Semiparametric method for estimating paleodemographic profiles from age indicator data

Paleodemography: From archaeology and skeletal age estimation to life in the past

Much of paleodemography, an interdisciplinary field with strong ties to archaeology, among other disciplines, is oriented toward clarifying the life experiences of past people and why they changed over time. We focus on how human skeletons contribute to our understanding of preindustrial demographic regimes, including when changes took place that led to the world as we know it today. Problems with existing paleodemographic practices are highlighted, as are promising directions for future work. The latter requires both better age estimates and innovative methods to handle data appropriately. Age-at-death estimates for adult skeletons are a particular problem, especially for adults over 50 years that undoubtedly are mistakenly underrepresented in published studies of archaeological skeletons. Better age estimates for the entirety of the lifespan are essential to generate realistic distributions of age at death. There are currently encouraging signs that after about a half-century of intensive, and sometimes contentious, research, paleodemography is poised to contribute much to understandings of evolutionary processes, the structure of past populations, and human-disease interaction, among other topics.

Twenty-first century bioarchaeology: Taking stock and moving forward

This article presents outcomes from a Workshop entitled "Bioarchaeology: Taking Stock and Moving Forward," which was held at Arizona State University (ASU) on March 6-8, 2020. Funded by the National Science Foundation (NSF), the School of Human Evolution and Social Change (ASU), and the Center for Bioarchaeological Research (CBR, ASU), the Workshop's overall goal was to explore reasons why research proposals submitted by bioarchaeologists, both graduate students and established scholars, fared disproportionately poorly within recent NSF Anthropology Program competitions and to offer advice for increasing success. Therefore, this Workshop comprised 43 international scholars and four advanced graduate students with a history of successful grant acquisition, primarily from the United States. Ultimately, we focused on two related aims: (1) best practices for improving research designs and training and (2) evaluating topics of contemporary significance that reverberate through history and beyond as promising trajectories for bioarchaeological research. Among the former were contextual grounding, research question/hypothesis generation, statistical procedures appropriate for small samples and mixed qualitative/quantitative data, the salience of Bayesian methods, and training program content. Topical foci included ethics, social inequality, identity (including intersectionality), climate change, migration, violence, epidemic disease, adaptability/plasticity, the osteological paradox, and the developmental origins of health and disease. Given the profound changes required globally to address decolonization in the 21st century, this concern also entered many formal and informal discussions.

Adult Skeletal Age-at-Death Estimation through Deep Random Neural Networks: A New Method and Its Computational Analysis

Age-at-death assessment is a crucial step in the identification process of skeletal human remains. Nonetheless, in adult individuals this task is particularly difficult to achieve with reasonable accuracy due to high variability in the senescence processes. To improve the accuracy of age-at-estimation, in this work we propose a new method based on a multifactorial macroscopic analysis and deep random neural network models. A sample of 500 identified skeletons was used to establish a reference dataset (age-at-death: 19–101 years old, 250 males and 250 females). A total of 64 skeletal traits are covered in the proposed macroscopic technique. Age-at-death estimation is tackled from a function approximation perspective and a regression approach is used to infer both point and prediction interval estimates. Based on cross-validation and computational experiments, our results demonstrate that age estimation from skeletal remains can be accurately (~6 years mean absolute error) inferred across the entire adult age span and informative estimates and prediction intervals can be obtained for the elderly population. A novel software tool, DRNNAGE, was made available to the community.

Conditional independence assumption and appropriate number of stages in dental developmental age estimation

When estimating the age of an individual it is critical that 1) age ranges are as narrow as possible while still capturing the true age of the individual with an acceptable frequency, and 2) this frequency is known. When multiple traits are used to produce a single age estimate, the simplest practice is to assume that the traits are conditionally independent from one another given age. Unfortunately, if the traits are correlated once the effect of age is accounted for, the resulting age intervals will be too narrow. The frequency at which the age interval captures the true age of the individual will be decreased below the expected value to some unknown degree. It is therefore critical that age estimation methods that include multiple traits incorporate the possible correlations between them. Moorrees et al. (1963) [1] scores of the permanent mandibular dentition from 2607 individuals between 2 and 23 years were used to produce and cross-validate a cumulative probit model for age estimation with an optimal number of stages for each tooth. Two correction methods for covariance of development between teeth were tested: the variance-covariance matrix for a multivariate normal, and the Boldsen et al. (2002) [2] ad-hoc method. Both correction methods successfully decreased age interval error rates from 21% to 23% in the uncorrected model to the expected value of 5%. These results demonstrate both the efficacy of these correction methods and the need to move away from assuming conditional independence in multi-trait age estimation.

