Table 2 Frequently used dose-response models

Linear

E[d _i |x _i ]=θ _1i x _i

1

Quadratic

\(\displaystyle \mathrm {E} \left [ \boldsymbol {d}_{i} | \boldsymbol {x}_{i} \right ] = \theta _{1i} \boldsymbol {x}_{i} + \theta _{2i} \boldsymbol {x}_{i}^{2}\)

2

E _max

\( \displaystyle \mathrm {E} \left [ \boldsymbol {d}_{i} | \boldsymbol {x}_{i} \right ] = \theta _{1i} \boldsymbol {x}_{i}^{\theta _{3i}}/ \left (\theta _{2i} + \boldsymbol {x}_{i}^{\theta _{3i}} \right)\)

3

Logistic

E[d _i |x _i ]=θ _1i /{1+exp[(θ _2i −x _i )]/θ _3i }

3