CHAPTER 7
Biostatistical Approaches for Modeling
U-Shaped Dose-Response Curves and Study
Design Considerations in Assessing the
Biological Effects of Low Doses
Tom Downs, School of Public Health, University of Texas,
Health Science Center, Houston, Texas
The first part of this two-part chapter deals with the probabilities of
determining qualitatively what kinds of health effects may result from
exposures to substances, and the second part with characterizing quantita
tive relationships between such health effects and exposures. The health
effects may be beneficial in some situations, and detrimental in others.
QUALITATIVE RISK-BENEFIT EVALUATION
IntroductionResults of a study are customarily called “positive” if they show a positive
association between substance exposure and disease, and “negative” other
wise.1 Negative results thus include those with beneficial effects as well as
those with no effect. But there have been numerous reports of substances
showing beneficial effects at low doses and detrimental effects at high
doses,2 3 so the customary terminology could be confusing. To avoid ambi
guities, results are referred to herein as harmful, neutral, or beneficial,
according to whether there is a statistically significant harmful or high
effect, no significant difference, or a significant low or beneficial effect.
The classification of a study result as one of these three may be incorrect
because of sampling or other sources of variability. Of paramount impor
tance in the design and planning of studies is the choice of study conditions
that maximize, so far as is feasible, the probability of correctly classifying
exposure effects as harmful, neutral, or beneficial. These probabilities
depend on parameters such as sample size, dose regimen, duration of the
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