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.     

Monitoring futility and efficacy in phase II trials with Bayesian posterior distributions—A calibration approach

A multistage single arm phase II trial with binary endpoint is considered. Bayesian posterior probabilities are used to monitor futility in interim analyses and efficacy in the final analysis. For a beta‐binomial model, decision rules based on Bayesian posterior probabilities are converted to “traditional” decision rules in terms of number of responders among patients observed so far. Analytical derivations are given for the probability of stopping for futility and for the probability to declare efficacy. A workflow is presented on how to select the parameters specifying the Bayesian design, and the operating characteristics of the design are investigated. It is outlined how the presented approach can be transferred to statistical models other than the beta‐binomial model.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Autoregressive models for capture-recapture data: a Bayesian approach

In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet.     

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. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

Semiparametric method for estimating paleodemographic profiles from age indicator data.

This paper addresses the problem of estimating an age-at-death distribution or paleodemographic profile from osteological data. It is demonstrated that the classical two-stage procedure whereby one first constructs estimates of age-at-death of individual skeletons and then uses these age estimates to obtain a paleodemographic profile is not a correct approach. This is a consequence of Bayes' theorem. Instead, we demonstrate a valid approach that proceeds from the opposite starting point: given skeletal age-at-death, one first estimates the probability of assigning the skeleton into a specific osteological age-indicator stage. We show that this leads to a statistically valid method for obtaining a paleodemographic profile, and moreover, that valid individual age estimation itself requires a demographic profile and therefore is done subsequent to its construction. Individual age estimation thus becomes the last rather than the first step in the estimation procedure. A central concept of our statistical approach is that of a weight function. A weight function is associated with each osteological age-indicator stage or category, and provides the probability that a specific age indicator stage is observed, given age-at-death of the individual. We recommend that weight functions be estimated nonparametrically from a reference data set. In their entirety, the weight functions characterize the relevant stochastic properties of a chosen age indicator. For actual estimation of the paleodemographic profile, a parametric age distribution in the target sample is assumed. The maximum likelihood method is used to identify the unknown parameters of this distribution. As some components are estimated nonparametrically, one then has a semiparametric model. We show how to obtain valid estimates of individual age-at-death, confidence regions, and goodness-of-fit tests. The methods are illustrated with both real and simulated data.     

Bayesian inference for prevalence in longitudinal two-phase studies

We consider Bayesian inference and model selection for prevalence estimation using a longitudinal two-phase design in which subjects initially receive a low-cost screening test followed by an expensive diagnostic test conducted on several occasions. The change in the subject's diagnostic probability over time is described using four mixed-effects probit models in which the subject-specific effects are captured by latent variables. The computations are performed using Markov chain Monte Carlo methods. These models are then compared using the deviance information criterion. The methodology is illustrated with an analysis of alcohol and drug use in adolescents using data from the Great Smoky Mountains Study.     

A preliminary method for estimating the age of brown kiwi (Apteryx mantelli) embryos

Morphological features of a collection of unknown-age wild kiwi (Apteryx mantelli) embryos from early development to point of hatch are described. Using these features, we assign developmental stages to each embryo and compare the progress of development to similar-staged ostrich (Struthio camelus) and chicken (Gallus gallus) embryos. Two ageing schemes for the kiwi embryos are developed by comparing measurements of their hindlimb segments, bills and crown–rump lengths with those of ostrich and chicken embryos at various stages of development. One of the 20 kiwi embryos was of known age. Both the ostrich model and the chicken model gave identical predictions for the marker and four other embryos. Developmental timing of some features differed between all three species, most markedly in the bill, with growth in the kiwi bill being relatively faster to achieve its larger relative and absolute size at hatch.     

