Statistica Sinica 24 (2014), 415-428

OPTIMAL DESIGNS FOR TWO-PARAMETER NONLINEAR

MODELS WITH APPLICATION TO SURVIVAL MODELS

Maria Konstantinou, Stefanie Biedermann and Alan Kimber

University of Southampton

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.

Key words and phrases: $c$-optimality, $D$-optimality, proportional hazards, survival analysis.