Likelihood interval for nonlinear regression

Abstract

Wald confidence interval has been used as the conventional method of interval estimation for the parameters in nonlinear models. Because Wald confidence interval is symmetric around the point estimate, it does not reflect the asymmetry of the likelihood profile in nonlinear regression. In contrast, a likelihood interval is estimated directly from the likelihood profile and does reflect the shape of the likelihood profile. However, the lack of software for the estimation of likelihood intervals and visualization of likelihood profiles posed an obstacle to the use of likelihood intervals in nonlinear models. There was a need for software implementation to tackle these tasks. Likelihood interval estimation and likelihood profile plotting for nonlinear models had not been previously implemented in R software. This article describes the implementation of likelihood interval estimation and likelihood profile plotting in the wnl R software package. To demonstrate the usage of implemented functions, an example of fitting a nonlinear pharmacokinetic model to concentration-time data is presented.