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PubMed1999

Anthropometric measurement error and the assessment of nutritional status.

Anthropometry involves the external measurement of morphological traits of human beings. It has a widespread and important place in nutritional assessment, and while the literature on anthropometric measurement and its interpretation is enormous, the extent to which measurement error can influence both measurement and interpretation of nutritional status is little considered. In this article, different types of anthropometric measurement error are reviewed, ways of estimating measurement error are critically evaluated, guidelines for acceptable error presented, and ways in which measures of error can be used to improve the interpretation of anthropometric nutritional status discussed. Possible errors are of two sorts; those that are associated with: (1) repeated measures giving the same value (unreliability, imprecision, undependability); and (2) measurements departing from true values (inaccuracy, bias). Imprecision is due largely to observer error, and is the most commonly used measure of anthropometric measurement error. This can be estimated by carrying out repeated anthropometric measures on the same subjects and calculating one or more of the following: technical error of measurement (TEM); percentage TEM, coefficient of reliability (R), and intraclass correlation coefficient. The first three of these measures are mathematically interrelated. Targets for training in anthropometry are at present far from perfect, and further work is needed in developing appropriate protocols for nutritional anthropometry training. Acceptable levels of measurement error are difficult to ascertain because TEM is age dependent, and the value is also related to the anthropometric characteristics of the group of population under investigation. R > 0.95 should be sought where possible, and reference values of maximum acceptable TEM at set levels of R using published data from the combined National Health and Nutrition Examination Surveys I and II (Frisancho, 1990) are given. There is a clear hierarchy in the precision of different nutritional anthropometric measures, with weight and height being most precise. Waist and hip circumference show strong between-observer differences, and should, where possible, be carried out by one observer. Skinfolds can be associated with such large measurement error that interpretation is problematic. Ways are described in which measurement error can be used to assess the probability that differences in anthropometric measures across time within individuals are due to factors other than imprecision. Anthropometry is an important tool for nutritional assessment, and the techniques reported here should allow increased precision of measurement, and improved interpretation of anthropometric data.

Anthropometry↗

PubMed1993

Quantitation of measurement error with Optimal Segments: basis for adaptive time course smoothing.

We introduce a novel technique for estimating measurement error in time courses and other continuous curves. This error estimate is used to reconstruct the original (error-free) curve. The measurement error of the data is initially assumed, and the data are smoothed with "Optimal Segments" such that the smooth curve misses the data points by an average amount consistent with the assumed measurement error. Thus the differences between the smooth curve and the data points (the residuals) are tentatively assumed to represent the measurement error. This assumption is checked by testing the residuals for randomness. If the residuals are nonrandom, it is concluded that they do not resemble measurement error, and a new measurement error is assumed. This process continues reiteratively until a satisfactory (i.e., random) group of residuals is obtained. In this case the corresponding smooth curve is taken to represent the original curve. Monte Carlo simulations of selected typical situations demonstrated that this new method ("OOPSEG") estimates measurement error accurately and consistently in 30- and 15-point time courses (r = 0.91 and 0.78, respectively). Moreover, smooth curves calculated by OOPSEG were shown to accurately recreate (predict) original, error-free curves for a wide range of measurement errors (2-20%). We suggest that the ability to calculate measurement error and reconstruct the error-free shape of data curves has wide applicability in data analysis and experimental design.

Animals↗

PubMed1997

Correcting for measurement error in the analysis of case-control data with repeated measurements of exposure.

The authors present a technique for correcting for exposure measurement error in the analysis of case-control data when subjects have a variable number of repeated measurements, and the average is used as the subject's measure of exposure. The true exposure as well as the measurement error are assumed to be normally distributed. The method transforms each subject's observed average by a factor which is a function of the measurement error parameters, prior to fitting the logistic regression model. The resulting logistic regression coefficient estimate based on the transformed average is corrected for error. A bootstrap method for obtaining confidence intervals for the true regression coefficient, which takes into account the variability due to estimation of the measurement error parameters, is also described. The method is applied to data from a nested case-control study of hormones and breast cancer.

Algorithms↗

PubMed1984

Assessing the validity of the achievement motive in the presence of random measurement error.

