An elusive paleodemography? A comparison of two methods for estimating the adult age distribution of deaths at late Classic Copan,Honduras

Comparison of different adult age estimation methods on the same skeletal sample with unknown ages could forward paleodemographic inference, while researchers sort out various controversies. The original aging method for the auricular surface (Lovejoy et al., 1985a) assigned an age estimation based on several separate characteristics. Researchers have found this original method hard to apply. It is usually forgotten that before assigning an age, there was a seriation, an ordering of all available individuals from youngest to oldest. Thus, age estimation reflected the place of an individual within its sample. A recent article (Buckberry and Chamberlain, 2002) proposed a revised method that scores theses various characteristics into age stages, which can then be used with a Bayesian method to estimate an adult age distribution for the sample. Both methods were applied to the adult auricular surfaces of a Pre-Columbian Maya skeletal population from Copan, Honduras and resulted in age distributions with significant numbers of older adults. However, contrary to the usual paleodemographic distribution, one Bayesian estimation based on uniform prior probabilities yielded a population with 57% of the ages at death over 65, while another based on a high mortality life table still had 12% of the individuals aged over 75 years. The seriation method yielded an age distribution more similar to that known from preindustrial historical situations, without excessive longevity of adults. Paleodemography must still wrestle with its elusive goal of accurate adult age estimation from skeletons, a necessary base for demographic study of past populations.     

Model life table fitting by maximum likelihood estimation: a procedure to reconstruct paleodemographic characteristics from skeletal age distributions

A procedure is presented that uses the regression coefficients for the Coale and Demeny west model life tables to model selected demographic characteristics from skeletal age-at-death distributions. Model death distributions were constructed and compared to a given skeletal distribution, using methods of maximum likelihood estimation to determine the best fit. Two chi-square tests are employed to evaluate the degree of fit. The resulting model includes estimates of demographic characteristics including gross reproductive rate, crude birth rate and life expectancy. The procedure is applied to three archaeological skeletal samples as test cases: two from eastern North America and one from Mexico. These display a range of correspondence (between the best fitting model and the data) from good to poor. The proposed procedure is a potentially powerful tool for both reconstructing paleodemographic rates and illuminating differences between typical human patterns and those found in archaeological populations.     

Constitution and By-Laws of the American Association of Physical Anthropologists

From parent populations (N = 50,000) statistically generated, representing different levels of correlation (r) between the age at death and a hypothetical biological indicator (r = 0.8-0.98), reference samples and target demographic samples are randomly drawn. Two iterative techniques, proportional fitting procedure and Bayesian, are used to estimate from the reference samples the age distribution of the targets. Due to the random fluctuations of the pattern of aging, both in the reference and target samples, these techniques converge only in expectation toward the true value of a distribution, but not in practice for any particular realization. Nevertheless, these techniques allow the estimation of the average of an age distribution, even if its shape is unknown. Under the hypothesis that the target sample is drawn from a stationary population, this average represents the life expectancy at 20 years (plus 20 years). Using this mean age at death for the adults and the juvenility index at death (D5-14/D20-ω), a new set of paleodemographic estimators were derived from 40 archaic life tables. For a hypothesized stable population, they give the life expectancy at birth and at 20 years, and the probability of death at 1 and 5 years. © 1996 Wiley-Liss, Inc.     

The short die young: the interrelationship between stature and longevity-evidence from skeletal remains

