Statistical Inference for Two-Compartment Model Parameters with Bootstrap Method and Genetic Algorithm

Abstract

Two-compartment model has common usage in modeling stage of dynamical systems. It is possible to consider the two-compartment model as a regression model which is intrinsically nonlinear in parameters. Evaluation of the nonlinear model parameters in statistical perspective will help to improve the compartmental system. In this study, statistical inference of two-compartment model parameters is achieved in respect to point estimation and interval estimation. The point estimates of compartment model parameters are obtained according to the nonlinear least squares (NLS) approach. Genetic algorithm (GA), a well-known population-based evolutionary algorithm, is preferred as an optimization tool. The main contribution of the study is obtaining bias-corrected point estimates and bias-corrected accelerated confidence interval (CI) estimates of compartment parameters. In order to obtain the CIs, sampling distribution of parameter estimates is defined with the application of fixed-X nonlinear bootstrap method which preserves the fixed nature of predictor variable. Two bootstrap methods are used for CI calculations: (i) Percentile and (ii) bias-corrected accelerated (BCa). A simulated data set and a real data set from the pharmacokinetic (PK) literature are chosen for application purpose. It is seen from the results that bias-reduced point estimates and sampling distribution of parameter estimates can be obtained by preserving the time-dependent nature of the dynamical system by using fixed-X bootstrapping. Besides, BCa method gives more realistic interval estimates than percentile method.