The presence of random measurement error in indicators of theoretical constructs biases observed estimates of relations among those constructs. Correcting for this bias is particularly important when random measurement error is substantial, or is substantially different for indicators of distinct constructs included in a theoretical model. Validity assessment in the case of thematic apperceptive measures of the achievement motive (TAT n Achievement) has been vulnerable to interpretive errors because these indicators of the achievement motive are typically much less reliable than indicators of other constructs to which the motive may be related, and no correction has been made for the bias introduced by such differential measurement error. Here we illustrate a causal modeling approach to validity assessment for TAT n Achievement that incorporates explicit true-score measurement models of theoretical constructs. We confirm the hypothesis that the achievement motive construct is positively related to work satisfaction in a representative sample of adult males in the United States, taken in 1976 (N = 413). Evidence for the discriminant validity of story content versus story length, an issue raised in the literature on the TAT, is also presented in this nomological network.

Achievement↗

PubMed1994

[Measurement errors and linear regression].

The consequences of a measurement error of known variance in the explanatory variable of a linear regression were assessed. On the average, the ordinary least squares (OLS) method underestimated the regression slope, the bias increasing with the variance of the measurement error and the strength of the relationship. Simulation results showed that the corrected-for-the-error estimate slightly overestimated the slope, the bias increasing with the variance of the measurement error and the strength of the relationship, but rapidly decreasing when the number of observations increased. In all cases the corrected estimate has a larger variance than the OLS estimate, Nevertheless, the mean square deviation of the corrected estimate to the "true" slope value can be smaller than the OLS one, even for a relatively small number of observations (< or = 100). In those conditions, the corrected estimate might be preferred when a "good estimation" of the regression slope is needed. Whereas a measurement error in the dependent variable, does not bias the slope estimator, when it is independent of the error in the explanatory variable, this is not the case when both measurement errors are correlated. An example of the need to correct for such a correlation is given.

Bias↗

PubMed2005

Measurement error and confidence intervals for ROC curves.

Measurement error in a continuous test variable may bias estimates of the summary properties of receiver operating characteristics (ROC) curves. Typically, unbiased measurement error will reduce the diagnostic potential of a continuous test variable. This paper explores the effects of possibly heterogenous measurement error on estimated ROC curves for binormal test variables. Corrected estimators for specific points on the curve are derived under the assumption of known or estimated measurement variances for individual test results. These estimators and associated confidence intervals do not depend on normal assumptions for the distribution of the measurement error and are shown to be approximately unbiased for moderate size samples in a simulation study. An application from a study of emerging imaging modalities in breast cancer is used to demonstrate the new techniques.

Computer Simulation↗

PubMed2006

Multiple-imputation for measurement-error correction.

BACKGROUND: There are many methods for measurement-error correction. These methods remain rarely used despite the ubiquity of measurement error. METHODS: Treating measurement error as a missing-data problem, the authors show how multiple-imputation for measurement-error (MIME) correction can be done using SAS software and evaluate the approach with a simulation experiment. RESULTS: Based on hypothetical data from a planned cohort study of 600 children with chronic kidney disease, the estimated hazard ratio for end-stage renal disease from the complete data was 2.0 [95% confidence limits (95% CL) 1.4, 2.8] and was reduced to 1.5 (95% CL 1.1, 2.1) using a misclassified exposure of low glomerular filtration rate at study entry (sensitivity of 0.9 and specificity of 0.7). The MIME correction hazard ratio was 2.0 (95% CL 1.2, 3.3), the regression calibration (RC) hazard ratio was 2.0 (95% CL 1.1, 3.7), and restriction to a 25% validation substudy yielded a hazard ratio of 2.0 (95% CL 1.0, 3.7). Based on Monte Carlo simulations across eight scenarios, MIME was approximately unbiased, had approximately correct coverage, and was sometimes more powerful than misclassified or RC analyses. Using root mean squared error as a criterion, the MIME bias correction is sometimes outweighed by added imprecision. CONCLUSION: The choice between MIME and RC depends on performance, ease, and objectives. The usefulness of MIME correction in specific applications will depend upon the sample size or the proportion validated. MIME correction may be valuable in interpreting imperfectly measured epidemiological data.

Bias↗

PubMed1990

The impact of dietary measurement error on planning sample size required in a cohort study.

