BIOSTATISTICAL APPROACHES TO ASSESSMENT 121or not, accordingly, and followed in time to observe ultimately the numbers
of subjects who acquire the specific disease in question.
These numbers, a and c, in the exposed group and in the comparison
group, will be independent in well-conducted studies and will be binomially
distributed as, say:where p, and p0 are the disease rates in the exposed and comparison groups,
respectively. Since the sample sizes nj and n0 have been fixed in advance,
knowledge of the numbers of diseased cases, a and c, will be sufficient to
determine the numerical values of all numbers in the table.
Exposure to the test substance will have a beneficial effect with regard tothe disease in question, and subject to the conditions of the study, when p, is
less than p0; no effect when pl equals p0; and a harmful effect when pj is
higher than p0. A U-shaped hormetic dose-response exists when pj is less
than p0 at lower doses, and higher than p0 at higher doses.
We shall examine how changes in the sample sizes n, and n0 and in the
disease rates pj and p0 affect the probabilities that the study outcome will be
significantly beneficial or harmful. Regardless of the actual effect of the
test substance, these parameters have a strong influence on the probabili
ties. It is possible, through various means, to exert some control over these.
Thus, the spontaneous rate p0 in the comparison group may be changed by
choosing more or less susceptible subjects, by varying the duration of
follow-up for the study, by altering the environment in which the study
takes place, by limiting or increasing the intensity of case-finding, by modi
fying the diet, etc. The rate pj for the exposed group may be altered by these
same devices, and if the substance does indeed have an effect, then pj may
also vary with such things as route of administration, dose regimen, and
synergistic effects with existing environmental conditions.
The dose regimen is crucially important to the study of hormetic effects.
It has been customary to employ relatively high doses in toxicological
research, and then to extrapolate detrimental effects downward to lower
dose levels. Low doses have seldom been employed. Such customs guaran
tee failure to detect any genuine beneficial effects at low doses.
Construction of High, Neutral, and Low RegionsIt will be assumed the data in the two-by-two table have been analyzed via
a two-sided chi-square test using Yates’ continuity correction. Values of chi-
square greater than 2.706 are statistically significant at the 10% significance
level with a two-sided test (5% in each tail), and provide evidence of a
beneficial effect when the odds ratio ad/bc is lower than unity, a neutral
effect when the odds ratio is equal to unity, and a detrimental effect when it
is higher than unity. Values of chi-square greater than 3.841 are interpreted
similarly, but at the 5% level (with 2.5% in each tail).