Measurement error. Measurement error is that which we have not yet explained.
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Data Interpretation, Statistical↗
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Association of serum total cholesterol with coronary disease and all-cause mortality: multivariate correction for bias due to measurement error.
Measurement error in the exposure under investigation is an important but often ignored source of bias in observational studies. The authors examined the impact of measurement error in the association between total serum cholesterol and 16-year coronary heart disease and all-cause mortality in a cohort of 6,137 middle-aged men of Japanese descent in the Honolulu Heart Program (1973-1988). A Cox regression model that enables modeling of survival time with correction for measurement errors in multiple covariates was employed. After controlling for age, body mass index, systolic blood pressure, smoking status, alcohol consumption, dietary cholesterol, and total calorie intake, a difference of one standard deviation (38 mg/dL) in total cholesterol was associated with a significant increase in the risk of coronary disease death (uncorrected hazard ratio = 1.35). After correction for measurement errors in total cholesterol and covariates (except smoking and age), the estimated hazard ratio increased to 1.65 (a 22% increase). A U-shaped relation was observed between total cholesterol levels and the risk of all-cause mortality. This association was then examined with a quadratic model and with a two-slope or V-shaped regression model. In the quadratic fit, the magnitude of the quadratic total cholesterol term increased threefold after the adjustment for measurement error. In the V fit, the hazard ratio of all-cause death corresponding to a change in one standard deviation above 214 mg/dL (the nadir of the V) was 1.15, and increased to 1.49 (by 29%) after the correction. The corresponding hazard ratio of a change in one standard deviation below 214 mg/dL was 1.11, and increased to 1.37 (by 23%) after the correction. The authors conclude that the impact of elevated total cholesterol on the risk of coronary disease and all-cause mortality may be greater than previously estimated with standard methods of analysis. In addition, the correction for measurement error in total cholesterol and covariates did not explain the excess mortality associated with low total cholesterol. More research is needed to elucidate the fundamental issues underlying the U-shaped association, i.e., confounding versus causal implications.
Aged↗
Cardiac volume measurement errors.
Measurements of cardiac volumes based on biplane radiographic data exhibit a cyclical variation as the heart is rotated with respect to the radiologic instrumentation. This study develops a theoretical basis for evaluating the measurement errors due to orientation, that explains the cyclical variation. Since this type of measurement error is always one of overestimation, better accuracy will be obtained if several views are performed at varying orientations and the smallest of the resulting values is used as the measurement.
Animals↗
The effect of sampling error and measurement error and its correlation on the estimation of multi-locus fixed-bin VNTR RFLP genotype probabilities.
Bootstrapping was used to examine the effect of sampling error and measurement error and its correlation on fixed-bin genotype probabilities. Bootstrap confidence intervals (Cls) were made relative to the point estimate using the log of the inverse of the probabilities. From databases of 200-250 genotypes, sampling error alone yielded median relative 95% CIs of from one order of magnitude out of five for one locus to one out of ten for four loci. Measurement error of the test genotype fragments increased the latter to about one order of magnitude out of eight. Database measurement error and its correlation had only a slight effect on multi-locus probability uncertainty. Together, these uncertainties are several orders of magnitude greater than error due to population substructuring of a race by its major component ethnic groups.
Confidence Intervals↗
[Experimental studies on influence of alignment errors on measurement in a corneal topographic system--relationship between degree of measurement error and working distance].
To evaluate the influence of alignment errors in focusing on the results of measurements in corneal topography, we experimented using polymethyl-methacrylate balls with definite radii of curvature as test objects. We used 3 different corneal topographic systems with different working distances to clarify the relationship between the degree of errors and the working distance. We determined the refractive power of the test balls by the topographic systems and studied changes in the values as the balls were slightly displaced from the alignment position axially, or horizontally. The test balls were set on the stage with a micrometer so that the distance of displacement could be determined precisely. When the test balls were placed precisely in alignment, there was no significant relationship in the magnitude of measurement errors with working distance of the topographical systems. When the test balls were displaced axially, the measurement values decreased as the balls come near from the alignment position and increased as they moved away from the alignment position. The magnitude of the measurement errors caused by back and forth displacement of the object became larger as the working distance of the topographic system became shorter. There was no specific relationship between the degree of measurement errors and the working distance when the balls were displaced horizontally.
Cornea↗
Inter- and intra-measurer error in the measurement of Reimers' hip migration percentage.
