Stature estimation in ancient Egyptians: a new technique based on anatomical reconstruction of stature

Trotter and Gleser's (Trotter and Gleser: Am J Phys Anthropol 10 (1952) 469-514; Trotter and Gleser: Am J Phys Anthropol 16 (1958) 79-123) long bone formulae for US Blacks or derivations thereof (Robins and Shute: Hum Evol 1 (1986) 313-324) have been previously used to estimate the stature of ancient Egyptians. However, limb length to stature proportions differ between human populations; consequently, the most accurate mathematical stature estimates will be obtained when the population being examined is as similar as possible in proportions to the population used to create the equations. The purpose of this study was to create new stature regression formulae based on direct reconstructions of stature in ancient Egyptians and assess their accuracy in comparison to other stature estimation methods. We also compare Egyptian body proportions to those of modern American Blacks and Whites. Living stature estimates were derived using a revised Fully anatomical method (Raxter et al.: Am J Phys Anthropol 130 (2006) 374-384). Long bone stature regression equations were then derived for each sex. Our results confirm that, although ancient Egyptians are closer in body proportion to modern American Blacks than they are to American Whites, proportions in Blacks and Egyptians are not identical. The newly generated Egyptian-based stature regression formulae have standard errors of estimate of 1.9-4.2 cm. All mean directional differences are less than 0.4% compared to anatomically estimated stature, while results using previous formulae are more variable, with mean directional biases varying between 0.2% and 1.1%, tibial and radial estimates being the most biased. There is no evidence for significant variation in proportions among temporal or social groupings; thus, the new formulae may be broadly applicable to ancient Egyptian remains.     

通过枕骨大孔测量值对若干化石人类身高的估计

身高是人类体质研究中的重要指标之一。对化石人类的身高的估计主要借助于基于现代人骨骼测量数据计算而得的身高推断公式。本文使用枕骨大孔长和枕骨大孔宽的测量值和相关身高估计公式,对郧县EV9001,郧县EV9002,大荔,柳江,山顶洞101,山顶洞102和考古遗址骨骼的身高进行了估计,并使用其他头部测量数据对所得结果进行了检验和校正。本文认为,这6个化石人类的身高分别为160.76、161.89、159.85、161.54、163.92和164.30cm。     

Body size estimation of small‐bodied humans: Applicability of current methods

Body size (stature and mass) estimates are integral to understanding the lifeways of past populations.Body size estimation of an archaeological skeletal sample can be problematic when the body size or proportions of the population are distinctive. One such population is that of the Holocene Later Stone Age (LSA) of southern Africa, in which small stature (mean femoral length = 407 mm, n = 52) and narrow pelves (mean bi‐iliac breadth = 210 mm, n = 50) produce a distinctive adult body size/shape, making it difficult to identify appropriate body size estimation methods. Material culture, morphology, and culture history link the Later Stone Age people with the descendant population collectively known as the Khoe‐San. Stature estimates based on skeletal “anatomical” linear measures (the Fully method) and on long bone length are compared, along with body mass estimates derived from “morphometric” (bi‐iliac breath/stature) and “biomechanical” (femoral head diameter) methods, in a LSA adult skeletal sample (n = 52) from the from coastal and near‐coastal regions of South Africa. Indices of sexual dimorphism (ISD) for each method are compared with data from living populations. Fully anatomical stature is most congruent with Olivier's femur + tibia method, although both produce low ISD. McHenry's femoral head body mass formula produces estimates most consistent with the bi‐iliac breadth/staturemethod for the females, although the males display higher degrees of disagreement among methods. These results highlight the need for formulae derived from reference samples from a wider range of body sizes to improve the reliability of existing methods. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.     

Model selection of generalized estimating equations with multiply imputed longitudinal data

Longitudinal data often encounter missingness with monotone and/or intermittent missing patterns. Multiple imputation (MI) has been popularly employed for analysis of missing longitudinal data. In particular, the MI‐GEE method has been proposed for inference of generalized estimating equations (GEE) when missing data are imputed via MI. However, little is known about how to perform model selection with multiply imputed longitudinal data. In this work, we extend the existing GEE model selection criteria, including the “quasi‐likelihood under the independence model criterion” (QIC) and the “missing longitudinal information criterion” (MLIC), to accommodate multiple imputed datasets for selection of the MI‐GEE mean model. According to real data analyses from a schizophrenia study and an AIDS study, as well as simulations under nonmonotone missingness with moderate proportion of missing observations, we conclude that: (i) more than a few imputed datasets are required for stable and reliable model selection in MI‐GEE analysis; (ii) the MI‐based GEE model selection methods with a suitable number of imputations generally perform well, while the naive application of existing model selection methods by simply ignoring missing observations may lead to very poor performance; (iii) the model selection criteria based on improper (frequentist) multiple imputation generally performs better than their analogies based on proper (Bayesian) multiple imputation.     

