
Basic exposure and exposure–response models 27
1−E
max
/(1+EC
50
/c
i
) is too clo se to zero. Often a very small positive number
can be added or E
max
is bounded lower than 1 to avoid this problem. E
max
can be negative if the e xposure effect is to increase y
i
from y
i0
.
Finally, it is important to note that dealing with zero exposur es (e.g.,
exposure of the control group) is difficult for log-transformation, e.g., log(y
i
) =
β log(c
i
) + ε
i
. T he ad hoc approach of replacing the zero value with a small
value may work fine. But sensitivity of the model fitting to the imputed value
should be examined. If the purpose is to extrapolate the exposure–response
relationship ...