Reimers' hip migration percentage is commonly used to document the extent of subluxation of the hip in children with spasticity. In this study, two measurers, with six months paediatric orthopaedic experience, measured the migration percentage on 44 pelvic radiographs of children with cerebral palsy, aged between two and eight years. Unknown to the measurers, each radiograph was duplicated, giving 22 non-identical radiographs (44 hips) which were measured twice at time 0 and twice six weeks later. The intra-measurer, intra-sessional absolute differences between the first and second measurements ranged from 0% to 23%, with median values of 2.5% to 3.6%. The intra-sessional median absolute differences were not statistically different between the two measurers and measuring sessions (p = 0.42, Kruskal-Wallis test). The inter-sessional absolute differences for measurements made by the same measurers ranged from 0% to 18% with a median absolute difference of 1.7% to 3.2%. Overall, only 5% of the intra-measurer measurement differences, within and between sessions, were above 13%. Repeated measurements by one measurer over time must, therefore, vary by more than 13% in order to be 95% confident of a true change. The inter-measurer error was higher with median absolute differences between the two measurers' measurements of the same hip of 3.25% to 5% (0% to 26%) and a 95th upper confidence interval of 21% to 23%. Averaging the four separate measurements over the two sessions reduced the inter-measurer error to a median absolute difference of 2.8%, but did not improve the 95th upper confidence interval, which measured 22.4%. Such inter-measurer errors may be clinically unacceptable.
Acetabulum↗
Estimating the independent effects of multiple pollutants in the presence of measurement error: an application of a measurement-error-resistant technique.
Misclassification of exposure usually leads to biased estimates of exposure-response associations. This is particularly an issue in cases with multiple correlated exposures, where the direction of bias is uncertain. It is necessary to address this problem when considering associations with important public health implications such as the one between mortality and air pollution, because biased exposure effects can result in biased risk assessments. The National Morbidity and Mortality Air Pollution Study (NMMAPS) recently reported results from an assessment of multiple pollutants and daily mortality in 90 U.S. cities. That study assessed the independent associations of the selected pollutants with daily mortality in two-pollutant models. Excess mortality was associated with particulate matter of aerodynamic diameter less than or equal to 10 microm/m3 (PM10), but not with other pollutants, in these two pollutant models. The extent of bias due to measurement error in these reported results is unclear. Schwartz and Coull recently proposed a method that deals with multiple exposures and, under certain conditions, is resistant to measurement error. We applied this method to reanalyze the data from NMMAPS. For PM10, we found results similar to those reported previously from NMMAPS (0.24% increase in deaths per 10-microg/m3) increase in PM10). In addition, we report an important effect of carbon monoxide that had not been observed previously.
Air Pollutants↗
Power and sample size calculations for generalized regression models with covariate measurement error.
Covariate measurement error is often a feature of scientific data used for regression modelling. The consequences of such errors include a loss of power of tests of significance for the regression parameters corresponding to the true covariates. Power and sample size calculations that ignore covariate measurement error tend to overestimate power and underestimate the actual sample size required to achieve a desired power. In this paper we derive a novel measurement error corrected power function for generalized linear models using a generalized score test based on quasi-likelihood methods. Our power function is flexible in that it is adaptable to designs with a discrete or continuous scalar covariate (exposure) that can be measured with or without error, allows for additional confounding variables and applies to a broad class of generalized regression and measurement error models. A program is described that provides sample size or power for a continuous exposure with a normal measurement error model and a single normal confounder variable in logistic regression. We demonstrate the improved properties of our power calculations with simulations and numerical studies. An example is given from an ongoing study of cancer and exposure to arsenic as measured by toenail concentrations and tap water samples.
Arsenic↗
Efficacy of repeated measures in regression models with measurement error.
Ignoring measurement error may cause bias in the estimation of regression parameters. When the true covariates are unobservable, multiple imprecise measurements can be used in the analysis to correct for the associated bias. We suggest a simple estimating procedure that gives consistent estimates of regression parameters by using the repeated measurements with error. The relative Pitman efficiency of our estimator based on models with and without measurement error has been found to be a simple function of the number of replicates and the ratio of intra- to inter-variance of the true covariate. The procedure thus provides a guide for deciding the number of repeated measurements in the design stage. An example from a survey study is presented.
Biometry↗
Multiple-component radiation-measurement error models.
Measurement error modeling and assessment are crucial to any assay method. Realistic error models prioritize future efforts to reduce key error components and provide a way to estimate total ("random" and "systematic") measurement error. This paper describes multiple-component error models for radiation-based assay, gives example applications, and describes strategies for choosing and then fitting error models.
