Multiple observers, humidity, and choice of precision statistics: factors influencing craniometric data quality

This study investigates three topics: (1) interobserver measurement error in craniometry, (2) the effects of humidity on craniometric measurements, and (3) the current status of estimators of measurement precision in craniometry and anthropometry. The results of the three-observer error analysis based on 24 linear measurements taken on 47 crania indicate that minor idiosyncratic variations in measurement technique can lead to high levels of statistical discrimination among the data produced by the different observers. The results of the humidity experiment substantiate the contention that increasing levels of relative humidity are associated with cranial expansion. The results of the comparison of 11 univariate precision estimators suggest that the combination of percentage agreement, the mean absolute difference, and Fisher's nonparametric sign test can give an instructive picture of the frequency, magnitude, and directionality of measurement imprecision. Information on the comparability of technique and measurement precision can then be used in the variable selection process prior to the application of multivariate statistical procedures to strengthen the substantive interpretation of craniometric data.     

The Application of Linear Piecewise Regression to Basal Body Temperature Data

In many situations one wishes to fit a piecewige regression which enables one to obtain estimates of the join points as well as the slopes and intercepts of the fitted submodels. This study developes a technique for fitting piecewise models to data which contain measurement error in an independent variable. The technique developed here combines the HUDSON (1966) procedure for estimating parameters in piecewise regression and the WALD (1940) Grouping Technique which obviates the problem of measurement error. If one assumes some knowledge of the position of the join point in relation to the data, methodology has been developed to estimate the parameters and study the asymptotic properties of the means and variances of the parameter estimates. However, in the more realistic case, when additional knowledge is limited, it is only possible to obtain the parameter estimates using an iterative technique (TEETER, 1982). The general technique for obtaining the join point estimate in the presence of measurement error is presented here and an example is given using data on women's basal body temperature during menstrual cycles.     

Measurement error in covariates in the marginal hazards model for multivariate failure time data

We consider measurement error in covariates in the marginal hazards model for multivariate failure time data. We explore the bias implications of normal additive measurement error without assuming a distribution for the underlying true covariate. To correct measurement-error-induced bias in the regression coefficient of the marginal model, we propose to apply the SIMEX procedure and demonstrate its large and small sample properties for both known and estimated measurement error variance. We illustrate this method using the Lipid Research Clinics Coronary Primary Prevention Trial data with total cholesterol as the covariate measured with error and time until angina and time until nonfatal myocardial infarction as the correlated outcomes of interest.     

When should one adjust for measurement error in baseline variables in observational studies?

Previously, we showed that in randomised experiments, correction for measurement error in a baseline variable induces bias in the estimated treatment effect, and conversely that ignoring measurement error avoids bias. In observational studies, non-zero baseline covariate differences between treatment groups may be anticipated. Using a graphical approach, we argue intuitively that if baseline differences are large, failing to correct for measurement error leads to a biased estimate of the treatment effect. In contrast, correction eliminates bias if the true and observed baseline differences are equal. If this equality is not satisfied, the corrected estimator is also biased, but typically less so than the uncorrected estimator. Contrasting these findings, we conclude that there must be a threshold for the true baseline difference, above which correction is worthwhile. We derive expressions for the bias of the corrected and uncorrected estimators, as functions of the correlation of the baseline variable with the study outcome, its reliability, the true baseline difference, and the sample sizes. Comparison of these expressions defines a theoretical decision threshold about whether to correct for measurement error. The results show that correction is usually preferred in large studies, and also in small studies with moderate baseline differences. If the group sample sizes are very disparate, correction is less advantageous. If the equivalent balanced sample size is less than about 25 per group, one should correct for measurement error if the true baseline difference is expected to exceed 0.2-0.3 standard deviation units. These results are illustrated with data from a cohort study of atherosclerosis.     

Meaning of biodistance statistics: a test case using adult monozygotic twins

Anthropometry, historically one of the primary research techniques in physical anthropology, has been widely utilized in biodistance studies. The complex genetic and environmental interaction that governs the expression of anthropometric dimensions, together with concerns over measurement error, have sometimes clouded the interpretation of biodistances based upon anthropometry. In this study, 51 pairs of adult monozygotic twins were analysed using discriminant analysis and Mahalanobis' generalized distance. Both male and female twins, grouped by first- versus second-born, displayed very small, statistically insignificant distances between groups. When literature estimates of intra-observer measurement errors were used as a frame of reference, the average absolute differences between the twin pairs were approximately twice the size of the measurement error estimates. The results of this study suggest that, first, the environmental effect upon the genetically influenced traits measured by anthropometry is not large enough to bring about significant multivariate differences between identical twin pairs; and, second, biodistance studies based upon anthropometry can be reliable so long as measurement error is minimized.     

