Intra- and interobserver error in craniometry: A cautionary tale

This study investigates intra- and interobserver measurement error in craniometry. Data consists of 72 craniometric measurements taken on a series of 28 Sadlermuit Eskimo crania. Utermohle measured the series twice; Zegura measured it once. Statistical procedures used to demonstrate measurement imprecision include the mean difference, the method error statistic, two-way anova without replication, the t-test for paired comparisons, Fisher's distribution-free sign test, and the t-test for independent samples. The results indicate less intraobserver repeatability than expected as well as an alarming lack of interobserver reproducibility for many of these craniometric measurements. We hope these results will serve as a caution against the widespread belief that craniometric measurements are always produced with a high degree of precision by experienced craniometrists. In addition, these results suggest that investigators employing craniometric measurements to study population affinities, functional morphology, forensics, fossil primates, and human microevolution might profit from conducting a measurement error analysis as an important baseline for the interpretation of the biological significance of their results.     

Technical note: Comparability of Hrdlička's Catalog of crania data based on measurement landmark definitions

Archival sources of data are critical anthropological resources that inform inferences about human biology and evolutionary history. Craniometric data are one of the most widely available sources of information on human population history because craniometrics were critical in early 20th century debates about race and biological variation. As such, extensive databases of raw craniometric data were published at the same time that the field was working to standardize measurement protocol. Hrdli?ka published between 10 and 16 raw craniometric variables for over 8,000 individuals in a series of seven catalogs throughout his career. With a New World emphasis, Hrdli?ka's data complement those of Howells ( 1973 , 1989 ) and the two databases have been combined in the past. In this note we verify the consistency of Hrdli?ka's measurement protocol throughout the Catalog series and compare these definitions to those used by Howells. We conclude that 12 measurements are comparable throughout the Catalogs, with five of these equivalent to Howells' measurements: maximum cranial breadth (XCB), basion‐bregma height (BBH), maximum bizygomatic breadth (ZYB), nasal breadth (NLB), and breadth of the upper alveolar arch (MAB). Most of Hrdli?ka's measurements are not strictly comparable to those of Howells, thus limiting the utility of combined datasets for multivariate analysis. Four measurements are inconsistently defined by Hrdli?ka and we recommend not using these data: nasal height, orbit breadth, orbit height, and menton‐nasion height. This note promotes Hrdli?ka's tireless efforts at data collection and re‐emphasizes observer error as a legitimate concern in craniometry as the field shifts to morphometric digital data acquisition. Am J Phys Anthropol, 2011. © 2011 Wiley‐Liss, Inc.     

Ratio estimation with measurement error in the auxiliary variate

Summary .  With auxiliary information that is well correlated with the primary variable of interest, ratio estimation of the finite population total may be much more efficient than alternative estimators that do not make use of the auxiliary variate. The well-known properties of ratio estimators are perturbed when the auxiliary variate is measured with error. In this contribution we examine the effect of measurement error in the auxiliary variate on the design-based statistical properties of three common ratio estimators. We examine the case of systematic measurement error as well as measurement error that varies according to a fixed distribution. Aside from presenting expressions for the bias and variance of these estimators when they are contaminated with measurement error we provide numerical results based on a specific population. Under systematic measurement error, the biasing effect is asymmetric around zero, and precision may be improved or degraded depending on the magnitude of the error. Under variable measurement error, bias of the conventional ratio-of-means estimator increased slightly with increasing error dispersion, but far less than the increased bias of the conventional mean-of-ratios estimator. In similar fashion, the variance of the mean-of-ratios estimator incurs a greater loss of precision with increasing error dispersion compared with the other estimators we examine. Overall, the ratio-of-means estimator appears to be remarkably resistant to the effects of measurement error in the auxiliary variate.     