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.

An informative prior probability distribution of the gompertz parameters for bayesian approaches in paleodemography

OBJECTIVES

In paleodemography, the Bayesian approach has been suggested to provide an effective means by which mortality profiles of past populations can be adequately estimated, and thus avoid problems of "age-mimicry" inherent in conventional approaches. In this study, we propose an application of the Gompertz model using an "informative" prior probability distribution by revising a recent example of the Bayesian approach based on an "uninformative" distribution.

METHODS

Life-table data of 134 human populations including those of contemporary hunter-gatherers were used to determine the Gompertz parameters of each population. In each population, we used both raw life-table data and the Gompertz parameters to calculate some demographic values such as the mean life-span, to confirm representativeness of the model. Then, the correlation between the two Gompertz parameters (the Strehler-Mildvan correlation) was re-established. We incorporated the correlation into the Bayesian approach as an "informative" prior probability distribution, and tested its effectiveness using simulated data.

RESULTS

Our analyses showed that the mean life-span (≥ age 15) and the proportion of living persons aging over 45 were well-reproduced by the Gompertz model. The simulation showed that using the correlation as an informative prior provides a narrower estimation range in the Bayesian approach than does the uninformative prior.

CONCLUSIONS

The Gompertz model can be assumed to accurately estimate the mean life-span and/or the proportion of old people in a population. We suggest that the Strehler-Mildvan correlation can be used as a useful constraint in demographic reconstructions of past human populations.

Multivariate cumulative probit for age estimation using ordinal categorical data

BACKGROUND

Multivariate ordinal categorical data have figured prominently in the age estimation literature. Unfortunately, the osteological and dental age estimation literature is often disconnected from the statistical literature that provides the underpinnings for rationale analyses.

AIM

The aim of the study is to provide an analytical basis for age estimation using multiple ordinal categorical traits.

SUBJECTS AND METHODS

Data on ectocranial suture closure from 1152 individuals are analysed in a multivariate cumulative probit model fit using a Markov Chain Monte Carlo (MCMC) method.

RESULTS

Twenty-six parameters in a five variable analysis are estimated, including the 10 unique elements of the five × five correlation matrix. The correlation matrix differs substantially from the identity matrix one would assume under conditional independence among the sutures.

CONCLUSION

While the assumption of conditional independence between traits greatly simplifies the use of parametric models in age estimation, this assumption is not a necessary step. Further, in the analysis discussed here there are considerable residual correlations between ectocranial suture closure scores even after 'regressing out' the effect of age.

Estimating the age structure of a buried adult population: a new statistical approach applied to archaeological digs in France

Paleodemographers have developed several methods for estimating the age structure of historical populations in absence of civil registration data. Starting from biological indicators alone, they use a reference population of known sex and age to assess the conditional distribution of the biological indicator given age. However, the small amount of data available and the unstable nature of the related statistical problem mean that most methods are disappointing. Using the most reliable reference data possible, we propose a simple statistical method, integrating the maximum amount of information included in the actual data, which quite significantly improves age estimates for a buried population. Here the method is applied to a French cemetery used from Late Antiquity to the end of the Early Middle Ages.

Estimation and evidence in forensic anthropology: age-at-death

A great deal has previously been written about the use of skeletal morphological changes in estimating ages-at-death. This article looks in particular at the pubic symphysis, as it was historically one of the first regions to be described in the literature on age estimation. Despite the lengthy history, the value of the pubic symphysis in estimating ages and in providing evidence for putative identifications remains unclear. This lack of clarity primarily stems from the fact that rather ad hoc statistical methods have been applied in previous studies. This article presents a statistical analysis of a large data set (n = 1766) of pubic symphyseal scores from multiple contexts, including anatomical collections, war dead, and victims of genocide. The emphasis is in finding statistical methods that will have the correct "coverage.""Coverage" means that if a method has a stated coverage of 50%, then approximately 50% of the individuals in a particular pubic symphyseal stage should have ages that are between the stated age limits, and that approximately 25% should be below the bottom age limit and 25% above the top age limit. In a number of applications it is shown that if an appropriate prior age-at-death distribution is used, then "transition analysis" will provide accurate "coverages," while percentile methods, range methods, and means (+/-standard deviations) will not. Even in cases where there are significant differences in the mean ages-to-transition between populations, the effects on the stated age limits for particular "coverages" are minimal. As a consequence, more emphasis needs to be placed on collecting data on age changes in large samples, rather than focusing on the possibility of inter-population variation in rates of aging.

