Optimal designs for two-parameter nonlinear models with application to survival models

Abstract

Censoring occurs in many industrial or biomedical 'time to event' experiments. Finding efficient designs for such experiments can be problematic since the statistical models involved are usually nonlinear, making the optimal choice of design parameter dependent. We provide analytical characterisations of locally D- and c-optimal designs for a class of models, thus reducing the numerical effort for design search substantially. We also investigate standadised maximin D-and c-optimal designs. We illustrate our results using the natural proportional hazards parameterisation of the exponential regression model. Different censoring mechanisms are incorporated and the robustness of designs against parameter misspecification is assessed.