Developments in cranial morphometrics

This paper sets out to describe a number of traditional and novel approaches to craniometry. These include linear and angular measurements, indices, shape factors, least squares, and Fourier analysis. A study is presented in which these different techniques are applied to a phenetic analysis of the crania of a variety of living and extinct hominoids, with the aim of assessing the relative merits of different approaches. The results allow an appraisal of the stability of phenetic groupings in the face of different data and suggest that the choice of data can considerably influence the observed pattern of between-group relationships. The choice of craniometric method should be made with due regard for the questions at hand and the interpretation of phenetic relationships should allow for the particular data.     

3D虚拟复原精度的差异对头骨测量数值的影响——以Mimics软牛为例

近年来,根据三维软件虚拟复原的头骨来获取测量数据的方法被越来越多地应用在古生物,特别是古人类学的研究中,然而对于三维软件不同精度虚拟复原的头骨,其测量数值是否有差异,研究者并不是很清楚。本文以Mimics软件为例,根据其复原模型简化规则,选择未精简的最佳精度模型作为标准进行配对t检验或非参数检验,通过对43例云南人头骨的顶骨矢状弦长、颅周长、头盖部面积、乳突小房表面积、颅容量、乳突小房体积等六个测量项目的对比和分析,对Mimics软件低、中、高、最佳四种精度3D虚拟复原头骨间的测量差异进行了研究。结果显示：颅周长、头盖部面积、颅容量、乳突小房体积四项的所有简化精度模型的测量数据均与最佳精度模型测量数据的差异具有显著性;而除高精度组外,顶骨矢状弦长及乳突小房表面积的其余精度组测量数据均与最佳精度组差异具有显著性;此外,顶骨矢状弦长、颅周长、头盖部面积、颅容量的简化精度与最佳精度的测量差异占比均小于3%.而乳突小房表面积的低精度与最佳精度测量差异占比可超过50%,乳突小房体积的低精度与最佳精度测量差异占比可超过120%。这一结果提示我们,在测量Mimics复原的三维模型时,体量大差异小的测量项可以在较低精度的复原模型上进行测量;而对头骨内部腔窦这样体量小表面粗糙的结构,复原模型的精度选择及测量数据比较需要格外谨慎。     

颅骨测量与X线头影测量方法的比较研究

本文对传统的颅骨测量法与口腔医学上使用的X线头影测量法在测量标志点的选取定位及测量结果的差异方面进行了对比研究。测量标志点重叠对比显示颅骨测量中的大多数标志点在X线片上可以较为准确地定位。方差分析表明两种测量方法测量结果差异不显著(P>0.05)。本文就如何准确地在X线片上确定标志点以及测量数据的放大误差问题进行了讨论并提出了将放大率划分为三个等级计算X线头影片测量值的标准。作者认为采用X线头影测量方法进行人类学研究有着良好的应用前景。     

High-precision,high-throughput stability determinations facilitated by robotics and a semiautomated titrating fluorometer

The use of statistical modeling to test hypotheses concerning the determinants of protein structure requires stability data (e.g., the free energy of denaturation in H(2)O, DeltaG(HOH)) from hundreds of protein mutants. Fluorescence-monitored chemical denaturation provides a convenient method for high-precision, high-throughput DeltaG(HOH) determination. For eglin c we find that a throughput of about 20 min per protein can be attained in a two-channel semiautomated titrating fluorometer. We find also that the use of robotics for protein purification and preparation of the solutions for chemical denaturation gives highly precise DeltaG(HOH) values in which the standard deviation of values from multiple preparations (+/-0.051 kcal/mol) differs very little from multiple measurements from a single preparation (+/-0.040 kcal/mol). Since the variance introduced into model fitting by DeltaG(HOH) increases as the square of measurement error, there is a premium on precision. In fact, the fraction of stability behavior explicable by otherwise perfect models goes from 98% to only 50% over the error range commonly reported for chemical denaturation measurements (0.1-0.6 kcal/mol). We have found that the precision of chemical denaturation DeltaG(HOH) measurements depends most heavily on the precision of the instrument used, followed by protein purity and the capacity to precisely prepare the solutions used for titrations.     

