The Importance of Numbers: What Large Skeletal Samples Can (and Cannot) Reveal About the Health Status of Earlier Human Population Phillip L. Walker Department.

The Importance of Numbers:What Large Skeletal Samples Can (and Cannot) Reveal About the Health Status of Earlier Human Population

Phillip L. WalkerDepartment of Anthropology

University of California, Santa Barbara

The history of paleopathology: from small to large numbers

•Stage I: Case Studies–Dominated almost the end of the 20th century–“Physician to the dead” approach–century took a descriptive, case study–Emphasis on determining the spatial temporal distribution of diseases.

•Stage II: Population Studies–Mainly during the last 50 years.–Emphasis on calculating the prevalence of common pathological conditions in cemetery collections– Bioarchaeological approach with an emphasis on cultural and ecological determinants of health status

Goals of Modern Paleopathology

• Describe the chronology and spatial distribution of health-related conditions in an earlier populations

• Determine the biocultural interactions that occur as a population responds to its environment, using disease as an index of the success or failure of adaptation

• Use the prevalence and pattern of disease to shed light on the adaptation of the population

• Investigate the processes involved in prehistoric the evolution of ancient diseases

What are the limitations of apopulation-based approach in

paleopahtology?

• How large are the samples that we will need to detect population differences we might reasonably expect to see in the frequency of pathological conditions?

• How significant are sample biases introduced by age, sex, and preservation differences between samples?

• What problems are there with pooling samples from different sites to increase sample sizes?

Western Hemisphere and History of Health in Europe Project Sites

893 sites, total n= 142,952

Europe

Most archaeological skeletal collections are

small! 0

510

15

0 100 200 300 400 500

Number of Burials

Pe

rcen

t of

Site

sSize Distribution of Cemetery Collections: N=893

Most archaeological skeletal collections are small!

01

02

03

040

0 500 1000 1500 2000

Number of Burials

Size Distribution of Cemetery Collections: N=893

Per

cen

t of S

ites

Cemetery collections from archaeological sites:median =59, mode= 1

01

02

03

04

0

0 50 100 150 200 250 300 350 400 450 500

Number of Burials

Size Distribution of Cemetery Collections: N=893

Pe

rcen

t of

Site

s

Number of skeletons required to detect a statistically significant difference in the proportion of people afflicted with a pathological

condition

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Sample Sizes Required

% D

iffe

ren

ce

Median size of bioarchaeological collections

Cutting up the Pie Makes Things Worse!

Testing bioarchaeological hypotheses typically requires subdividing site samples

AgeSexSocial Status

Sex is a big part of the pie!

• % 39.8 of burials in the Western Hemisphere sample are younger than 15 years old and thus probably not subject to reliable sex determination.

<15 years old technically unsexable

40%

>15technically

sexable60%

The real world situation is worse..

• Only 41% of the Western Hemisphere sample could be sexed to the level of “probable male” or “probable” female.

• This means that about 24 burials in a sample with the median size of 59 can be reliably sexed.

• Assuming a balanced sex ratio, this would mean that within-site sex comparisons would typically involve 12 males and 12 femailes

Unsexed59%

Sexed41%

Age

Subadults: 59 x 0.38= 22

Adults: 59 x 0.62= 37

Subadults38%

Adults62%

The effects of preservation biases can be significant!

0

10

20

30

40

50

Femur Tibia Fibula Humerus Ulna Radius

We

igh

ted

% W

ith

Pe

rio

sti

tis

Historic Prehistoric

Malibu

0

10

20

30

40

50

Femur Tibia Fibula Humerus Ulna Radius

% B

on

es W

ith P

erio

stiti

s

How should frequencies of pathological lesions be measured?

The under-representation of pathological conditions in skeletal samples

• Many diseases such as tuberculosis only leave lesions on a small proportion of individuals

• Many lethal injuries leave no skeletal traces• Poor preservation of ancient skeletal

material means that often subtle signs of disease and traumatic injury will either be unobservable or uninterpretable

Bone Damage In Indian War Arrow Wounds: 30%

0

20

40

60

80

100

Head &Neck

Thorax Abdomen Upper Limb Lower Limb

% o

f In

juri

es

What can large samples tell us?