Technical note: a re-evaluation of stature estimation from skeletal length in the grave

Several methods for stature estimation have been proposed over the years. Among these methods is anatomical reconstruction, regression based on long bone lengths, and measuring skeletal vertex - talus length in the grave for individuals buried in a supine position. Recent studies have dealt with the applicability of skeletal length in the grave (Petersen: Int J Osteoarchaeol 15 (2005) 106-114) and anatomical reconstruction (Raxter et al.: Am J Phys Anthropol 130 (2006) 374-384). The results from the latter study calls into question the results of the former study. Therefore an investigation of the potential bias of using skeletal length in the grave as an estimate of living stature has been performed. Twenty Medieval Danish skeletons were measured both in situ and in the laboratory, and the anatomically reconstructed stature (Raxter et al.: Am J Phys Anthropol 130 (2006) 374-384) was compared with the skeletal length in the grave. The results show that 2.5 cm should be added to skeletal length in the grave in order to obtain an unbiased estimate ofliving stature.     

Body mass and stature estimation based on the first metatarsal in humans

Archaeological assemblages often lack the complete long bones needed to estimate stature and body mass. The most accurate estimates of body mass and stature are produced using femoral head diameter and femur length. Foot bones including the first metatarsal preserve relatively well in a range of archaeological contexts. In this article we present regression equations using the first metatarsal to estimate femoral head diameter, femoral length, and body mass in a diverse human sample. The skeletal sample comprised 87 individuals (Andamanese, Australasians, Africans, Native Americans, and British). Results show that all first metatarsal measurements correlate moderately to highly (r = 0.62-0.91) with femoral head diameter and length. The proximal articular dorsoplantar diameter is the best single measurement to predict both femoral dimensions. Percent standard errors of the estimate are below 5%. Equations using two metatarsal measurements show a small increase in accuracy. Direct estimations of body mass (calculated from measured femoral head diameter using previously published equations) have an error of just over 7%. No direct stature estimation equations were derived due to the varied linear body proportions represented in the sample. The equations were tested on a sample of 35 individuals from Christ Church Spitalfields. Percentage differences in estimated and measured femoral head diameter and length were less than 1%. This study demonstrates that it is feasible to use the first metatarsal in the estimation of body mass and stature. The equations presented here are particularly useful for assemblages where the long bones are either missing or fragmented, and enable estimation of these fundamental population parameters in poorly preserved assemblages.     

Application of the anatomical method to estimate the maximum adult stature and the age‐at‐death stature

This study focuses on the age adjustment of statures estimated with the anatomical method. The research material includes 127 individuals from the Terry Collection. The cadaveric stature (CSTA)–skeletal height (SKH) ratios indicate that stature loss with age commences before SKH reduction. Testing three equations to estimate CSTA at the age at death and CSTA corrected to maximum stature from SKH indicates that the age correction of stature should reflect the pattern of age‐related stature loss to minimize estimation error. An equation that includes a continuous and linear age correction through the entire adult age range [Eq. (1)] results in curvilinear stature estimation error. This curvilinear stature estimation error can be largely avoided by applying a second linear equation [Eq. (2)] to only individuals older than 40 years. Our third equation [Eq. (3)], based on younger individuals who have not lost stature, can be used to estimate maximum stature. This equation can also be applied to individuals of unknown or highly uncertain age, because it provides reasonably accurate estimates until about 60/70 years at least for males. Am J Phys Anthropol 152:96–106, 2013. © 2013 Wiley Periodicals, Inc.     

