Algorithm 2 Virtual individual generation: reduced individual variance. Takes as input posterior draws of $\alpha ,\beta ,{\sigma }_0,{\sigma }_1$ in Equation (2) and $\eta$

1:procedure VirtualIndividualReducedVariance ($\eta ,\alpha ,\beta ,{\sigma }_0,{\sigma }_1$) 2:    For all ${\alpha }_i$ posterior draws, shrink towards the grand mean: ${\alpha }_i={\alpha }_i+(\overline{\alpha }-{\alpha }_i)(1-\eta )$ where $\overline{\alpha }$ is the posterior mean 3:    For all ${\beta }_i$ posterior draws, shrink towards the grand mean: ${\beta }_i={\beta }_i+(\overline{\beta }-{\beta }_i)(1-\eta )$ where $\overline{\beta }$ is the posterior mean 4:    Uniformly sample a set of random $(\alpha ,\beta )$ values from the variance-reduced posterior draw set 5:    Uniformly sample a set of random $({\sigma }_0,{\sigma }_1)$ values from the posterior draw set 6:    Sample $a^{\prime }$ from a kernel density approximation of empirical distribution using inverse transform sampling (see [30]) 7:    Calculate $a=a^{\prime }+(a_{50}-a^{\prime })(1-\eta )$ where $a_{50}$ indicates the median value of the empirical distribution 8:    Calculate $\sigma =\eta ({\sigma }_0+{\sigma }_{1}a)$ 9:    Draw a value of $logb\sim \mathrm{normal}(\alpha +\beta a_i,\sigma )$ 10:    Use $ed\left(x\right)={10}^{a{(-1+1/(1-x))}^{1/b}}$ to calculate $E{D}_{25}$ ($x=0.25$) and $E{D}_{75}$ ($x=0.75$) for that individual 11:    If $E{D}_{25}$ is less than half the minimum $E{D}_{25}$ in estimates from [22], reject $(a,b)$ and call VirtualIndividualReducedVariance 12:    If $E{D}_{75}$ is greater than 1.5 times the maximum $E{D}_{75}$ in estimates from [22], reject $(a,b)$ and call VirtualIndividualReducedVariance 13:    return $(a,b)$ which characterize a dose-response curve 14:end procedure