Reduction of dimensionality in Bayesian nonlinear regression with a pharmacokinetic application

Application of Bayes's theorem to the analysis of nonlinear regression models is limited by numerical problems associated with calculation of integrals of functions of several variables. For k-parameter models that are linear in l of the parameters, a dimension-reduction procedure is described for factoring the posterior distribution into the product of a multivariate normal density and a function of k- l nonlinear parameters. Integrals can then be calculated with ( k- l)-dimensional numerical integration. A four-parameter, two-compartment pharmacokinetic model of lidocaine disposition is analyzed using a change of variables in order to obtain a model that is linear in two parameters. It is shown that a Bayesian analysis, with reduction of dimensionality, applied to this model produces appropriate results with reasonable CPU-time requirements.