Dietary measurement error has two consequences relevant to epidemiologic studies: first, a proportion of subjects are misclassified into the wrong groups, and second, the distribution of reported intakes is wider than the distribution of true intakes. While the first effect has been dealt with by several other authors, the second effect has not received as much attention. Using a simple errors-in-measurement model, the authors investigate the implications of measurement error for the distribution of fat intake. They then show how the inference of a more narrow distribution of true intakes affects the calculation of sample size for a cohort study. The authors give an example of the calculation for a cohort study investigating dietary fat and colorectal cancer. This shows that measurement error has a profound effect on sample size, requiring a six- to eightfold increase over the number required in the absence of error, if the correlation coefficient between reported and true intakes is 0.65. Reliable detection of a relative risk of 1.36 between a true intake of greater than 47.5% calories from fat and less than 25% calories from fat would require approximately one million subjects.

Bias↗

PubMed2006

Estimation of health risks associated with occupational radiation exposure: addressing measurement error and minimum detectable exposure level.

Occupational exposures are subject to several types of measurement errors. This paper considers two of the most common types of measurement error associated with occupational exposures: the error due to below minimum detection level and doses due to random measurement error. Doses are often recorded as zero when the exposure is below the minimum detection level. Values that are below the minimum detection level and are entered as zero lead to underestimation of the true exposure and can result in either an overestimate or underestimate of risk associated with the exposure. Random measurement error leads to an inefficient and attenuated estimate of risk associated with exposure. However, the levels of bias and inefficiency that can result from the simultaneous presence of both types of measurement error have not previously been studied. In addition, the impact of these measurement errors on the type I error and type II error for an exposure-response effect is unclear. Since the magnitude of the random error associated with cumulative exposure may vary with individuals and across time within an individual, traditional methods to correct for random measurement errors are not applicable here. Further, correcting errors for minimum detectable levels and random errors simultaneously is too complex for analytical solutions. Therefore, this paper uses simulation studies to quantitatively evaluate the magnitude of the bias, inefficiency, and type I and type II errors associated with them. The simulation results are applied to a sample of historical occupational radiation exposure data from the Oak Ridge National Laboratory. We conclude that after taking into consideration random measurement error and missed doses due to falling below the minimum detection level, radiation exposure is not significantly associated with all-cause mortality in that cohort.

Bias↗

PubMed2000

What is the potential measurement error in occupational exposure studies?

This paper demonstrates statistical methods that estimate measurement error from available industrial hygiene data. Errors in measuring a continuous exposure variable may arise when all individuals in a work area are assigned the same exposure. An example is when the mean of exposure measurements obtained on a sample of individuals is assigned to all workers with similar jobs. This may lead to inaccurate point and interval estimates in exposure-response modeling. A method of simulating the distribution of true (i.e., unobserved) individual exposures is described in order to estimate the mean and variance of measurement error. The minimum variance unbiased estimator approximates the mean of lognormally distributed exposure measurements. The distribution of true individual exposures is approximated by the distribution of simulated estimates of mean exposure. The methodology is illustrated by exposure data from work areas manufacturing refractory ceramic fiber (RCF) and RCF products. Results show that exposure is slightly underestimated in work areas with between 25 and 113 exposure measurements; measurement error variance averages about 1.3% of the total variance.

Air Pollution, Indoor↗

PubMed1996

Measurement error and results from analytic epidemiology: dietary fat and breast cancer.

