Comparison of various estimation methods for the parameters of Michaelis-Menten equation based on in vitro elimination kinetic simulation data

The Michaelis-Menten equation is one of the best-known models describing the enzyme kinetics of in vitro drug elimination experiments, and takes a form of equation relating reaction rate (V) to the substrate concentration ([S]) via the maximum reaction rate (V(max)) and the Michaelis constant (K(m)). The current study was conducted to compare the accuracy and precision of the parameter estimates in the Michaelis-Menten equation from various estimation methods using simulated data. One thousand replicates of simulated [S] over serial time data were generated using the results of a previous study, incorporating additive or combined error models as a source of random variables in the Monte-Carlo simulation using R. From each replicate of simulated data, V(max) and K(m) were estimated by five different methods, including traditional linearization methods and nonlinear ones without linearization using NONMEM. The relative accuracy and precision of the estimated parameters were compared by the median values and their 90% confidence intervals. Overall, V(max) and K(m) estimation by nonlinear methods (NM) provided the most accurate and precise results from the tested 5 estimation methods. The superiority of parameter estimation by NM was even more evident in the simulated data incorporating the combined error model. The current simulation study suggests that NMs using a program such as NONMEM provide more reliable and accurate parameter estimates of the Michaelis-Menten equation than traditional linearization methods in in vitro drug elimination kinetic experiments.