130 BIOLOGICAL EFFECTS OF LOW LEVEL EXPOSURES
workers are self-selected because they were healthy enough to work, and
thus they may form a biased group in relation to the “standard” population
they are being compared to. This potential bias could, in theory, be avoided
by choosing the standard population more appropriately; but in practice
this is not possible because the rates for calculating expected numbers are
ordinarily only compiled for the population as a whole —and not special
subgroups like the working population. Thus, significant beneficial effects
observed in an occupational cohort should be viewed cautiously; they may
be real, or they may be manifestations of the healthy worker effect. The
situation is further exacerbated by the fact that the magnitude of the healthy
worker effect varies from one disease to another; it is likely to be most
pronounced in those diseases that occur and are debilitating early in life,
and less pronounced in those diseases, such as cancer, that occur later in
life.7 8 The healthy worker effect is most pronounced in younger workers
and diminishes over time as the workers age.
The second source of bias has historically been in the opposite direction,
toward false high results. These are brought about by wholesale computa
tion of vast combinations, arrays, and varieties of tests of statistical hypoth
eses with the aim of finding statistically significant results. This phenome
non has been dubbed the “multiple comparison problem” by statisticians.
The proliferation of computers and statistical software in recent years has
aggravated the situation.
Construction of High, Neutral, and Low RegionsThere is a wealth of sound theoretical and empirical evidence to the effect
that, as a general rule, the number of observed cases or deaths in a defined
group of subjects follows a Poisson probability distribution. Thus, this
distribution may then be used to construct H, N, and L regions for testing
the null hypothesis that the observed number has average value equal to the
expected number, as calculated above from standard rates.
Construction of such regions is much simpler than for two-by-two tables
since the Poisson distribution (and hence the regions) are determined com
pletely by just the expected number of cases. Bailar and Ederer provide
tables for two-sided tests of significance of the null hypothesis that the SR is
unity.9 Table 7.5 can be used to obtain 95% “normal limits” for the
observed number of cases as a function of the expected number of cases. It
can also be used to construct a 95% confidence interval for the true Poisson
mean as a function of the observed number of cases. In addition, it can be
used to construct a 95% confidence interval for the true SR as a function of
the observed and the expected number of cases.
To find normal limits for the observed number of cases as a function of
the expected number, locate the smallest entry in Table 7.5A that is as big or
bigger than the expected number. Then
lower normal limit = (10 x row number) + (column number)