Missing data in craniometrics: a simulation study

Craniometric measurements represent a useful tool for studying the differentiation of mammal populations. However, the fragility of skulls often leads to incomplete data matrices. Damaged specimens or incomplete sets of measurements are usually discarded prior to statistical analysis. We assessed the performance of two strategies that avoid elimination of observations: (1) pairwise deletion of missing cells, and (2) estimation of missing data using available measurements. The effect of these distinct approaches on the computation of inter-individual distances and population differentiation analyses were evaluated using craniometric measurements obtained from insular populations of deer micePeromyscus maniculatus (Wagner, 1845). In our simulations, Euclidean distances were greatly altered by pairwise deletion, whereas Gower’s distance coefficient corrected for missing data provided accurate results. Among the different estimation methods compared in this paper, the regression-based approximations weighted by coefficients of determination (r ²) outperformed the competing approaches. We further show that incomplete sets of craniometric measurements can be used to compute distance matrices, provided that an appropriate coefficient is selected. However, the application of estimation procedures provides a flexible approach that allows researchers to analyse incomplete data sets.     

Are geometric morphometric analyses replicable? Evaluating landmark measurement error and its impact on extant and fossil Microtus classification

Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis‐based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining >30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis‐specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations.     

Measurement error in heat tolerance assays

Biological measurements inherently involve some measurement error (ME), which is a major concern because measurement accuracy (how closely a measurement reproduces the true value of the attribute being measured) and statistical power steadily decrease with increasing ME. However, ME has been largely overlooked in the thermal biology literature, which can be explained by the fact that thermotolerance estimates often involve the collapse or death of the tested individuals and measurements cannot be repeated in vivo with the same specimen under identical conditions. Here we assess inter- and intra-researcher (test-retest) reliability of heat tolerance measured as knockdown time from digital recordings of Drosophila subobscura flies individually assayed in vials with a dynamic method. We provide a summary of various estimators used to compute measurement reliability (the degree to which the measurement is affected by ME) together with their statistical properties. Our results indicate that the estimation of heat knockdown time has poor reliability: intra-researcher ME=29% and inter-researcher ME=34%. This difference is attributed to lack of ‘accurateness’ (the difference in the marginal distributions of the measurements taken by the two researchers) because measurement imprecision was essentially the same in both estimates (27%). In view of our results we conclude that thermal biologists should report the reliability of thermotolerance estimates and, when necessary, adopt some straightforward guidelines suggested here to improve measurement reliability.     

On latent-variable model misspecification in structural measurement error models for binary response

Summary .  We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods.     

How long is a piece of Strix? Methods in measuring and measuring the measurers

An experiment to quantify intra- and interobserver error in anatomical measurements found that interobserver measurements can vary by over 14% of mean specimen length; disparity in measurement increases logarithmically with the number of contributors; instructions did not reduce variation or measurement disparity; scale of the specimen influenced the precision of measurement (relative error increasing with specimen size); different methods of taking a measurement yielded different results, although they did not differ in terms of precision, and topographical complexity of the elements being considered may potentially influence error (error increasing with complexity). These results highlight concerns about introduction of noise and potential bias that should be taken into account when compiling composite datasets and meta-analyses.     

Measurement error in a random walk model with applications to population dynamics

Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets.     

The effect of size variation on univariate assessments of morphological difference in human crania.

The present research was undertaken to determine the contribution of general size to craniometric variation in two previously described Paleo-Amerindian series, and to evaluate the effect of size variation on univariate assessments of morphological difference between the two. The analysis was based upon 19 measurements of 81 crania representing the Iswanid and Fort Ancient Muskogid varieties. The results of principal components analysis indicate that the 19 measurements can be represented as five principal component variates. Inspection of component eigenvectors indicates that variation in body size accounts for 40% of the variation within the metric data. Analysis of covariance lends support to the hypothesis that this size variation contributes substantially to statistical tests of difference between the two groups based on Student's t.     