Data Interpretation, Statistical↗
The Youden Index and the optimal cut-point corrected for measurement error.
Random measurement error can attenuate a biomarker's ability to discriminate between diseased and non-diseased populations. A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1-specificity, the probability of incorrectly classifying health individuals. We present an approach for estimating the Youden index and associated optimal cut-point for a normally distributed biomarker that corrects for normally distributed random measurement error. We also provide confidence intervals for these corrected estimates using the delta method and coverage probability through simulation over a variety of situations. Applying these techniques to the biomarker thiobarbituric acid reaction substance (TBARS), a measure of sub-products of lipid peroxidation that has been proposed as a discriminating measurement for cardiovascular disease, yields a 50% increase in diagnostic effectiveness at the optimal cut-point. This result may lead to biomarkers that were once naively considered ineffective becoming useful diagnostic devices.
Biomarkers↗
Random measurement error in visual acuity measurement in clinical settings.
PURPOSE: To estimate the random measurement error in visual acuity (VA) determination in the clinical environment in cataractous, pseudophakic and healthy eyes. METHODS: The VAs of patients referred for cataract surgery or consultation by ophthalmic professionals were re-examined and the VA results for distance using projector acuity charts were compared. Refractive errors were also remeasured. A total of 99 eyes (41 cataractous, 36 pseudophakic and 22 healthy eyes) were examined. The healthy comparison group consisted of hospital staff. Only one eye of each person and eyes with Snellen VAs of 0.3-1.3 (logMAR 0.52 to - 0.11) were included. The mean time interval between the first and second examinations was 45 days. RESULTS: The estimated standard deviation of measurement error (SDME) of repeated VA measurements of all eyes was logMAR 0.06. Eyes with the lowest VA (0.3-0.45) had the largest variability (SDME logMAR 0.09), and eyes with VA > or = 0.7 had the smallest (SDME logMAR 0.04). The variability may be partly explained by the line size progression in lower VAs, partly by the difference in the remeasurement of the refractive error. The difference in the average VA between examinations 1 and 2 (logMAR 0.15 versus 0.12) was considered to be of some interest because it indicates that some learning effect is possible. CONCLUSION: Visual acuity results in clinical settings have a certain degree of inherent variability. In this series variability ranged from SDME logMAR 0.04 (eyes with good vision) to logMAR 0.09 (in the lower vision group) in the Snellen VA range of 0.3-1.3. Changes should be judged with caution, especially in cases of decreased VA.
Adult↗
Measurement error in clinical perinatal data.
The error measurement of clinical perinatal variables obtained during the standardization and data-collection periods of a large prospective epidemiologic study is presented. The error is considerably larger during the data-collection period, particularly with regard to uterine height, birth weight, and blood pressure values. This information strongly supports the need to continuously supervise and monitor perinatal data collection systems, even after standardization.
Data Collection↗
Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error.
If several risk factors for disease are considered in the same multiple logistic regression model, and some of these risk factors are measured with error, the point and interval estimates of relative risk corresponding to any of these factors may be biased either toward or away from the null value. A method is provided for correcting point and interval estimates of relative risk obtained from logistic regression for measurement error in one or more continuous variables. The method requires a separate validation study to estimate the coefficients from the multivariate linear regression model relating the surrogate variables to the vector of true risk factors. Similar methods have been suggested by other authors, but none provides a means of correcting the confidence intervals which include a component of variability due to estimation of the measurement error parameters from a validation study. An example is provided from a prospective study of dietary fat, calories, and alcohol in relation to breast cancer, and from a validation study of the questionnaire used to assess these nutrients. Before correcting for measurement error, the age-adjusted relative risk for a 25 g increment in alcohol intake was 1.33 (95% confidence interval (CI) 1.14-1.55); after correcting for measurement error, the relative risk increased to 1.62 (95% CI 1.23-2.12). Similarly, for a 10 g increment in saturated fat intake, the age-adjusted relative risk was 0.94 (95% CI 0.83-1.06); after correcting for measurement error, the relative risk was 0.84 (95% CI 0.59-1.20). These results indicate that the failure to find a substantial positive association between breast cancer risk and saturated fat intake cannot be explained by measurement error in fat, calories, or alcohol.
Bias↗
Design and interpretation of studies of differential exposure measurement error.
