  Inference in hierarchical nonlinear models needs careful consideration about
targeting parameters that have either a conditional or population-average
interpretation. For the special case of mixed-effects nonlinear sigmoidal
models we propose a method for the estimation of derived parameters with a
marginal interpretation, but also maintaining the random effect structure of
the nonlinear model, by using a combination of numerical quadrature and the
delta method, integrating over the random effect distribution conditional on
the estimated variance components. The difference between these marginalized
estimates, generalized nonlinear least squares estimates, and conditional
estimation is characterised by means of two representative case studies. The
case studies consist of the estimation of effective dose levels in a human
toxicology study, and the relative potency estimation for two herbicides in an
agricultural field trial. Both case studies exhibit an experimental design that
results in data with at least one hierarchical level of between- and
within-cluster variation. A user-friendly software implementation is made
available with the R package medrc, providing an automated framework for
mixed-effects dose-response modelling.