BACKGROUND: International correlational analyses have suggested a strong positive association between fat consumption and breast cancer incidence, especially among post-menopausal women. However, case-control studies have been taken to indicate a weaker association, and a recent, pooled cohort analysis reported little evidence of an association. Differences among study results could be due to differences in the populations studied, differences in the control for total energy intake, recall bias in the case-control studies, and dietary measurement error biases. Existing measurement error models assume either that the sample data used to validate dietary self-report instruments are without measurements error or that any such error is independent of both the true dietary exposure and other study subject characteristics. However, growing evidence indicates that total energy and, presumably, both total fat and percent energy from fat are increasingly underreported as percent body fat increases. PURPOSE: A relaxed dietary measurement model is introduced that allows all measurement error parameters to depend on body mass index (weight in kilograms divided by the square of height in meters) and incorporates a random underreporting quantity that applies to each dietary self-report instrument. The model was applied to results from international correlational analyses to determine whether the differing associations between dietary fat and postmenopausal breast cancer can be explained by measurement errors in dietary assessment. METHODS: The relaxed measurement model was developed by use of data on total fat intake and percent energy from fat from 4-day food records (4DFRs) and food-frequency questionnaires (FFQs) from the original Women's Health Trial. This trial was a randomized, controlled, feasibility study of a low-fat dietary intervention carried out from 1985 through 1988 in Cincinnati (OH), Houston (TX), and Seattle (WA) among 303 women (184 intervention and 119 control) who were 45-69 years of age. The relaxed model was used to project results from the international correlational analyses onto 4DFR and FFQ fat-intake categories. RESULTS AND CONCLUSIONS: If measurement errors in dietary assessment are overlooked entirely, the projected relative risks (RRs) for breast cancer based on the international data vary substantially across percentiles of total fat intake. The projected RR for the 90% versus the 10% fat-intake percentile is 3.08 with the 4DFR and 4.00 with the FFQ. If random (i.e., noise) aspects of measurement error are acknowledged, the projected RR for the same comparison is reduced to 1.54 with the 4DFR and 1.42 with the FFQ. If both systematic and noise aspects of measurement error are acknowledged, the projected RR is reduced to about 1.10 with either instrument. Acknowledgment of measurement error also leads to a projected RR of about 1.10 for the 90% versus the 10% percentile of percent energy from fat with either dietary instrument. IMPLICATIONS: Dietary self-report instruments may be inadequate for analytic epidemiologic studies of dietary fat and disease risk because of measurement error biases.

Aged↗

PubMed1990

The effects of measurement errors on relative risk regressions.

This paper concerns the effects of random error in numerical measurements of risk factors (covariates) in relative risk regressions. When not dependent on outcome (nondifferential), such error usually attenuates relative risk estimates (shifts them toward one) and leads to spuriously narrow confidence intervals. The presence of measurement error also reduces precision of estimates and power of significance tests. However, significance levels obtained by using the approximate measurements are usually valid and as powerful as possible given the measurement error. The attenuation in risk estimate depends not only on the size (variance) of the measurement error, but also on its distributional form, on whether it is dependent on the true level of the risk factor (whether it is of "Berkson" type), on the variance and distributional form of true levels of the risk factor, on the functional form of the regression (exponential or linear), and on the confounding variables included in the model. Error in measuring confounding variables leads to loss of control of confounding, leaving residual bias. Uncomplicated techniques of correcting the effects of measurement error in simple models in which distributions are assumed normal are available in the statistical literature. For these corrections, information on measurement error variance is required. Some approaches appropriate for more general models have been proposed, but these appear to be insufficiently developed for routine application.

Bias↗

PubMed1999

Evaluation of regression calibration and SIMEX methods in logistic regression when one of the predictors is subject to additive measurement error.

BACKGROUND: This paper presents an evaluation of two methods of measurement error adjustment based on recently-developed computer routines (RCAL and SIMEX) under logistic regression models, when one of the two predictors is subject to additive measurement error or Berkson error. METHODS: Computer simulations were used to generate data under a variety of conditions and the methods compared in terms of bias, mean squared error and confidence interval coverage of the regression estimates. RESULTS: Based on our investigations, RCAL was shown to perform very well in all situations considered, except in the presence of Berkson error when the predictor variables were highly correlated. CONCLUSIONS: Since measurement error can lead to misleading inference, it is important to adjust for measurement error in the application of logistic regression. Until better measurement error adjustment methods become available, we recommend RCAL on the basis of our simulation results.

Algorithms↗

PubMed2006

Determination of facial symmetry in unilateral cleft lip and palate patients from three-dimensional data: technical report and assessment of measurement errors.

OBJECTIVE: To assess measurement errors of a novel technique for the three-dimensional determination of the degree of facial symmetry in patients suffering from unilateral cleft lip and palate malformations. DESIGN: Technical report, reliability study. SETTING: Cleft Lip and Palate Center of the University of Erlangen-Nuremberg, Erlangen, Germany. PATIENTS: The three-dimensional facial surface data of five 10-year-old unilateral cleft lip and palate patients were subjected to the analysis. Distances, angles, surface areas, and volumes were assessed twice. MAIN OUTCOME MEASURES: Calculations were made for method error, intraclass correlation coefficient, and repeatability of the measurements of distances, angles, surface areas, and volumes. RESULTS: The method errors were less than 1 mm for distances and less than 1.5 degrees for angles. The intraclass correlation coefficients showed values greater than .90 for all parameters. The repeatability values were comparable for cleft and noncleft sides. CONCLUSION: The small method errors, high intraclass correlation coefficients, and comparable repeatability values for cleft and noncleft sides reveal that the new technique is appropriate for clinical use.

