The effects of different experimental designs on parameter estimation in the kinetics of a reversible chemical reaction

The common methods used by chemists to obtain the estimates of the kinetic rate constants are deterministic ones. The statistical methods, such as D-optimum design (DOD), can offer a better way to deal with this problem. But the kinetic model of a reversible reaction is nonlinear, the DOD is locally optimal at the value of the initial chosen parameters. The goal of this article is to try to put different experimental design techniques, i.e., uniform design (UD), orthogonal design (OD) and DOD into a common framework, and to attempt to gain some insight on when, where and which of these three experimental methods can be expected to work well. The extensive Monte Carlo experiments have been done in order to compare the performances of these methods. The results show that the DOD often gives the best performance, but it is easy to break down in estimation of parameters, when the initial parameters are far away from the true parameters. The OD also breaks down in some situations. The UD is the most stable, and it works well in all situations.