从中指骨长度推算身高的研究

作者对近年在华南地区收集的,已知生前身高的汉族成年男性骨骼的中指骨近节、中节进行了测量。用直线回归方程、多元回归方程对从中指骨长度推算身高进行了研究。并用50例国人骨骼标本对这些推算身高的方法作了检验。结果表明,中指骨与四肢大型长骨,以及从中指骨长度推算身高的直线回归方程与多元回归方程,对推算身高的价值都是相同的。     

Calcaneal measurement in estimation of stature of South African blacks

Stature (height) is an important factor in establishing the identity of a person in the living as well as in the skeletonized state. When stature is estimated from the bones of the limbs, regression equations, which estimate the ratios of the lengths of bones to the height of the individual, are generated. The majority of bones that were used previously were the long bones. The calcaneus was used for estimating stature only in American whites and blacks (Holland [1995] Am. J. Phys. Anthropol. 96:315-320). The regression equations that he generated were found to be useful for stature estimation in these population groups. Since the calcaneus has not been used for the same purpose in South Africa, the aim of this study was to derive regression equations that will allow this bone to be used for stature estimation in South African blacks. In total, 116 complete skeletons (60 males and 56 females) were selected from the Raymond A. Dart Collection of Human Skeletons, School of Anatomical Sciences, University of the Witwatersrand (Johannesburg, South Africa). The skeletal heights of these sets of skeletons were calculated using the anatomical method of Fully ([1956] Ann. Med. Leg. 35:266-273). Nine parameters of the calcaneus were measured and matched against skeletal heights, using univariate and multivariate regression methods. Regression equations were obtained for estimation of the stature of the South African black population from the calcaneus. The standard error of estimate that was obtained with univariate regression analysis was higher than the corresponding values using multivariate regression analysis. In both cases, the standard errors of estimate compared well with the values obtained for fragmentary long bones by previous authors.     

Gaussian mixture clustering and imputation of microarray data

MOTIVATION: In microarray experiments, missing entries arise from blemishes on the chips. In large-scale studies, virtually every chip contains some missing entries and more than 90% of the genes are affected. Many analysis methods require a full set of data. Either those genes with missing entries are excluded, or the missing entries are filled with estimates prior to the analyses. This study compares methods of missing value estimation. RESULTS: Two evaluation metrics of imputation accuracy are employed. First, the root mean squared error measures the difference between the true values and the imputed values. Second, the number of mis-clustered genes measures the difference between clustering with true values and that with imputed values; it examines the bias introduced by imputation to clustering. The Gaussian mixture clustering with model averaging imputation is superior to all other imputation methods, according to both evaluation metrics, on both time-series (correlated) and non-time series (uncorrelated) data sets.     

Stature estimation in prehistoric Native Americans of Ohio

In the present report we investigate stature estimation techniques in a sample of 64 (35 male, 29 female) prehistoric Native Americans from Ohio. Because living stature is unknown for these 64 individuals, we use Fully's (1956) anatomical method to provide the best estimates of living stature. In this method all osseous components of skeletal height are measured and soft tissue correction is added. Comparisons of regression equations commonly used for stature estimation in prehistoric Eastern Woodland Native American populations, but developed for East Asian and East Asian-derived populations (using lower extremity components), show that these commonly used equations consistently yield stature estimates 2 to 8 cm in excess of the best estimates from Fully's method. Based on the skeletal height measures of the 64 individuals in the present sample, we develop regression equations for the estimation of stature. These equations yield stature estimates virtually identical to estimates from Fully's method and may prove useful for stature reconstruction in other prehistoric Eastern Woodland Native American populations.     

Wealth, inequality, and insolation effects across the 19th century white US stature distribution

Sources associated with 19th century stature variation have been widely considered. Using US state prison records and robust statistics, this paper illustrates that 19th century US white statures were positively associated with a broad combination of wealth, equality, and environmental characteristics. Individuals from geographic areas characterized by low wealth and high inequality had shorter statures. After controlling for various factors, direct sunlight – the primary source of vitamin D – was also positively associated with stature. After controlling for wealth, inequality, and insolation, farmers were taller than workers in other occupations. These wealth, insolation, and socioeconomic relationships are significant across the stature distribution.     

Regression equations for the estimation of stature and body mass using a Greek documented skeletal collection

Body size is an important variable in bioarchaeological and forensic studies, making the accurate calculation of stature and body mass imperative. Given that anatomical and morphometric approaches offer accurate results but require a particularly good preservation of the skeletal material, whereas mathematical and mechanical methods are more easily applicable but they are largely population-specific, the present paper uses a ‘hybrid’ approach in order to generate regression equations for the prediction of stature and body mass in a modern Greek sample. Specifically, anatomical and morphometric methods were used to calculate the stature and body mass of the individuals and regression equations using the Ordinary Least Squares and Reduced Major Axis methods were generated with long bone lengths and femoral head breadth as predictors. The obtained equations exhibit low random and directional error and perform better than existing equations designed using different samples from the United States, Europe, and the Balkans. Therefore, these equations are more appropriate for modern Greek material.     

