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

Censoring may occur in many industrial or biomedical time to event experiments. Efficient designs for such experiments are needed but finding such designs can be problematic since the statistical models involved will usually be nonlinear, making the optimal choice of design parameter dependent. We provide analytical characterisations of locally D- and c-optimal designs for a large class of models. Our results are illustrated using the natural proportional hazards parameterisation of the exponential regression model, thus reducing the numerical effort for design search substantially. We also determine designs based on standardised optimality criteria when a range of parameter values is provided by the experimenter. Different censoring mechanisms are incorporated and the robustness of designs to parameter misspecification is assessed. We demonstrate that, unlike traditional designs, the designs found perform well across a broad range of scenarios.