Dose-Response models vary in time: A comparison of non-linear least squares and a two-step method

Dose-response studies are widely used in toxicology to investigate the potency of a compound. Dose-response data are typically evaluated by using a three or four-parameter log-logistic model that includes the upper and lower limits of the response, steepness of the dose-response curve, and the effective dose ED50. Multiple dose-response experiments are conducted to determine the estimation of these four parameters and time related parameters, requiring the aggregation of estimates of these four parameters from various experiments. In this context, non-linear least squares are used as direct methods, which are easy to operate but fitting dose-response models is complicated and often have convergence problems. An alternative estimation method is the two-step method, in which four parameters are estimated before linear regression is used. Similarly, the meta analysis and longitudinal analysis are also implemented based on the estimation of four parameters in the first step. These methods are compared in both practical actual datasets and simulation. We conclude that the two-step method is a more robust estimation method in the complex situation.