3. general considerations for the analysis of case-control ... - IARC

MEASURES OF DISEASE 55
exposed versus a non-exposed group, for example by comparing confirmed cigarette
smokers with non-smokers, or lifelong urban with lifelong rural residents. In order to
introduce the concept of risk factor/disease association, we suppose here that the
population has been divided into two such subgroups, one exposed to the risk factor
in question and the other not exposed.
As shown in the earlier examples, incidence rates may vary widely within the population
according to such factors as age, sex and calendar year of observation. Thus
whatever measure is used to compare incidence rates in the exposed versus nonexposed
subgroups, this too is likely to vary by age, sex and time. What is clearly
desired in this situation is a measure of association which is as stable as possible over
the various subdivisions of the population; the more nearly constant it is, the greater
is the justification for expressing the effect of exposure in a single summary number;
the more it varies, the greater is the necessity to describe how the effect of exposure
is modified by demographic or other relevant factors on which information is available.
Suppose that the population has been divided into I strata on the basis of age, sex,
calendar period of observation, or combinations of these and other features. Denote
by ,Ili the incidence rate of disease in the ith stratum for the exposed subgroup and by
,Ioi the rate for the non-exposed subgroup in that stratum. The first measure of association
we consider is the excess risk of disease, defined as the difference between the
stratum-specific incidences
Since the measure is defined in terms of incidence rates, rather than risks, it would
perhaps be more accurate to refer to it as the excess rate of disease. We follow convention
by allowing the distinction between risks and rates to be blurred somewhat
in discussing measures of association, except when it is critical to the point in question.
The intuitive idea underlying this approach is that cases contributing to the "natural"
or background disease incidence rate in the ith stratum are due to the presence of
general factors which operate on exposed and non-exposed individuals alike. Cases
caused by exposure to the particular agent under investigation are represented in
the excess risk bi (Rothman, 1976). If these two causes of disease, the general and
the specific, were in some sense operating independently of each other, one might
expect the number of excess cases of disease occurring per person-year of observation
to reflect only the level of exposure and to be unrelated to the underlying natural risk.
Thus the excess risk would be relatively constant from stratum to stratum, apart from
random statistical fluctuations.
The idea of a constant excess risk due to the particular exposure may be formally
expressed by hypothesizing an additive model for the two dimensional sets of rates.
With b representing the additive effect of exposure, the model states
Unfortunately the concept of independence leading to this model is rather simplistic
and breaks down when one considers plausible mechanisms for the disease process
(Koopman, 1977). Suppose, for example, that a disease was caused in infancy or
early childhood but took many years to develop. If the age distribution of the cases