Revival: Biological Effects of Low Level Exposures to Chemical and Radiation (1992)

BIOSTATISTICAL APPROACHES TO ASSESSMENT 125

equal disease rates it is now equal exposure rates. All this is simply accom­

plished in practice by interchanging the exposure-disease labeling for the

rows and columns in the data table while leaving everything else intact; then

all the original notation and results are applicable.

Data Layout: Standardized Ratios

In many nonexperimental epidemiological studies, the study subjects
form a well-defined cohort, such as all the employees, past and present, of a
petrochemical plant. In such studies the outcome measure often takes the
form of a standardized ratio (SR). The SR is defined as the ratio of the
observed number of disease events occurring among the members of the
study population, to some theoretically derived number. This theoretical
number is the number of cases that would ordinarily be expected to occur if
the study population suffered disease rates similar to a “standard” popula­
tion whose rates were used to obtain the expected number.
Briefly, the expected numbers are calculated by applying the standard
population rates — usually on a race-, age-, sex-, time-, place-, and disease-
specific basis —to the study population over the time frame of the study.
The resulting SR ratio of observed-to-expected cases is called a standardized
mortality ratio (SMR) if the outcome is death from a specific cause, and a
standardized incidence ratio (SIR) if the study outcome is contraction of a
specific disease.
Most studies of the effects of occupational exposures on worker health
employ some form of standardized ratio to measure the outcome. The study
results are usually reported separately by race, sex, and disease. Results for
a wide variety of diseases and subgroups of the study population are ordi­
narily reported.5 Computation of the expected numbers becomes cumber­
some when the data sets are large. A vast array of statistical rate tables is
also required. Computer programs with built-in rate tables have been writ­
ten and employed to carry out these mechanical tasks.6 The program devel­
oped by Monson ordinarily computes 40-50 standardized ratios for each
subgroup of workers. These subgroups may be cross-classified (e.g., by
race, sex, exposure histories, length of employment), so the number of SRs
generated can become very large.
When the SR is lower than unity, the observed number of events is less
than the expected number, and a beneficial effect has been observed. When
the SR is unity, the effect is neutral, and when the SR is higher than unity,
the observed number is greater than the expected, and a detrimental effect
occurs. In terms of statistical significance (e.g., false high results, etc.), the
same terminology is used here as above, with H and L representing statisti­
cally significant SRs, and N a neutral SR that is not significantly different
from unity.
There are two serious sources of bias commonly affecting SRs. First is the
bias toward significant L effects due to the “healthy worker effect” —