Reported versus measured adult statures

Reported and measured statures were obtained for 100 husband-wife pairs. In addition, wives were asked to specify whether their husbands were tall, medium, or short. Correlations between reported and measured statures are high (0.84–0.97) and wives tend to overestimate their own measured stature by about 1 cm, and that of their husbands by about 1.3 cm. Wives correctly classify their husbands as tall, medium, or short in about 70% of the cases, using terciles of the stature distribution of American men as the standard. Reported statures may be useful proxies for measured statures for certain purposes. In the absence of measured or reported statures, a wife's categorization of her husband as tall, medium, or short may be satisfactory for some group studies.     

From footprint morphometrics to the stature of fossil hominins: A common but uncertain estimate

Hominin footprints are a particular remain in paleoanthropology representing brief moments of life of extinct individuals. Footprints not only provide information on the locomotor behavior of fossil taxa but also on their body characteristics such as their stature. This stature is usually estimated from the length of the footprints based on the well-known foot length to stature ratio. However, footprint length does not result only from the foot length but of a combination of factors. Therefore, it is necessary to investigate the relationships between footprint length and stature of individuals using experimental approaches. Secondly, recent discoveries of fossil footprints have led to the estimation of statures from isolated footprints. However, such estimates may be biased because of the intraindividual morphometric variation of the footprints. Moreover, footprints may also be incomplete making it impossible to measure the length and therefore the estimation of a stature. The search for relationships between stature and other morphometric variables is therefore necessary to have the most accurate picture possible of the individuals who left these tracks. In this context, this article reports the results of an experimental study that aims to determine the relationships between the stature of individuals and different morphometric variables and to quantify the intraindividual variation of each variable. Thus, 21 morphometric variables were measured on a total of 175 experimental footprints left by 20 individuals in an experimental area composed of loose sand. Statistical analyses show that footprint lengths are not only the variables most correlated with stature but also those with the least intraindividual variation. However, estimation of stature from footprints left by fossil hominins is subject to three types of uncertainties: residuals from linear regression, intraindividual variation that can be particularly large in soft substrates, and the application of relationships defined on modern populations to fossil taxa.     

Estimation of stature and body mass from the skeleton among coastal and mid-altitude Andean populations

Adult stature and body mass represent fundamental biological characteristics of individuals and populations, as they are relevant to a range of problems from assessing nutrition and health to longer term evolutionary processes. Stature and body mass estimation from skeletal dimensions are therefore key to addressing biological and social questions about past populations. Anatomical reconstruction provides the most direct proxy for living stature but is only suitable for well-preserved remains. Regression equations for estimating stature from bone lengths are therefore extremely useful, though it is well recognized that differences in body proportions limit the cross-application of equations between samples. Here, we assess the accuracy of published stature estimation equations from worldwide and New World groups applied to archaeological samples from the central Andean coast and highlands of South America. As no existing equations are clearly appropriate, new sample-specific regression equations are presented. Anatomical stature reconstruction is further complicated by artificial cranial modification (ACM) influencing cranial height in Andean samples, so this problem is investigated in the current sample. Although ACM has minimal impact here, the possibility should be explored in other samples before anatomical stature estimation is attempted. Recommendations are also made for estimating body mass from femoral head diameter. The mean of three previously published equations is shown to offer minimal bias and the most reliable estimate of body mass in the study samples.     

Iterated local least squares microarray missing value imputation

Microarray gene expression data often contains multiple missing values due to various reasons. However, most of gene expression data analysis algorithms require complete expression data. Therefore, accurate estimation of the missing values is critical to further data analysis. In this paper, an Iterated Local Least Squares Imputation (ILLSimpute) method is proposed for estimating missing values. Two unique features of ILLSimpute method are: ILLSimpute method does not fix a common number of coherent genes for target genes for estimation purpose, but defines coherent genes as those within a distance threshold to the target genes. Secondly, in ILLSimpute method, estimated values in one iteration are used for missing value estimation in the next iteration and the method terminates after certain iterations or the imputed values converge. Experimental results on six real microarray datasets showed that ILLSimpute method performed at least as well as, and most of the time much better than, five most recent imputation methods.