Demography - Research Methods in Human Skeletal Biology - page 284

1994; Bocquet-Appel, 1994; Bocquet-Appel and Bacro, 1997, 2008; Aykroyd et al., 1999; Wood
et al., 2002; Hoppa and Vaupel, 2002b; Boldsen et al., 2002; Frankenberg and Konigsberg,
2006; DeWitte and Wood, 2008; Redfern and DeWitte, 2011 ) is transforming the field. In its
current configuration, demographic analysis of skeletal samples cannot be separated from
the processes of age estimation or sex estimation. In other words, individual age or sex esti-
mates cannot be produced until after the demographic analyses have been performed . We
demonstrate how and why one should conduct demographic analyses prior to generating
individual age and sex estimates, starting with sex estimation and estimation of the sex ratio
since this is a simpler problem than age estimation. We then turn our attention to age estima-
tion, the estimation of the age-at-death distribution, and the role of hazard models, including
their relationship to traditional life table analysis. Finally, we briefly discuss the uses to which
the results of such analyses can be put. These goals are relatively modest, but as the one thing
demographers tend to do is enumerate things, we would do well to list the “order of oper-
ations” for this chapter. They are as follows:
1. Estimating the sex ratio : in this section we examine how to estimate the sex ratio (or really,
the proportion of one of the sexes) such that it makes the observed “sexing” data as likely
as possible to have been observed.
2. Estimating the sex of individuals : in this section we examine how to estimate individual
sexes (or really, the probability that individuals are one particular sex) following on
having already estimated the sex ratio from Step 1.
3. Presentation of hazard models as a summary of mortality : in this section we present
hazard models as a direct alternative to life tables for summarizing mortality data.
4. Simulating long bone growth: in this section we show how to simulate long bone growth
as a preamble to analyzing simulated data.
5. Estimating the age-at-death structure : in this section we use simulated data on long bone
lengths (see Step 4) in order to demonstrate how one can fit a hazard model using “age
indicator” data rather than using age estimates.
6. Estimating ages-at-death : in this section we show how to estimate “point ages” and the
variance of the estimates from Bayes' theorem using the information on long bone growth
and the hazard model fit in Step 5. By “point ages” we mean specific decimal ages such as
7.34 years old. Clearly, such estimates will require a statement about the possible error
around the stated age, which is why we calculate the variance of the estimate.
Two explanations are in order before we dive into demographic analysis. First, demog-
raphy is inherently technical, and requires a certain level of mathematical/statistical anal-
ysis and computer savvy. There is no avoiding algebra or calculus in this chapter. For those
unfamiliar or uncomfortable with calculus, the integrals in Equations 11.17, 11.19, 11.21,
and 11.22 can be thought of as summations across large spans with very small intervals.
While Hoppa and Vaupel (2002b) have pointed out that “Pencil and paper or a computer
is required,” we note that neither pencil and paper nor computer spreadsheets or canned
statistical packages are sufficient for the analyses presented here. Instead, we use an open
source graphics, mathematical, and statistical package known as “R” (R Development Core
Team, 2011 ), which “has become a de-facto standard among statisticians for the develop-
ment of statistical software” ( http://openwetware.org/wiki/R_Statistics ). While the
learning curve is a bit steep, there are a number of introductions and tutorials freely