An algorithm for computing profile likelihood based pointwise confidence intervals for nonlinear dose-response models

This study was inspired by the need to estimate pointwise confidence intervals (CIs) for a nonlinear dose-response model from a dose-finding clinical trial. Profile likelihood based CI for a nonlinear dose response model is often recommended. However, it is still not commonly used in dose-finding studies because it cannot generally be calculated explicitly. Most previous research has mainly focused on the performance of the profile likelihood based CI method compared with other common approaches. However, there are still no reports on computing profile likelihood based pointwise CIs for an entire dose-response curve. Based on a previous dose-finding trial with binary-response data, this present study proposed to calculate profile likelihood based pointwise CIs by using the bisection method with proper calculation order for doses in the curve plus crude search when the expected response is close to a boundary. The convergence could be improved by applying appropriate starting values for the optimization procedure with straightforward programming techniques. The algorithm worked well in most cases based on the simulation study and it can be applied more generally to other dose-response models, and other type of data like normally distributed response. It would indeed be great to be able to use profile likelihood approaches more routinely when constructing pointwise CIs for nonlinear dose-response models.