It has long been observed that tall people display longer life spans. The current data were employed to verify this association within the bioarchaeological context. To this end, stature and its association with age-at-death were analyzed in a pooled sample of 2,923 skeletons. Height was estimated from proxy indicators based on the maximum length of the humerus, radius, femur, and tibia. Stature estimation followed the procedure outlined by Pearson ([1899] Philos. Trans. R. Soc. Lond. [A] 192:169-244), incorporating minor modifications by R?sing ([ 1988] Handbuch der vergleichenden Biologie des Menschen; Stuttgart: Gustave Fischer, p 586-600). Individual age estimates were classified into three mutually exclusive age groups: 20-39 years (591 males, 667 females), 40-59 years (876 males, 499 females), and 60+ years (171 males, 119 females). The results document that both sexes display a statistically significant inverse relationship between adult height and age-at-death (males, P < 0.01; females, P < 0.05). Taking an epidemiological approach, the risk model implies that the estimated odds of survival beyond age 40 improve by approximately 16% for 1 SD in bone length. However, not all bones may be equally adept at displaying the association. The radius failed to support the positive association between stature and longevity, which may be indicative of a relatively greater contribution of environmental factor to radius length. Overall, the relationship between body height and longevity is not causal but coincidental: mitigated by diverse environmental factors such as nutrition, socioeconomic stressors, and disease load.     

Ectocranial suture closure: a revised method for the determination of skeletal age at death based on the lateral-anterior sutures

A new method for estimation of age-at-death based on the degree of suture closure is presented. The method employs simple ectocranial scoring of specific sites on the external table. Composite scores for two groups of sutures, lateral-anterior and vault systems, which are used to provide estimates of age-at-death, have been developed from a sample of 236 crania from the Hamann-Todd Collection. A variety of tests show that the lateral-anterior sutures are superior to the sutures of the vault, that ectocranial is superior to endocranial observation, and that age estimates are independent of race and sex. It is concluded that suture closure can provide valuable estimates of age-at-death in both archaeological and forensic contexts when used in conjunction with other skeletal age indicators.     

A new method for estimating age-at-death from the first rib

A new method for estimating adult age-at-death from the first rib was developed as a modification of the Kunos et al. (Am J Phys Anthropol 110 (1999) 303-323) method. Data were collected on three aspects of the first rib (costal face, rib head, and tubercle facet) for 470 known-age males of Balkan ancestry collected as evidence during investigations conducted by the International Criminal Tribunal for the former Yugoslavia (ICTY). Ages-at-death range from 12 to 90 years (mean of 47.7 years). Several variables were extracted from the original study utilizing all three skeletal aspects of the first rib. This list was modified to 11 variables as preliminary tests on seriations of the samples were undertaken. A cumulative probit model with age measured on a log scale was used to calculate the mean and standard deviation of the ages-of-transition for each component. Multivariate analysis of the three components was also performed. The lowest correlation (r = 0.079, controlling for age) was between the geometric shape of the costal face and the surface texture of the tubercle facet. Assuming a correlation of zero, these two traits were used to calculate the highest posterior density regions for estimating individual ages-at-death. Age-at-death estimates generated from 50 and 95% posterior density regions indicate that this method captures age-related change reaching the ninth decade. The Bayesian statistical approach used here produced a valuable and promising new method for estimating age-at-death. Additional research is necessary to determine if these highest posterior density regions produce results highly correlated with age in other samples and its applicability to females.     

过渡分析在先秦时期人骨年龄估计中的应用

成人骨骼年龄的估计向来是存在许多困难和争议的。通过对其发展历程的回顾可知,尽管早已研发出了相对较可靠的用耻骨联合、髂骨耳状关节面等特征部位的形态估计年龄的方法,但鉴于“年龄模拟效应”的存在,这些方法都不可避免地会使估计的结果出现偏差。建立在贝叶斯方法和最大似然估计的基础上,Jesper Boldsen等研发出的“过渡分析”能够有效地消除上述不良影响。借助ADBOU软件,通过对山西先秦时期人骨样本进行过渡分析的实践,发现传统的形态观察法和过渡分析法会造成估计得到的死亡年龄结构出现差异。由于年龄估计结果的差异会对古人口学研究造成显著影响,因此建议在借鉴过渡分析的基础上,加强对年龄估计方法的改进。     

Comparison of a Bone Criterion and a dental Criterion for estimation of age at death in the study of an Ancient Cemetery

Two methods, a visual method based on the appearance of the auricular surface of the ilium and a metric method based on two dental criteria, were used in conjunction for estimation of skeletal age at death in paleodemographic study of an ancient cemetery, and were found to be coherent. However, the paleodemographic profiles differed according to sex, indicating a sexual difference in the evolution of the sacroiliac joint.     

