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

Abstract

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 against parameter misspecification is assessed. We demonstrate that, unlike traditional designs, the designs found perform well across a broad range of scenarios.

Model robust designs for survival trials

“…It is minimax c-optimal for both contamination classes, is (in the limit) minimax D-optimal for G 1 , and is also highly efficient if Cox's proportional hazard model is fitted via partial likelihood estimation (see Konstantinou et al (2015)). It is also easy to find using the results in Konstantinou et al (2014).…”

“…Finding designs which are robust to both sources of uncertainty could be an interesting area of future research. A promising starting point for such an investigation could be the 15 parameter robust designs derived in Konstantinou et al (2014).…”

“…The corresponding locally optimal designs for the case of the exponential-based proportional hazards model being the true model are readily available in Konstantinou et al (2014).…”

Adaptive Optimal Designs for Dose-Finding Studies with Time-to-Event Outcomes

“…In this case, for a given dose-response regression model, an optimal design problem is to determine a set of optimal doses and the probability mass distribution at these doses to maximize some convex criterion of the model Fisher information matrix. Optimal designs for two-parameter exponential regression models with different censoring mechanisms were investigated in (8)(9)(10). Optimal designs for most efficient estimation of specific quantiles of censored Weibull or log-normal observations were developed in (11).…”

Simulation-based Bayesian optimal ALT designs for model discrimination

“…More recent discussions of optimal ALT plans and/or robust ALT plans can be found in, e.g., Xu [5], McGree and Eccleston [6], Monroe et al [7], Yang and Pan [8], Konstantinou et al [9], Haghighi [10]. In the previous study, the associated confidence intervals of an estimate reflect the uncertainty arising from limited sample size and censoring at test, but do not account for model form inadequacy.…”