Semiparametric regression modeling with mixtures of Berkson and classical error, with application to fallout from the Nevada test site

We construct Bayesian methods for semiparametric modeling of a monotonic regression function when the predictors are measured with classical error. Berkson error, or a mixture of the two. Such methods require a distribution for the unobserved (latent) predictor, a distribution we also model semiparametrically. Such combinations of semiparametric methods for the dose response as well as the latent variable distribution have not been considered in the measurement error literature for any form of measurement error. In addition, our methods represent a new approach to those problems where the measurement error combines Berkson and classical components. While the methods are general, we develop them around a specific application, namely, the study of thyroid disease in relation to radiation fallout from the Nevada test site. We use this data to illustrate our methods, which suggest a point estimate (posterior mean) of relative risk at high doses nearly double that of previous analyses but that also suggest much greater uncertainty in the relative risk.     

Indices of reproductive skew depend on average reproductive success

Several indices of reproductive skew, which quantify the degree of unequal partitioning of reproductive output among members in an animal society, have been proposed. Here we point out the drawbacks of these indices. The most serious problem is the dependence of the indices on mean reproductive success: skew values tend to be larger, as average numbers of offspring decrease, due to random sampling error in numbers of offspring. Thus it is difficult to compare societies with different average lifetime reproductive success using these indices, even though we have presented methods to calculate the expected reproductive skew caused by random sampling error, especially when average numbers of offspring are small, as is often the case with cooperatively breeding vertebrates. As an alternative, we propose using the spatial dispersion indices of population ecology (Morisita's index or its standardized version) for the measurement of reproductive skew. These indices are almost independent of average fecundity and have their own method of testing for random variation in offspring numbers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sharing is caring? Measurement error and the issues arising from combining 3D morphometric datasets

Geometric morphometrics is routinely used in ecology and evolution and morphometric datasets are increasingly shared among researchers, allowing for more comprehensive studies and higher statistical power (as a consequence of increased sample size). However, sharing of morphometric data opens up the question of how much nonbiologically relevant variation (i.e., measurement error) is introduced in the resulting datasets and how this variation affects analyses. We perform a set of analyses based on an empirical 3D geometric morphometric dataset. In particular, we quantify the amount of error associated with combining data from multiple devices and digitized by multiple operators and test for the presence of bias. We also extend these analyses to a dataset obtained with a recently developed automated method, which does not require human‐digitized landmarks. Further, we analyze how measurement error affects estimates of phylogenetic signal and how its effect compares with the effect of phylogenetic uncertainty. We show that measurement error can be substantial when combining surface models produced by different devices and even more among landmarks digitized by different operators. We also document the presence of small, but significant, amounts of nonrandom error (i.e., bias). Measurement error is heavily reduced by excluding landmarks that are difficult to digitize. The automated method we tested had low levels of error, if used in combination with a procedure for dimensionality reduction. Estimates of phylogenetic signal can be more affected by measurement error than by phylogenetic uncertainty. Our results generally highlight the importance of landmark choice and the usefulness of estimating measurement error. Further, measurement error may limit comparisons of estimates of phylogenetic signal across studies if these have been performed using different devices or by different operators. Finally, we also show how widely held assumptions do not always hold true, particularly that measurement error affects inference more at a shallower phylogenetic scale and that automated methods perform worse than human digitization.     

On the effect of misclassification on bias of perfectly measured covariates in regression

This note clarifies under what conditions a naive analysis using a misclassified predictor will induce bias for the regression coefficients of other perfectly measured predictors in the model. An apparent discrepancy between some previous results and a result for measurement error of a continuous variable in linear regression is resolved. We show that similar to the linear setting, misclassification (even when not related to the other predictors) induces bias in the coefficients of the perfectly measured predictors, unless the misclassified variable and the perfectly measured predictors are independent. Conditional and asymptotic biases are discussed in the case of linear regression, and explored numerically for an example relating birth weight to the weight and smoking status of the mother.     