A Bayesian approach for estimating values for prevalence and diagnostic test characteristics of porcine cysticercosis

Several diagnostic techniques are used to estimate the prevalence of the zoonotic tapeworm Taenia solium in pigs, but none of these tests are perfect, making interpretation of results difficult. A Bayesian approach was used to estimate values for the prevalence and diagnostic test characteristic of porcine cysticercosis by combining results of four imperfect tests. Village pigs (N = 868) slaughtered in Lusaka (Zambia), were bled, and tongue and routine meat inspected; and serum antibody and parasite antigen concentrations were determined by ELISA. A model, based on a multinomial distribution and including all possible interactions between the individual tests required 31 parameters to be estimated, but actually allowed only 15 parameters (i.e. had 15 degrees of freedom) to be estimated. Therefore, prior expert opinion on specificity and (in)-dependence of the tests was entered in the model, resulting in a reduction of the number of parameters to be estimated. The estimated prevalence of porcine cysticercosis was 0.642 (95% confidence interval 0.54-0.91). The performances of the tests were (sensitivity (se)-specificity (sp)): tongue inspection (se 0.210-sp 1.000), meat inspection (se 0.221-sp 1.000), Ab-ELISA (se 0.358-sp 0.917), Ag-ELISA (se 0.867-sp 0.947). To validate the estimates obtained from the model we performed a second study: 65 randomly purchased Zambian village pigs were bled for serum antibody and antigen determination, their tongue and meat inspected; and in addition, the carcasses were dissected for total cysticercus counts (gold standard). Cysticerci were found in 31 pigs (prevalence 0.477, 95% confidence interval 0.35-0.60), overlapping with the estimated prevalence in the first study. Sensitivity and specificity values obtained for the aforementioned tests in this study were in agreement with those estimated. A Bayesian analysis framework offers the possibility to combine prior opinion with experimental data to more accurately estimate the real prevalence of porcine cysticercosis in the absence of a gold standard.     

Investigation of growth phases for bottlenose dolphins using a Bayesian modeling approach

The Gompertz function is the most commonly used growth function for cetacean studies. However, this function cannot represent multiple phases of growth. In this study, we present a Bayesian framework fitting parameters of a triple-logistic growth function to describe multiple phases of growth for bottlenose dolphins ( Tursiops truncatus ), simultaneously fitting and comparing all growth parameters between South Carolina (SC), Mississippi Sound (MSS), and Indian River Lagoon (IRL) cohorts. The fitted functions indicated a preliminary early, rapid growth phase, followed by a second phase of slower growth, and then a moderate growth spurt later in life. Growth parameters between geographic cohorts did not show obvious differences, although asymptotic length for SC dolphins was lower than MSS and IRL dolphins and significantly lower between females from SC and the IRL. Growth rate velocities between the sexes showed females exceed males initially (<1 yr), followed by males gaining an advantage around the ages of 3–4 yr until the age of around 15 yr when growth rates for both sexes approached zero (asymptotic length). This study demonstrates age-related changes in growth rates between bottlenose dolphin sexes and evidence of at least some differences ( i.e. , asymptotic length) across geographic cohorts.     

Brief communication: Comparison of methods for estimating chronological age at linear enamel formation on anterior dentition

Linear enamel hypoplasia (LEH) is an enamel defect that records the effects of physiological stress on tooth formation. Estimating the age at which LEH defects form is integral to the reconstruction of population health in bioarcheological studies. Two principal methods for aging LEH defects have been introduced in the literature. The conventional approach employs regression equations based on a linear model of tooth growth. The newer, Reid and Dean [Am J Phys Anthropol 113 (2000) 135-139] approach, is based upon a histologically derived curvilinear model of enamel development and therefore likely provides more accurate age estimates. However, the extent to which the Reid and Dean method produces estimated ages at defect formation differing from those of the regression equations has not, until now, been determined. This study quantifies the differences between these two methods. Evaluating the degree to which these methods differ is essential for interpreting the accuracy of LEH age estimates given in previous bioarcheological studies. Age estimates of LEH defects on 338 anterior teeth from the Hamann-Todd osteological sample were calculated using both methods. The resulting estimated ages were compared through a randomized block ANOVA. However, the mean differences between the estimated ages yielded by both methods range from 4 months or less depending on the tooth type with an overall average of 2.63 months. The discussion focuses on the degree to which this difference affects answers to bioarcheological questions.     