A Caveat: variation among contemporaneous populations within a

region can be significant

1213

1415

1617

-15.5 -15 -14.5 -14 -13.5 -13 -12.5δ13C (PDB)

δ15N

(A

ir)

Males

Early Period on Santa Cruz Island (SCRI-3)

Females

1012

1416

1820

-12.5-13.5-14.5-15.5-16.5-17.5

δ13C (PDB)

δ15N

(A

ir)

Males

Sex Difference in Malibu Isotopes

Females

Variations in the bathtub curve

• Wide differentials in the excess mortality occurring at the youngest and oldest ages

• Marked differences in the timing of the decline in juvenile mortality or the rise in adult mortality

Could we detect minor variations in the bathtub curve?

• The adolescent “accident hump”

• Apparent slowing down of the rate of increase of mortality among the oldest of the old

United States Death Rates (1999)

1,000

10,000

100,000

1,000,000

Age in Year

Num

ber

of D

eath

s (lo

g sc

ale) MALE FEMALE

What are our chances of detecting the “Basic” human mortality pattern?

• The “bathtub curve” this is a species-wide theme in human mortality

• Basic features– Excess mortality at

the youngest ages of the life span

– Rapid decline to a lifetime low at around 10-15 years of age

– Accelerating, roughly exponential, rise in mortality at later ages

Conclusions

• Small sample sizes and preservation biases mean that paleodemographers will ever be able to reconstruct the fine details of any set of mortality rates.

• At best, we can hope to learn something about the overall level and age pattern of death in the distant past - and perhaps something about the gross differences in material conditions that led to variation in level and age pattern.

• Paleodemographers will probably never be able to reconstruct the "bumps and squiggles" in ancient mortality patters.

• Reconstructing the general shape and level of the bathtub curve will be challenging enough.

Statistical Power

• The probability of rejecting a false statistical null hypothesis.

• Performing power analysis and sample size estimation is an important aspect of experimental design, because without these calculations, sample size may be too high or too low.

• If sample size is too low, the experiment will lack the precision to provide reliable answers to the questions it is investigating.

• If sample size is too large, time and resources will be wasted, often for minimal gain.

Determining Sample Size

• What kind of statistical test is being performed. Some statistical tests are inherently more powerful than others.

• Sample size. In general, the larger the sample size, the larger the power. • However, generally increasing sample size involves tangible costs, both in

time, money, and effort. • Consequently, it is important to make sample size "large enough," but not

wastefully large. • In paleopathological studies increasing sample size is typically impossible• The size of experimental effects. If the null hypothesis is wrong by a

substantial amount, power will be higher than if it is wrong by a small amount. • The level of error in experimental measurements. Measurement error acts like

"noise" that can bury the "signal" of real experimental effects. Consequently, anything that enhances the accuracy and consistency of measurement can increase

Regional Variation

Bioarchaeologically Interesting Differences

• Time: how does health status vary through time• Space: What regional or intraregional differences

are there• Age: What is the relationship between age at death

and the presence of pathological lesions indicative of specific diseases

• Sex: how does a person’s sex influence their health status

• Social Status: How do social stratification and gender roles influence health status.

• alpha specifies the significance level of the test; the default is alpha (.05).

• power(#) is power of the test. Default is power(.90).

Age determination is a blunt sword…

A priori sample size estimation

• Based on the acceptable statistical significance of your outcome measure.

• Specify the smallest effect you want to detect of the Type I and Type II error rates

Error Types

• Type 1 error: The chance of accepting the research hypothesis when the null hypothesis is actually true ("false positive").

• Type 2 error: The chance of accepting the null hypothesis when the research hypothesis is actually true ("false negative").

Age Related Changes in Bones Mass

Osteoperiostitis

0

5

10

15

20

25

Slight Moderate Severe

% w

ith

Tib

ial

Os

teo

pe

rio

stit

is

Inland Coastal

Osteoperiostitis

0

10

20

30

40

% B

uri

als

wit

h T

ibia

l Os

teo

per

iost

itis

Early PeriodEarly EarlyLate Late

Middle PeriodLate

Period

SBA-52

0

2

4

6

1 2 3 4 5 6 >6

Long Bones with Periosteal Lesions

Nu

mb

er

of

Bu

ria

ls

Long Bones Affected

Malibu

0

5

10

15

1 2 3 4 5 6

Long Bones with Periosteal Lesions

Nu

mb

er

of

Bu

ria

ls

Historic Prehistoric

Temporal Variation