Optimal design methods that are robust to uncertainty

Assumptions are usually made when optimising design for an experiment. Unexpected departure from the assumptions may result in suboptimal design. This thesis aims to address the issue of optimal design under uncertainties. Various optimisation methods were proposed to locate optimal design that is efficient even if the assumptions do not fully hold. A hypercube optimal design (HClnD) was proposed to address the issue of uncertainty in the parameter space, where D-optimal design for nonlinear models has an issue of dependency on the parameter values. The HClnD criterion is presented in Chapter 2 and was compared to other robust design criteria in terms of efficiency, relative errors and computational cost with simulation studies. The performance of HClnD was further evaluated in Chapter 3 where the optimality criteria in this chapter are solved analytically whenever possible and numerically otherwise for two simple nonlinear models. HClnD was shown to be as efficient as other robust methods and consumed less computational cost. This robust criterion was applied prospectively to design a three arm double blind pharmacokinetic (PK) clinical study for two drugs (midazolam and droperidol). The design was evaluated in Chapter 4. An adaptive optimal design method was proposed in Chapter 5 to design experiments for PK bridging studies. In a PK bridging study the researcher uses knowledge of the PK model from a prior-population to design the experiment for a target-population. The design is suboptimal if the PK profile of prior and target-populations are widely diverged. The proposed adaptive optimal design was compared to optimal design for target-population based solely on the prior-population information. The proposed method was superior in the estimation precision when the PK profiles of the two populations are widely divergent and comparable precision when the PK profiles are similar. Sampling windows is used to ensure certain degree of design efficiency under execution uncertainty, where samples may not be collected following exactly the optimal design. Two methods to construct sampling windows for nonlinear mixed effects models were proposed in Chapter 6. Initially a naïve adaptive method that determines the window for the next sample when the previous and current samples become available was proposed. Another method is a recursive random sampling method that is based on the Gibbs sampling techniques. Both methods were applied to locate sampling windows for a population PK study and tested via simulation. Finally, an optimal design method to minimise the cost for phase II PK clinical studies was proposed in Chapter 7. An additional level of uncertainty when designing phase II clinical study based on the population PK estimates from healthy volunteers in phase I study was incorporated in the form of hyperprior distribution. In this design, the expected cost is minimised. The resulted optimal design accounts for both cost of the study and the probability of study failure. The proposed optimisation method was shown to locate designs that attained high power, without the need to define the power a priori, and without the need to define upper constraints in the design space