Variation in cortical bone histology within the human femur and its impact on estimating age at death

Histological methods for the estimation of age at death using cortical bone are based on the evaluation of microstructural changes over time. Since histological analysis is a destructive method, most techniques attempt to limit the amount of cortical bone needed for analysis. Sample location, however, can have a significant effect on the accuracy of these methods. Furthermore, research demonstrates that both intersection and intrasection variation is present at the midshaft of the femur, which is the primary location for estimating age at death in humans. This research determines the extent of regional variation within the adult human femur and its effect on age estimation. Secondary osteon lamellae and Haversian canal ratio and cortical thickness were quantified. Thompson's All Males Left Femur regression equation was used to estimate age. Results show that significant regional variation occurs in the estimated ages derived from the posterior aspect of the femoral shaft and significant intrasection variation occurs in age estimates from the mid and mid-distal cross-sections. Thus, the inter and intrasection variation that occurs in bone remodeling within the femoral cortex has the potential to produce significant differences amongst age estimates taken from various femoral diaphyseal locations compared to the age estimated from the standard location used in Thompson's core method (1978). The results indicate that the use of this histological method is dependant on the ability to correctly identify the four anatomical locations, but the extracted core used for age estimation is not necessarily confined to the anterior midshaft.     

Technical note: Error in Olivier and Pineau's regression formulae for calculation of stature and lunar age from radial diaphyseal length in forensic fetal remains

Stewart ([1979] Essentials of Forensic Anthropology, pp. 128–131) cites five regression formulae presented by Olivier and Pineau ([1960] Ann. Méd. Lég. 40:141–144) for estimation of fetal stature from diaphyseal length. Of these formulae, one appears problematic: the formula for calculation of stature from the radius yields values which suggest the fetus has a much greater crown-heel (CH) length than do the remaining formulae for the diaphyses of other long bones. Moreover, when this stature estimate, so derived, is then inserted into these authors' earlier general formula for estimation of lunar age (Olivier and Pineau [1958] Arch. Anat. 6:21–28) the error is compounded. A fetus is now indicated to be nearly a trimester older than when the CH lengths obtained by the other long bone formulae are used. Accordingly, we believe this particular formula, unlike the others, is incorrect and should not be used to estimate lunar age from fetal remains. © 1996 Wiley-Liss, Inc.     

Testing for size and allometric differences in fossil hominin body mass estimation

Body size reconstructions of fossil hominins allow us to infer many things about their evolution and lifestyle, including diet, metabolic requirements, locomotion, and brain/body size relationships. The importance of these implications compels anthropologists to attempt body mass estimation from fragmentary fossil hominin specimens. Most calculations require a known “calibration” sample usually composed of modern humans or other extant apes. Caution must be taken in these analyses, as estimates are sensitive to overall size and allometric differences between the fossil hominin and the reference sample. Am J Phys Anthropol 151:215–229, 2013. © 2013 Wiley Periodicals, Inc.     

Hierarchical Bayesian integrated model for estimating migratory bird harvest in Canada

The Canadian Wildlife Service (CWS) requires reliable estimates of the harvest of migratory game birds, including waterfowl, to effectively manage populations of these hunted species. The National Harvest Survey is an annual survey of hunters who purchase Canada's mandatory migratory game bird hunting permit, integrating information from a survey of hunting activity with information from a separate survey of species composition in the harvest. We used these survey data to estimate the number of birds harvested for each species and hunting activity metrics (e.g., number of active hunters, days spent hunting). The analytical methods used to generate these estimates have not changed since the survey was first designed in the early 1970s. We describe a new hierarchical Bayesian integrated model, which replaces the series of ratio estimators that comprised the old model. We are using this new model to generate estimates for migratory bird harvests as of the 2019–2020 hunting season, and to generate updated estimates for all earlier years. The hierarchical Bayesian model uses over-dispersed Poisson distributions to model mean hunter activity and harvest (zero-inflated Poisson and zero-truncated Poisson, respectively). It also includes multinomial distributions to model some key components (e.g., variation in harvest across periods of the hunting season, the species composition of the harvest within each of those periods, the age and sex composition in the harvests of a given species). We estimated the parameters of the Poisson and the multinomial distributions for each year as random effects using first-difference time-series. This time-series component allows the model to share information across years and reduces the sensitivity of the estimates to annual sampling noise. The new model estimates are generally very similar to those from the old model, particularly for the species that occur most commonly in the harvest, so the results do not suggest any major changes to harvest management decisions and regulations. Estimates for all species from the new model are more precise and less susceptible to annual sampling error, particularly for species that occur less commonly in the harvest (e.g., sea ducks, other species of conservation concern). This new model, with its hierarchical Bayesian framework, will also facilitate future improvements and elaborations, allowing the incorporation of prior information from the rich literature and knowledge in game bird management and biology.