A technique to measure the volume of diving birds during voluntary dives

Buoyancy has a substantial contribution to the total mechanical cost of diving in waterbirds. Most of the techniques currently employed to estimate buoyancy are based on measuring the volume of carcasses or forcibly submerged birds using the water displacement (Archimedes) principle. In such techniques, the voluntary control the bird might have over plumage and respiratory air volumes is neglected. Here, I propose an adjustment to the water displacement measurement that allows the measurement of buoyancy in real-time from unrestrained live birds diving voluntarily. The novelty and accuracy of the technique lie in using a pressure sensor to continuously measure the water level inside the dive tank while filtering out the interference from surface waves. The error of the volume measurement in the proposed technique was only ±2.4%. Feasibility of measurement is demonstrated on captive Great Cormorants (Phalacrocorax carbo sinensis). The measured volumes of Great Cormorants exceeded predictions made based on the volume of carcasses and on average resembled values measured from live restrained birds. However the technique highlighted the high variation in buoyancy of live birds (up to 30%) as a result of small changes in the air volumes taken with the bird underwater.     

Regression of calculated variables in the presence of shared measurement error

To test hypotheses regarding relations between meaningful parameters, it is often necessary to calculate these parameters from other directly measured variables. For example, the relationship between O2 consumption and O2 delivery may be of interest, although these may be computed from measurements of cardiac output and blood O2 contents. If a measured variable is used in the calculation of two derived parameters, error in the measurement will couple the calculated parameters and introduce a bias, which can lead to incorrect conclusions. This paper presents a method of correcting for this bias in the linear regression coefficient and the Pearson correlation coefficient when calculations involve the nonlinear and linear combination of the measured variables. The general solution is obtained when the first two terms of a Taylor series expansion of the function can be used to represent the function, as in the case of multiplication. A significance test for the hypothesis that the regression coefficient is equal to zero is also presented. Physiological examples are provided demonstrating this technique, and the correction methods are also applied in simulations to verify the adequacy of the technique and to test for the magnitude of the coupling effect. In two previous studies of O2 consumption and delivery, the effect of coupled error is shown to be small when the range of O2 deliveries studied is large, and measurement errors are of reasonable size.     

The effect of intraspecific sample size on type I and type II error rates in comparative studies

Comparative studies have increased greatly in number in recent years due to advances in statistical and phylogenetic methodologies. For these studies, a trade-off often exists between the number of species that can be included in any given study and the number of individuals examined per species. Here, we describe a simple simulation study examining the effect of intraspecific sample size on statistical error in comparative studies. We find that ignoring measurement error has no effect on type I error of nonphylogenetic analyses, but can lead to increased type I error under some circumstances when using independent contrasts. We suggest using ANOVA to evaluate the relative amounts of within- and between-species variation when considering a phylogenetic comparative study. If within-species variance is particularly large and intraspecific sample sizes small, then either larger sample sizes or comparative methods that account for measurement error are necessary.     

The genetic structure of a tribal population, the Yanomama indians. VII. Anthropometric differences among Yanomama villages

Anthropometric data on 12 variables in 19 villages of the Yanomama Indians demonstrate significant heterogeneity in physique among villages of this tribe. Mahalanobis' distances (D²) calculated from the data lead to the tentative conclusion of a general correspondence between anthropometric and geographic distances separating villages. The mean stature of the Yanomama is smaller than that of most other South American tribes which have been measured, and the Yanomama are genetically distinct from the other small Indians as shown by genetic distances based on allele frequencies for a variety of genetic markers. Since some subjects were measured more than once by the same and by different observers, it was possible to calculate approximate estimates of variance within and between observers. Univariate analysis indicates that face height and nose height are especially susceptible to systematic differences in technique between observers. The variances obtained in this field study compare favorably with those of some classical laboratory studies described in the literature. It was found that measurement error nevertheless probably makes a substantial contribution to anthropometric distance between villages. The median error variance as a fraction of that of Herskovits ('30) is 0.62 for the seven measurements in common with this study. The median value of the error variance for the 12 variables in this study is between 16% and 17% of the total variance.     

How reliable are our vegetation analyses?

Abstract. Two sets of 40 relevés, made independently by two observers on the same 5m x 5m sample plots, were compared to estimate the sampling error and to assess the effect of this sampling error on (1) estimates of species richness and diversity (2) results of multivariate analyses, and (3) estimation of species turnover in repeated sampling. The relevés were made according to the standard Braun-Blanquet method. The sampling error was estimated for (1) recording of species in sample plots and (2) visual estimation of the degree of cover (or of the general population size). Despite the fact that the sample plots were searched thoroughly for 30 - 40 min, the number of overlooked species was high with a discrepancy of 13% between corresponding relevés. Regarding multivariate analysis, the error caused by missing species was at least as important as the error in visual estimation of species cover. The estimates of degree of cover using the Braun-Blanquet scale are sufficiently reliable for use in multivariate analysis when they are subjected to ordinal transformation. When average cover values are used, the patterns detected are based solely on dominants. Species richness and species diversity could be reliably estimated from the relevés, but the estimates of equitability are very unreliable. The classical relevé method remains one of the most efficient survey methods for recognition of vegetation types on the macro-community and landscape scales.     

