Marginalization in nonlinear mixed-effects models with an application to dose-response analysis
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.