Differential exposure measurement error can have more adverse effects on estimates of exposure-disease associations than nondifferential measurement error, yet relatively little has been written about the design and interpretation of validity and reliability studies to assess differential measurement error. In this paper, a simple approximate equation is given for the effect of differential measurement error in a continuous exposure measure on the bias in the odds ratio. From this, it is shown that two parameters need to be estimated in validity/reliability studies in order to interpret the results in terms of the bias in the odds ratio in an epidemiologic study that will use the measure. The first is the correlation between the mismeasured and true exposure. The second is the differential bias (difference between cases and controls in the difference between mean measured and true exposure) relative to the true difference in exposure between cases and controls. It is shown that this latter parameter can be estimated in a method comparison study if one has a comparison measure that is unbiased or has nondifferential bias, so a perfect criterion measure is not needed. Researchers should consider measuring and reporting this parameter in validity/reliability studies when feasible.
Bias↗
Study design for epidemiologic studies with measurement error.
Exposure measurement error in epidemiological studies is recognized as a feature that must be considered because of the potential bias that can result in estimates of the exposure-disease association. Most of the work to date has focused on methods of analysis that adjust for the resultant bias, but the implications of this work to the design of epidemiologic studies is not as well understood. An overview of the issues involved in the use of methods for dealing with errors in exposure information is discussed along with some design options that have been proposed for providing information necessary for their use. Validation studies compare somewhat crude and inexpensive measures of exposure to a gold standard, and study designs that incorporate these into the overall plan can realize some advantages in terms of cost. In addition, repeated assessments of exposure can realize efficiency for measures of exposure that are unbiased. However, much work remains to be done in the development of efficient designs for studying disease aetiology and prevention.
Bias↗
Measurement error in grip and pinch force measurements in patients with hand injuries.
BACKGROUND AND PURPOSE: There is limited documentation of measurement error of grip and pinch force evaluation methods. The purposes of this study were (1) to determine indexes of measurement error for intraexaminer and interexaminer measurements of grip and pinch force in patients with hand injuries and (2) to investigate whether the measurement error differs between measurements of the injured and noninjured hands and between experienced and inexperienced examiners. SUBJECTS: The subjects were a consecutive sample of 33 patients with hand injuries who were seen in the Department of Rehabilitation Medicine of Erasmus MC-University Medical Center Rotterdam in the Netherlands. METHODS: Repeated measurements were taken of grip and pinch force, with a short break of 2 to 3 minutes between sessions. For the grip force in 2 handle positions (distance between handles of 4.6 and 7.2 cm, respectively), tip pinch (with the index finger on top and the thumb below, with the other fingers flexed) and key pinch force (with the thumb on top and the radial side of the index finger below) data were obtained on both hands of the subjects by an experienced examiner and an inexperienced examiner. Intraclass correlation coefficients (ICCs), standard errors of measurement (SEMs), and associated smallest detectable differences (SDDs) were calculated and compared with data from previous studies. RESULTS: The reliability of the measurements was expressed by ICCs between .82 and .97. For grip force measurements (in the second handle position) by the experienced examiner, an SDD of 61 N was found. For tip pinch and key pinch, these values were 12 N and 11 N, respectively. For measurements by the inexperienced examiner, SDDs of 56 N for grip force and 13 N and 18 N for tip pinch and key pinch were found. DISCUSSION AND CONCLUSION: Based on the SEMs and SDDs, in individual patients only relatively large differences in grip and pinch force measurements can be adequately detected between consecutive measurements. Measurement error did not differ between injured and noninjured hands or between experienced and inexperienced examiners. Criteria for judging whether the measurement error does allow application of the measurements in individual patients are discussed.
Adolescent↗
Beyond alpha: an empirical examination of the effects of different sources of measurement error on reliability estimates for measures of individual differences constructs.
On the basis of an empirical study of measures of constructs from the cognitive domain, the personality domain, and the domain of affective traits, the authors of this study examine the implications of transient measurement error for the measurement of frequently studied individual differences variables. The authors clarify relevant reliability concepts as they relate to transient error and present a procedure for estimating the coefficient of equivalence and stability (L. J. Cronbach, 1947), the only classical reliability coefficient that assesses all 3 major sources of measurement error (random response, transient, and specific factor errors). The authors conclude that transient error exists in all 3 trait domains and is especially large in the domain of affective traits. Their findings indicate that the nearly universal use of the coefficient of equivalence (Cronbach's alpha; L. J. Cronbach, 1951), which fails to assess transient error, leads to overestimates of reliability and undercorrections for biases due to measurement error.
Bias↗