Encyclopedia of Environmental Science and Engineering, Volume I and II

EPIDEMIOLOGY 381

provide important information on carcinogenic hazards

in the area to which it refers. The different proportions by

site throughout the world, where data are available, affect

climatic, geographical, and lifestyle variations but are not

always simple to analyze. Furthermore, some sources of data

may consist of numerator information only (e.g., deaths or

diagnosed cases of disease) without the corresponding pop-

ulation fi gures by sex and age, which enable the construc-

tion of rates of mortality and morbidity. Rather than have to

ignore such partial information, it is possible to present it in

the form of proportionate mortality or morbidity rates. In its

simplest form this method expresses the omitting age, since

it may not be available; then it may facilitate comparison

with another source of data that may have affi nities, perhaps

in the likely age structure or in climate, to one under study.

PROPORTIONATE MORTALITY RATE

A situation somewhat similar to what has just been described

can occur when a factory may be able to provide details (of

cause, sex, and age) of the deaths of former employees over a

period of time, but without adequate additional information to

permit further analysis (see below). The pattern of their mor-

tality, by cause and sex, can then be compared with the general

patterns of the area where the factory is situated. Usually the

deaths will be categorized into broad groups (e.g., cardiovas-

cular, neoplasms, respiratory) (Lange et al., 2003b), but if

there is a reason to examine certain sites of cancer individu-

ally, they can be included. Each observed death is allotted an

age group in the general population; the proportions of deaths

(as fractions of 1) occurring in each of the chosen cause cat-

egories are entered and summed after all the observed deaths

have been included. The accumulated fractions in each group

will then constitute the expected number of deaths to compare

with the number observed. Accumulated by age into numbers

of expected and observed deaths by sex and cause, the com-

parison can be evaluated statistically for its signifi cance (see

below). If the observed deaths are spread over a number of

years, the expected deaths should be strictly obtained from

the corresponding calendar years, though they can usually be

taken in quinquennial groups without serious loss of accu-

racy. It will be evident that an assumption implicit in the

method is that the factory population has been suffi ciently

similar to the general population to justify the comparison.

Thus, proportionate mortality rates (PMRs) are commonly

used for occupational cohorts.

ANALYTICAL EPIDEMIOLOGY

It is conventional to divide epidemiology into two distinct

branches: descriptive and analytical. Up to this point we have

been concerned mainly with the description of the health

status of a population by means of rates of mortality and

morbidity, by sex, age, and cause; for geographical and other

subgroups; and in calendar time. Some of the methods of

comparison we have discussed, necessitating standardization

of the calculation of expected fi gures, have touched on the

analytic division, though the defi nitions are not always clear-

cut. Other methods that will be discussed are experimental in

their design, such as clinical trials where the treatments of a

disease by two different regimes forms the basis of a compar-

ison of their relative effi ciency, the numbers of patients being

decided by consideration of the statistical power required or

attainable.

SCATTERGRAMS

A method that has been frequently used in searching for fac-

tors related, possibly in an etiological way, to the incidence of

disease is to display in graphical form a correlation diagram—

a scatter diagram or “scattergram” where the incidence (or

mortality rate) of the disease is measured on one scale and

the factor of interest on the other. Figure 7 gives an example

of the method, whereby each point represents a country

whose (standardized) rate of colon cancer is set against the

per-capita consumption of fat in that country. It is clear that

there is a relationship between these two measures, such that

as one increases so does the other. This apparent movement

together may suggest a possible causative relationship, such

that the higher the average consumption of fats, the greater

the risk of colon cancer. But note fi rst that it is the aver-

age per-capita factor, which is obtained from the total fat

consumed in a country divided by population. Clearly, indi-

viduals in the population will vary in their mean levels of

consumption; some average more while others less than the

average. If there is a causative relationship, we would expect

80 100 120 140 160 180

5

10

15

20

25

30

TOTAL FAT (g/day)1977–79

AGE-ADJUSTED DEATH RATE/100,000 (1978–79)

GREECE

HONGKONG FINLAND

SINGAPORE

JAPAN

ISRAEL

AUSTRALIA

GERMANY

IRELAND

DENMARK

AUSTRIA BELGIUM

SWEDENUS WHITE

E+W FRANCE

NEW ZEALAND SWITZERLAND

ITALYNORWAYCANADA NETHERLAND

r=0.53

t=2.80

p=0.01

FIGURE 7 Cancer of the colon and fat consumption (scattergram).

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