Anthropometry↗

PubMed2005

A longitudinal measurement error model with a semicontinuous covariate.

Covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value. However, such an assumption does not hold for the measurement error of sleep-disordered breathing (SDB) in the Wisconsin Sleep Cohort Study (WSCS). The true covariate is the severity of SDB, and the observed surrogate is the number of breathing pauses per unit time of sleep, which has a nonnegative semicontinuous distribution with a point mass at zero. We propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model. The estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable. Modeling and model-fitting strategies are explored and illustrated through an example from the WSCS.

Blood Pressure↗

PubMed2006

Seemingly unrelated measurement error models, with application to nutritional epidemiology.

Motivated by an important biomarker study in nutritional epidemiology, we consider the combination of the linear mixed measurement error model and the linear seemingly unrelated regression model, hence Seemingly Unrelated Measurement Error Models. In our context, we have data on protein intake and energy (caloric) intake from both a food frequency questionnaire (FFQ) and a biomarker, and wish to understand the measurement error properties of the FFQ for each nutrient. Our idea is to develop separate marginal mixed measurement error models for each nutrient, and then combine them into a larger multivariate measurement error model: the two measurement error models are seemingly unrelated because they concern different nutrients, but aspects of each model are highly correlated. As in any seemingly unrelated regression context, the hope is to achieve gains in statistical efficiency compared to fitting each model separately. We show that if we employ a "full" model (fully parameterized), the combination of the two measurement error models leads to no gain over considering each model separately. However, there is also a scientifically motivated "reduced" model that sets certain parameters in the "full" model equal to zero, and for which the combination of the two measurement error models leads to considerable gain over considering each model separately, e.g., 40% decrease in standard errors. We use the Akaike information criterion to distinguish between the two possibilities, and show that the resulting estimates achieve major gains in efficiency. We also describe theoretical and serious practical problems with the Bayes information criterion in this context.

Bias↗

PubMed1989

Measuring measuring errors.

The assessment of errors of measurement and their effects needs to take into account the structure of the data in which the errors occur. This is illustrated and the appropriate analysis of variance specified for a variety of contexts. The notion of an acceptable level of measurement error is discussed in terms of decision theory and illustrated by a simplified example.

Analysis of Variance↗

PubMed2002

Adjusting for measurement error in the Cox proportional hazards regression model.

BACKGROUND: The Harvard Six Cities Study (Dockery et al.) was the first large-scale cohort study to demonstrate an association between long-term exposure to fine particulate matter less than 2.5 microns in aerodynamic diameter (PM2.5) and mortality in urban centres in the United States. Because of the pivotal role of this study in the establishment of the first U.S. national ambient air quality objective for PM2.5 in 1997 (Greenbaum et al.), the results of this study were subjected to an independent detailed re-analysis to test the robustness of the findings to alternative analytic methods (Krewski et al.), including an assessment of the effect of exposure measurement error on estimates of risk based on the Cox proportional hazards model. It is well-known that random measurement error leads to downward bias in estimates of risk, and overstatement of the precision of such estimates. METHODS: Data from the Harvard Six Cities Study were used to evaluate the potential impact of measurement error on estimates of risk. After introducing a known amount of measurement error into the original data, estimates of risk were calculated using two methods for adjusting for measurement error: regression calibration (RCAL) and simulation extrapolation (SIMEX). With RCAL, the observed value of PM2.5 is replaced by its expected value with respect to the measurement error distribution. SIMEX adjusts for measurement error by adding progressively larger errors to the data and then extrapolating back to the case of no measurement error. Computer simulation was used to evaluate the accuracy and precision of both RCAL and SIMEX, and to assess the robustness of RCAL to mis-specification of the measurement error distribution. RESULTS AND CONCLUSIONS: When the measurement error distribution was correctly specified, RCAL greatly reduced the downward bias in risk estimates induced by random measurement error, even when the degree of measurement error was relatively large. SIMEX, on the other hand, failed to adequately adjust for the effects of random measurement error in the Cox model, even in the presence of a moderate degree of measurement error. Although RCAL is thus preferable to SIMEX, RCAL was not robust against mis-specification of the measurement error distribution, seriously overestimating (underestimating) risk when the measurement error was overstated (understated).

Air Pollution↗