is available and it is reasonable to assume that the errors in this method are uncorrelated with the errors in the other two exposure assessment methods, point and interval estimates of the correlation between the errors in X and Z are derived. These methods are illustrated here with data on the measurement of physical activity, vitamins A and E, and poly- and monounsaturated fat. In addition, when a third exposure assessment method is available, a modification of standard regression calibration is derived which can be used to calculate point and interval estimates of relative risk that are corrected for measurement error in both X and Z. This new method is illustrated here with data from the Health Professionals Follow-up Study, a study investigating the associations between physical activity and colon cancer incidence and between vitamin E intake and coronary heart disease. It is shown that in these examples, correlations of the errors in X and Z tended to be small. Even when moderate, estimates of relative risk corrected for error in both X and Z were not very different from the estimates which assumed that X was a true gold standard.

Bias↗

PubMed2001

Semiparametric maximum likelihood for measurement error model regression.

This paper presents an EM algorithm for semiparametric likelihood analysis of linear, generalized linear, and nonlinear regression models with measurement errors in explanatory variables. A structural model is used in which probability distributions are specified for (a) the response and (b) the measurement error. A distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood. For various types of extra information about the measurement error distribution, the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of (a) and (b) if the true x were available. Simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption. The approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution.

Algorithms↗

PubMed1989

Further results on covariate measurement errors in cohort studies with time to response data.

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.

Analysis of Variance↗

PubMed2003

Misclassification associated with measurement error in the assessment of dietary intake.

OBJECTIVE: Dietary assessment has been used for certification to receive food supplements or other nutrition services and to provide feedback for educational purposes. The proportion of individuals correctly certified as eligible is a function of the amount of error that exists in the dietary measures and the level of dietary intake used to establish eligibility. Whether individuals are correctly counselled to increase or decrease the consumption of selected foods or nutrients is a function of the same factors. It is not clear, however, what percentage of individuals would be correctly classified under what circumstances. The objective of this study is to demonstrate the extent to which measurement error and eligibility criteria affect the accuracy of classification. DESIGN: Hypothetical distributions of dietary intake were generated with varying degrees of measurement error. Different eligibility criteria were applied and the expected classification rates were determined using numerical methods. SETTING AND SUBJECTS: Simulation study. RESULTS: Cut points of dietary intake at decreasing levels below the 50th percentile of true intake were associated with lower sensitivity and predictive value positive rates, but higher specificity and predictive value negative rates. The correct classification rates were lower when two cut points of dietary intake were used. Using a single cut point that was higher than the targeted true consumption resulted in higher sensitivity but lower predictive value positive, and lower specificity but higher predictive value negative. CONCLUSIONS: Current methods of dietary assessment may not be reliable enough to attain acceptable levels of correct classification. Policy-makers and educators must consider how much misclassification error they are willing to accept and determine whether more intensive methods are necessary.

Bias↗

PubMed2001

Statistical inference for the area under the receiver operating characteristic curve in the presence of random measurement error.

The area under the receiver operating characteristic curve is the most commonly used measure of the ability of a biomarker to distinguish between two populations. Some markers are subject to substantial measurement error. Under normality assumptions, the authors develop a confidence interval procedure for the area under the receiver operating characteristic curve that adjusts for measurement error. This procedure assumes the availability of data from a reliability study of the biomarker. A simulation study was used to check the validity of the proposed confidence interval. Furthermore, it was shown that not adjusting for measurement error could result in a serious understatement of the effectiveness of the biomarker.

Analysis of Variance↗

PubMed1997

Effect of training and experience on cephalometric measurement errors on surgical patients.

The aim of this study was to quantify and compare the cephalometric measurement errors (interexaminer errors) between two orthodontic residents and two oral and maxillofacial surgical residents with differing years of experience. It was hypothesized that the measurement errors would differ between observers with different training backgrounds and experience and that this would lead to significant disagreements in the cephalometric assessment of patients to receive combined orthodontic and orthognathic surgical treatment. Thirty cephalograms were used in the evaluation. Each examiner independently digitized all cephalograms twice. Common cephalometric skeletal and dental variables, 18 angular and 9 linear, were measured. Interexaminer errors were calculated using two-sample t tests for every pair of examiners. The interexaminer error was large in both landmark identification and in angular and linear measurements. The amount of error did not depend on training or experience but probably on individual conception of landmark definition and perception of landmark location. Methods to limit interexaminer measurement errors are described.