Mortality incidence estimation using federal death certificate and natality data with an application to Tay–Sachs disease

For confidentiality reasons, US federal death certificate data are incomplete with regards to the dates of birth and death for the decedents, making calculation of total lifetime of a decedent impossible and thus estimation of mortality incidence difficult. This paper proposes the use of natality data and an imputation‐based method to estimate age‐specific mortality incidence rates in the face of this missing information. By utilizing previously determined probabilities of birth, a birth date and death date are imputed for every decedent in the dataset. Thus, the birth cohort of each individual is imputed, and the total on‐study time can be calculated. This idea is implemented in two approaches for estimation of mortality incidence rates. The first is an extension of a person‐time approach, while the second is an extension of a life table approach. Monte Carlo simulations showed that both approaches perform well in comparison to the ideal complete data methods, but that the person‐time method is preferred. An application to Tay–Sachs disease is demonstrated. It is concluded that the imputation methods proposed provide valid estimates of the incidence of death from death certificate data without the need for additional assumptions under which usual mortality rates provide valid estimates.     

Combining capture–recapture data and known ages allows estimation of age‐dependent survival rates

In many animal populations, demographic parameters such as survival and recruitment vary markedly with age, as do parameters related to sampling, such as capture probability. Failing to account for such variation can result in biased estimates of population‐level rates. However, estimating age‐dependent survival rates can be challenging because ages of individuals are rarely known unless tagging is done at birth. For many species, it is possible to infer age based on size. In capture–recapture studies of such species, it is possible to use a growth model to infer the age at first capture of individuals. We show how to build estimates of age‐dependent survival into a capture–mark–recapture model based on data obtained in a capture–recapture study. We first show how estimates of age based on length increments closely match those based on definitive aging methods. In simulated analyses, we show that both individual ages and age‐dependent survival rates estimated from simulated data closely match true values. With our approach, we are able to estimate the age‐specific apparent survival rates of Murray and trout cod in the Murray River, Australia. Our model structure provides a flexible framework within which to investigate various aspects of how survival varies with age and will have extensions within a wide range of ecological studies of animals where age can be estimated based on size.     

Statistical basis for positive identification in forensic anthropology

Forensic scientists are often expected to present the likelihood of DNA identifications in US courts based on comparative population data, yet forensic anthropologists tend not to quantify the strength of an osteological identification. Because forensic anthropologists are trained first and foremost as physical anthropologists, they emphasize estimation problems at the expense of evidentiary problems, but this approach must be reexamined. In this paper, the statistical bases for presenting osteological and dental evidence are outlined, using a forensic case as a motivating example. A brief overview of Bayesian statistics is provided, and methods to calculate likelihood ratios for five aspects of the biological profile are demonstrated. This paper emphasizes the definition of appropriate reference samples and of the "population at large," and points out the conceptual differences between them. Several databases are introduced for both reference information and to characterize the "population at large," and new data are compiled to calculate the frequency of specific characters, such as age or fractures, within the "population at large." Despite small individual likelihood ratios for age, sex, and stature in the case example, the power of this approach is that, assuming each likelihood ratio is independent, the product rule can be applied. In this particular example, it is over three million times more likely to obtain the observed osteological and dental data if the identification is correct than if the identification is incorrect. This likelihood ratio is a convincing statistic that can support the forensic anthropologist's opinion on personal identity in court.     