Selectivity of black death mortality with respect to preexisting health

Was the mortality associated with the deadliest known epidemic in human history, the Black Death of 1347-1351, selective with respect to preexisting health conditions ("frailty")? Many researchers have assumed that the Black Death was so virulent, and the European population so immunologically naïve, that the epidemic killed indiscriminately, irrespective of age, sex, or frailty. If this were true, Black Death cemeteries would provide unbiased cross-sections of demographic and epidemiological conditions in 14th-century Europe. Using skeletal remains from medieval England and Denmark, new methods of paleodemographic age estimation, and a recent multistate model of selective mortality, we test the assumption that the mid-14th-century Black Death killed indiscriminately. Skeletons from the East Smithfield Black Death cemetery in London are compared with normal, nonepidemic cemetery samples from two medieval Danish towns (Viborg and Odense). The results suggest that the Black Death did not kill indiscriminately-that it was, in fact, selective with respect to frailty, although probably not as strongly selective as normal mortality.

Double lamellae in trabecular osteons: towards a new method for age estimation by bone microscopy

The study of anatomical ageing has a dual purpose in biological anthropology. On the one hand, it can provide insights into age associated changes in the body and thus widen the understanding of human senescence; and on the other hand it can provide means of estimation of age at death. This paper explores normal ageing in the pattern of remodelling of trabecular bone in humans. The material consists of necropsies of bone from the ilium of 25 males. A 1 cm2 prism extending from the outer to the inner surface of the iliac bone was removed from men who had died with no clinical signs of diseases, which would usually affect bone structure and metabolism. The samples were cut, and studied by light microscopy at a magnification of 100 x. New trabecular bone is formed in disk-shaped osteons with a clear double lamellar structure. In each sample, the number of double lamellae in a mean of 21 complete osteons was counted. The mean number of lamellae was taken as the measurement of interest. The log of the mean counts was found to regress linearly and with no evidence for heteroscedacity on age. The correlation between the two was high and negative (r=-0.83, p<0.001). The material is too limited to provide a useful basis for age estimation as such, but the study demonstrates the potential for palaeodemographic application of the method.

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.

Demographic window to aging in the wild: constructing life tables and estimating survival functions from marked individuals of unknown age

Summary We address the problem of establishing a survival schedule for wild populations. A demographic key identity is established, leading to a method whereby age-specific survival and mortality can be deduced from a marked cohort life table established for individuals that are randomly sampled at unknown age and marked, with subsequent recording of time-to-death. This identity permits the construction of life tables from data where the birth date of subjects is unknown. An analogous key identity is established for the continuous case in which the survival schedule of the wild population is related to the density of the survival distribution in the marked cohort. These identities are explored for both life tables and continuous lifetime data. For the continuous case, they are implemented with statistical methods using non-parametric density estimation methods to obtain flexible estimates for the unknown survival distribution of the wild population. The analytical model provided here serves as a starting point to develop more complex models for residual demography, i.e. models for estimating survival of wild populations in which age-at-entry is unknown and using remaining information in randomly encountered individuals. This is a first step towards a broad new concept of 'expressed demographic information content of marked or captured individuals'.

Deconstructing death in paleodemography

In 1992 in this Journal (Konigsberg and Frankenberg [1992] Am. J. Phys. Anthropol. 89:235-256), we wrote about the use of maximum likelihood methods for the "estimation of age structure in anthropological demography." More specifically, we presented a particular method (the "iterated age-length key") from the fisheries literature and suggested that the method could be used in human and primate demography and paleodemography as well. In our paper (section titled "Some Future Directions"), we spelled out two broad areas that we expected to see develop over the ensuing years. First, we felt that the use of explicit likelihood methods would open up interest in basic estimation issues, such as the calculation of standard errors for demographic estimates and the formulation of tests for whether samples differed in their demographic structure. Second, we felt that the time was ripe for hazards analyses that would incorporate the uncertainty in estimation that follows from using age "indicators" rather than known ages. While some of these developments have occurred during the last decade, few have been reported in the American Journal of Physical Anthropology. In this paper we resolve some issues from our 1992 paper, and attempt to redress this deficit in the literature by reviewing some recent developments in paleodemography over the past decade.