Bayesian L-optimal exact design of experiments for biological kinetic models

Abstract

Data from experiments in steady state enzyme kinetic studies and radioligand binding assays are usually analysed by fitting non-linear models developed from biochemical theory. Designing experiments for fitting non-linear models is complicated by the fact that the variances of parameter estimates depend on the unknown values of these parameters and Bayesian optimal exact design for non-linear least squares analysis is often recommended. It has been difficult to implement Bayesian L-optimal exact design, but we show how it can be done by using a computer algebra package to invert the information matrix, sampling from the prior distribution to evaluate the optimality criterion for candidate designs and implementing an exchange algorithm to search for candidate designs. These methods are applied to finding optimal designs for the motivating applications in biological kinetics, in the context of which some practical problems are discussed. A sensitivity study shows that the use of a prior distribution can be essential, as is careful specification of that prior. © 2011 Royal Statistical Society.