Maximum likelihood estimate of life expectancy in the prehistoric Jomon: Canine pulp volume reduction suggests a longer life expectancy than previously thought

Recent theoretical progress potentially refutes past claims that paleodemographic estimations are flawed by statistical problems, including age mimicry and sample bias due to differential preservation. The life expectancy at age 15 of the Jomon period prehistoric populace in Japan was initially estimated to have been ～16 years while a more recent analysis suggested 31.5 years. In this study, we provide alternative results based on a new methodology. The material comprises 234 mandibular canines from Jomon period skeletal remains and a reference sample of 363 mandibular canines of recent‐modern Japanese. Dental pulp reduction is used as the age‐indicator, which because of tooth durability is presumed to minimize the effect of differential preservation. Maximum likelihood estimation, which theoretically avoids age mimicry, was applied. Our methods also adjusted for the known pulp volume reduction rate among recent‐modern Japanese to provide a better fit for observations in the Jomon period sample. Without adjustment for the known rate in pulp volume reduction, estimates of Jomon life expectancy at age 15 were dubiously long. However, when the rate was adjusted, the estimate results in a value that falls within the range of modern hunter‐gatherers, with significantly better fit to the observations. The rate‐adjusted result of 32.2 years more likely represents the true life expectancy of the Jomon people at age 15, than the result without adjustment. Considering ～7% rate of antemortem loss of the mandibular canine observed in our Jomon period sample, actual life expectancy at age 15 may have been as high as ～35.3 years.     

Estimation of age structure in anthropological demography.

The past decade has produced considerable debate over the feasibility of paleodemographic research, with much attention focusing on the question of reliability of age estimates. We show here that in cases where age is estimated rather than known, the traditional method of assigning individuals to age classes will produce biased estimates of age structure. We demonstrate the effect of this bias both mathematically and by computer simulation, and show how a more appropriate method from the fisheries literature (the "iterated age length key") can be used to estimate age structure. Because it is often the case that ages are also estimated for extant groups, we suggest that our results are relevant to the general field of anthropological demography, and that it is time for us to improve the statistical basis for age structure estimation. We further suggest that the oft noted paucity of older individuals in skeletal collections is a simple result of the use of inappropriate methods of age estimation, and that this problem can be rectified in the future by using maximum likelihood estimates of life table or hazard functions incorporating the uncertainty of age estimates.     

Stage-classified matrix models and age estimates

When the size of individuals is a better indicator of their chances to survive, grow, and reproduce than their age, the suitable matrix population model is stage-classified. Cochran and Ellner developed a method to assess age-based parameters from such models. We present here, for these age estimates, simplified formulas that are valid whenever there is neither retrogression nor fission: individuals may only die, survive in the same stage, or survive and recruit to the next stage. Our formulas enable one to understand better why, and under which hypotheses, it is possible to compute age estimates from a stage-classified model, and point out some limitations of the method. These limitations in fact come from the basic hypothesis of stage-classified matrix models: stage is considered to be the only variable that influences survival and recruitment rates. As a consequence, age estimates using stage-classified models should be valid if the stages describe precisely enough the life cycles of the studied species, and particularly if senescence is taken into account.     

Technical note: Regression analysis in adult age estimation

Accurate estimation of human adult age has always been a problem for anthropologists, archaeologists and forensic scientists. The main factor contributing to the difficulties is the high variability of physiological age indicators. However, confounding this variability in many age estimation applications is a systematic tendency for age estimates, regardless of physiological indicator employed, to assign ages which are too high for young individuals, and too low for older individuals. This paper shows that at least part of this error is the inevitable consequence of the statistical procedures used to extract an estimate of age from age indicators, and that the magnitude of the error is inversely related to how well an age indicator is correlated with age. The use of classical calibration over inverse calibration is recommended for age estimation. Am J Phys Anthropol 104:259–265, 1997. © 1997 Wiley-Liss, Inc.     

Bayesian semiparametric copula estimation with application to psychiatric genetics

This paper proposes a semiparametric methodology for modeling multivariate and conditional distributions. We first build a multivariate distribution whose dependence structure is induced by a Gaussian copula and whose marginal distributions are estimated nonparametrically via mixtures of B‐spline densities. The conditional distribution of a given variable is obtained in closed form from this multivariate distribution. We take a Bayesian approach, using Markov chain Monte Carlo methods for inference. We study the frequentist properties of the proposed methodology via simulation and apply the method to estimation of conditional densities of summary statistics, used for computing conditional local false discovery rates, from genetic association studies of schizophrenia and cardiovascular disease risk factors.     