Adult↗

PubMed1993

A Bayesian approach to logistic regression models having measurement error following a mixture distribution.

To estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error, we take a Bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value. We allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure. We apply the method to study the risk of alcohol consumption on breast cancer using the Nurses Health Study data. We estimate measurement error from a small subsample where we compare true with reported consumption. Some of the self-reported non-drinkers truly do not drink. The resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error.

Age Factors↗

PubMed2000

The effect of random measurement error on receiver operating characteristic (ROC) curves.

In this paper confidence intervals for the area under the ROC curve are adjusted for the presence of measurement error. A parametric normal model is assumed. The ratio of intra-individual to inter-individual variance provides a relative measure of the amount of measurement error. An exact adjusted confidence interval is developed for the equal variance case and an approximation is derived for the unequal variance case. We illustrate, using an example, the effect of ignoring the measurement error on the confidence interval for the area and show that the effect can be substantial on the decision as to the diagnostic effectiveness of the marker. We also examine, by means of a simulation study, the coverage probability of the unadjusted confidence interval and show that it can be far from its nominal value when measurement error is present.

Breast↗

PubMed2006

Structural inference in transition measurement error models for longitudinal data.

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.

Aged↗

PubMed2006

Use of itemized Till receipts to adjust for correlated dietary measurement error.

Recent studies suggest that measurement error in food frequency questionnaires includes a person-specific component correlated with that of other self-reported dietary assessments. Use of biomarkers has been recommended to adequately calibrate dietary assessment tools for unbiased estimation of associations between diet and disease. Data on biomarkers of intake are often collected only in small subsamples, because collection of biomarker data can be expensive and inconvenient for participants. In this paper, the authors propose a novel approach using itemized household grocery till receipts to calibrate dietary assessment. Till receipts are not self-recorded and the data obtained from them are not subject to person-specific bias, but the data need to be supported by self-completed diaries for foods eaten away from home. Till receipts may also prove cheaper to collect in larger samples. The authors discuss the many methodological challenges of using household-level data and discuss how till receipts might be used in practice, with or without the use of biomarkers.

Biomarkers↗

PubMed2003

[An analysis of measurement error in Orbscan topography system].

OBJECTIVE: To discuss the measurement error and the influence factor of Orbscan Topography to provide more accurate data for clinical application. METHODS: Orbscan Topography System and A-scan ultrasonography were used to measure the corneal thickness and anterior chamber depths pre-operatively and post-operatively, including 200 cases (400 eyes) undergoing laser in situ keratomileusis (Lasik) and 50 cases (100 eyes) undergoing photorefractive keratectomy (PRK). The curvature of posterior corneal surface was measured by Orbscan topography before and after the operations, and the result of measurement was compared. RESULTS: Pre-operatively, the value of corneal thickness was (18.83 - 24.29) microm lower measured by Orbscan topography than that by A-ultrasonography, and post-operatively the value was (56.32 - 139.52) micro m lower than that by A-ultrasonography. The postoperative value was obviously higher than the pre-operative one. The value of central anterior chamber depth was (0.16 - 0.25) mm lower measured by Orbscan system than that by A-ultrasonography pre-operatively and post-operatively. There was no clinical significance. The difference in the comparison of posterior corneal surface curvature before and after Lasik was -0.60 D measured by Orbscan System. The difference in the comparison of posterior corneal surface curvature before and after PRK was -0.51 D in the lower diopter group and -1.12 D in medium diopter group. CONCLUSIONS: It is necessary to improve the accuracy of Orbscan Topography System. The Haze and the change of anterior corneal surface curvature after Lasik and PRK are the main causes of measurement error in Orbscan Topography System. Clinically, it is an un-negligible important problem in the measurement of Orbscan system.

Adolescent↗