A mover-stayer model for longitudinal marker data

Studies of chronic disease often focus on estimating prevalence and incidence in which the presence of active disease is based on dichotomizing a continuous marker variable measured with error. Examples include hypertension, asthma, and depression, where active disease is defined by setting a threshold on a continuous measure of blood pressure, respiratory function, and mood, respectively. This paper proposes a model for inference about prevalence and incidence when active disease is determined by dichotomizing a continuous marker variable in a population-based study. In this formulation, it is postulated that there are three groups of people, those that are not susceptible to the disease, those who are always in the disease state, and those who have the potential to transition between the disease and the disease-free states over time. The model is used to estimate the prevalence and incidence of the disease in the population while accounting for measurement error in the marker. An EM algorithm is used for parameter estimation and the methodology is illustrated on Framingham heart study hypertension data. A simulation study is conducted in order to demonstrate the importance of accounting for measurement error in estimating prevalence and incidence for this example.     

Interobserver errors in anthropometry

To present basic information on the interobserver precision and accuracy of 32 selected anthropometric measurement items, six observers measured each of 37 subjects once in two days. The data were analyzed by using ANOVA, and mean absolute bias, standard deviation of bias, and mean absolute bias in standard deviation unit were used as measures of bias. By comparing the results of the two days, the effects of the practice on measurement errors were also investigated. Variance was overestimated by more than 10% in five measurements. Interobserver error variance and random error variance were highly correlated with each other. Measures of the bias were significantly correlated with interobserver and especially with random error variances. The interobserver errors were drastically reduced on the second day in the measurement items in which the causes of the interobserver errors could be specified. It was speculated that even when the definitions of the landmarks and measurement items were clear, the ambiguity in the practical procedures in locating landmarks, applying instruments, and so on, permitted each observer to develop his or her own measurement technique, and it in turn caused interobserver errors. To minimize interobserver and random errors, the standardization of measurement technique should be extended to the details of the practical procedures.     

Inter-daily variability in body composition among young men

Background

The present study analyses changes in body composition over the course of a working week. The purpose of the study is to identify the size of the changes in the observed parameters by means of typical error of measurement (TE) as the initial value for the interpretation of the detected changes in the repeated measurement in diagnostic practice.

Methods

The researched group consisted of 86 males, aged 21.4 ± 1.0 years. All the participants were free of any medical conditions. The measurement of each participant took place over 1 week from Monday till Friday, in the morning hours. Parameters measured: body mass (BM), total body water (TBW), and body fat (BF). The measurement employed two devices using the bioelectric impedance analysis. These devices were the analyzers Tanita BC 418 MA and Nutriguard MS. In order to assess the differences between the average values, the analysis of repeated measurements was used. To assess the material significance, eta squared was used. TE was used to express the size of the changes in the observed parameters.

Results

A statistically significant difference between the average values of the observed parameters was only detected when using the Tanita BC 418 MA analyzer. Based on the post-hoc tests, these differences in the average values were always detected on Monday and Friday. No material significance was proved, however. The highest TE values were also detected in measurements carried out on Monday and Friday. For BM, the value of TE was 0.6 kg, for TBW 1.0–1.1 %, 0.8–0.9 kg, and for BF 1.2–1.6 %, 1.1–1.3 kg depending on the analyzer used.

Conclusions

The results of the present study demonstrate the stability of parameters of body composition throughout a working week, with the provision that standard measuring conditions are fulfilled. For the purpose of diagnostic practice, when interpreting the results of the repeated measurements, it is advisable to take as provable change caused by the observed factors only the ones whose values exceed the value of a weekly TE or the upper limit of the interval of the measurement reliability.     

Laplace approximation in measurement error models

Likelihood analysis for regression models with measurement errors in explanatory variables typically involves integrals that do not have a closed-form solution. In this case, numerical methods such as Gaussian quadrature are generally employed. However, when the dimension of the integral is large, these methods become computationally demanding or even unfeasible. This paper proposes the use of the Laplace approximation to deal with measurement error problems when the likelihood function involves high-dimensional integrals. The cases considered are generalized linear models with multiple covariates measured with error and generalized linear mixed models with measurement error in the covariates. The asymptotic order of the approximation and the asymptotic properties of the Laplace-based estimator for these models are derived. The method is illustrated using simulations and real-data analysis.     

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.