Longitudinal Data Analysis with Event Time as a Covariate

We consider the estimation of a nonparametric smooth function of some event time in a semiparametric mixed effects model from repeatedly measured data when the event time is subject to right censoring. The within-subject correlation is captured by both cross-sectional and time-dependent random effects, where the latter is modeled by a nonhomogeneous Ornstein–Uhlenbeck stochastic process. When the censoring probability depends on other variables in the model, which often happens in practice, the event time data are not missing completely at random. Hence, the complete case analysis by eliminating all the censored observations may yield biased estimates of the regression parameters including the smooth function of the event time, and is less efficient. To remedy, we derive the likelihood function for the observed data by modeling the event time distribution given other covariates. We propose a two-stage pseudo-likelihood approach for the estimation of model parameters by first plugging an estimator of the conditional event time distribution into the likelihood and then maximizing the resulting pseudo-likelihood function. Empirical evaluation shows that the proposed method yields negligible biases while significantly reduces the estimation variability. This research is motivated by the project of hormone profile estimation around age at the final menstrual period for the cohort of women in the Michigan Bone Health and Metabolism Study.     

Nonparametric estimation of asymptomatic duration from a randomized prospective cancer screening trial

We propose a nonparametric estimation of preclinical duration distribution in cancer based on data from a randomized early detection trial. In cancer screening studies, the preclinical duration of a disease is of great interest for better understanding the natural history of the disease, and for developing optimal screening strategies. To estimate the sojourn time distribution nonparametrically, we first estimate the distribution of the age at onset of preclinical disease nonparametrically using data from the screening arm in a randomized screening trial, and the distribution for the age at onset of clinical disease from the control arm of the randomized screening trial. Finally, by using deconvolution the two estimated distributions lead to a nonparametric estimate of the distribution for the gap time between the onset of preclinical disease and the onset of clinical disease. We illustrate the methodology using data from a randomized breast cancer screening trial.     

Reconstruction of paleodemographic characteristics from skeletal age at death distributions: perspectives from Hitotsubashi, Japan

This is a demographic exploration of the city of Edo, which reveals the changes that accompanied its urbanization and analyzes the skeletal remains of 207 individuals from a specific site in Tokyo (Hitotsubashi), using several paleodemographic approaches. A comparison of the three methods employed herein suggests that the Bayesian and maximum likelihood estimation techniques provide more plausible mortality patterns than the direct method of age estimation because the direct method of age estimation relies on published age intervals for the auricular surface and that would account for the underestimation of old people relative to the other two methods. Analyses using these new approaches indicate a short life span tendency for the people of Hitotsubashi. Although we cannot rule out methodological problems of adult-age estimation, one plausible interpretation of that life expectancy is an inadequate food supply and a poor public health situation. This study suggests that, in Tokugawa Japan, urbanization might have imposed health risks, increasing the risk of mortality. Analysis of demographic data from Hitotsubashi has refined our understanding on the impact of urbanization on the Edo period, and presents new perspectives on paleodemography in Japan.     

Paleodemographic comparison of a catastrophic and an attritional death assemblage

The aim of this contribution is to examine the effect of an indiscriminate epidemic on a population to assess whether or not a catastrophic event can be identified from examination of paleodemographic data. Using paleodemographic techniques, the death assemblage from the Royal Mint site, London, a Black Death cemetery dated 1349 AD, is compared with that from St. Helen-on-the-Walls, York, which dates from the twelfth to the sixteenth centuries AD. The Royal Mint site represents a catastrophic cemetery, while that of St. Helen-on-the-Walls is of an attritional type. Certain features of the paleodemographic profile of the plague victims suggest that the population had been affected by factors other than natural wastage. Three factors are proposed which may define an indiscriminate catastrophic event in preindustrial populations.