Expected estimating equations for missing data, measurement error, and misclassification, with application to longitudinal nonignorable missing data

Summary .   Missing data, measurement error, and misclassification are three important problems in many research fields, such as epidemiological studies. It is well known that missing data and measurement error in covariates may lead to biased estimation. Misclassification may be considered as a special type of measurement error, for categorical data. Nevertheless, we treat misclassification as a different problem from measurement error because statistical models for them are different. Indeed, in the literature, methods for these three problems were generally proposed separately given that statistical modeling for them are very different. The problem is more challenging in a longitudinal study with nonignorable missing data. In this article, we consider estimation in generalized linear models under these three incomplete data models. We propose a general approach based on expected estimating equations (EEEs) to solve these three incomplete data problems in a unified fashion. This EEE approach can be easily implemented and its asymptotic covariance can be obtained by sandwich estimation. Intensive simulation studies are performed under various incomplete data settings. The proposed method is applied to a longitudinal study of oral bone density in relation to body bone density.     

On Method of Moments Estimation in Linear Mixed Effects Models with Measurement Error on Covariates and Response with Application to a Longitudinal Study of Gene-Environment Interaction

We study a linear mixed effects model for longitudinal data, where the response variable and covariates with fixed effects are subject to measurement error. We propose a method of moment estimation that does not require any assumption on the functional forms of the distributions of random effects and other random errors in the model. For a classical measurement error model we apply the instrumental variable approach to ensure identifiability of the parameters. Our methodology, without instrumental variables, can be applied to Berkson measurement errors. Using simulation studies, we investigate the finite sample performances of the estimators and show the impact of measurement error on the covariates and the response on the estimation procedure. The results show that our method performs quite satisfactory, especially for the fixed effects with measurement error (even under misspecification of measurement error model). This method is applied to a real data example of a large birth and child cohort study.     

Influence of relative humidity on analyzing electric field exposure using ELF electric field measurements

The objective of the study was to investigate the influence of humidity on analyzing electric field exposure using extremely low frequency (ELF) electric field measurements. The study included 322 measurements in a climate room. We used two commercial three‐axis meters, EFA‐3 and EFA‐300, and employed two measurement techniques in the climate room where we varied the temperature from 15 to 25 °C, the relative humidity from 55% to 95%, and the electric field from 1 to 25 kV/m. We calculated Pearson correlations between humidity and percentage errors for all data and for data at different levels of humidity. When the relative humidity was below 70%, the results obtained by the different measurement methods in terms of percentage errors were of the same order of magnitude for the considered temperatures and field strength, but the results were less reliable when the relative humidity was higher than 80%. In the future, it is important to take humidity into account when electric field measurement results will be compared to the values given in different exposure guidelines. Bioelectromagnetics 34:414–418, 2013. © 2012 Wiley Periodicals, Inc.     

Nonparametric variance estimation in the analysis of microarray data: a measurement error approach

We investigate the effects of measurement error on the estimationof nonparametric variance functions. We show that either ignoringmeasurement error or direct application of the simulation extrapolation,SIMEX, method leads to inconsistent estimators. Nevertheless,the direct SIMEX method can reduce bias relative to a naiveestimator. We further propose a permutation SIMEX method thatleads to consistent estimators in theory. The performance ofboth the SIMEX methods depends on approximations to the exactextrapolants. Simulations show that both the SIMEX methods performbetter than ignoring measurement error. The methodology is illustratedusing microarray data from colon cancer patients.     

Weighted Estimation of the Accelerated Failure Time Model in the Presence of Dependent Censoring

Independent censoring is a crucial assumption in survival analysis. However, this is impractical in many medical studies, where the presence of dependent censoring leads to difficulty in analyzing covariate effects on disease outcomes. The semicompeting risks framework offers one approach to handling dependent censoring. There are two representative estimators based on an artificial censoring technique in this data structure. However, neither of these estimators is better than another with respect to efficiency (standard error). In this paper, we propose a new weighted estimator for the accelerated failure time (AFT) model under dependent censoring. One of the advantages in our approach is that these weights are optimal among all the linear combinations of the previously mentioned two estimators. To calculate these weights, a novel resampling-based scheme is employed. Attendant asymptotic statistical results for the estimator are established. In addition, simulation studies, as well as an application to real data, show the gains in efficiency for our estimator.