Efficient and robust willingness-to-pay designs for choice experiments: some evidence from simulations.

We apply a design efficiency criterion to construct conjoint choice experiments specifically focused on the accuracy of marginal estimates. In a simulation study and a numerical example, the resulting optimal designs are compared to alternative designs suggested in the literature. It turns out that optimal designs not only improve the estimation accuracy of the marginal, as expected on the basis of the nature of the efficiency criterion, but they also considerably reduce the occurrence of extreme estimates, which also exhibit smaller deviations from the real values. The proposed criterion is there for evaluable for non-market valuation studies as it reduces the sample size required for a given degree of accuracy and it produces estimates with fewer outliers.Willingness-to-pay; Optimal design; Choice experiments; Conditional logit model; Robust;

Rank-order conjoint experiments: efficiency and design.

In a rank-order conjoint experiment, the respondent is asked to rank a number of alternatives instead of choosing the preferred one, as is the standard procedure in conjoint choice experiments. In this paper, we study the efficiency of those experiments and propose a D-optimality criterion for rank-order conjoint experiments to find designs yielding the most precise parameter estimators. For that purpose, an expression of the Fisher information matrix for the rank-ordered multinomial logit model is derived which clearly shows how much additional information is provided by each extra ranking step made by the respondent. A simulation study shows that Bayesian D-optimal ranking designs are slightly better than Bayesian D-optimal choice designs and (near-)orthogonal designs and perform considerably better than other commonly used designs in marketing in terms of estimation and prediction accuracy. Finally, it is shown that improvements of about 50% to 60% in estimation and prediction accuracy can be obtained by ranking a second alternative. If the respondent ranks a third alternative, a further improvement of 30%in estimation and prediction accuracy is obtained.

Design criteria to develop choice experiments to measure the WTP accurately.

To measure the willingness-to-pay (WTP) accurately, Vermeulen et al.[2008] apply the c-optimality criterion to generate designs for conjoint choice experiments. This criterion is based on minimizing the sum of the variances of the WTP estimators approximated by the delta method. Designs generated based on this criterion lead to more accurate WTP estimates than the ones obtained by standard designs and reduce considerably the occurrence of extreme WTP estimates, although they do not exclude them. In this paper, other optimality criteria are considered to tackle this problem. We distinguish between criteria in preference space on the one hand and criteria in WTP-space on the other hand. In a simulation study and a numerical example, we compare the accuracy of the WTP and the utility coefficient estimates yielded by the designs based on these new criteria.conjoint choice experiment; Bayesian optimal design; willingness-to-pay; conditional logit model;

Two-stage designs robust to model uncertainty.

D-optimal designs are known to depend quite critically on the particular model that is assumed. These designs tend to concentrate all the experimental runs on a small number of design points and are ideally suited for estimating the coefficients of the assumed model, but they provide little or no ability for model checking. To address this problem we use the notion of empirical models that have both important and potential terms. We propose within the Bayesian paradigm, a two-stage design strategy for planning experiments in the face of model uncertainty. In the first stage, the experimenter's prime interest is to highlight the uncertainties in the specification of the model in order to refine or modify the model(s) initially entertained. A design criterion is used that accounts for precision of the important terms but also facilitates the improvement of the proposed model(s) by detecting lack of fit. Data from the first stage provide model information enabling the second stage design to be chosen efficiently with reduced model uncertainty. The design in the second stage is obtained using a weighted criterion with weights being posterior model probabilities computed from first stage data. The criterion in the second stage also takes into account precise estimation of important terms as in the first stage but now attempts to minimize bias with respect to potential terms. Results from simulations show that the proposed two-stage strategy performs well. The combined first and second stage design has good properties with respect to precision of important terms, lack of fit and also excellent bias properties with respect to a true assumed model in various simulation studies.Bayesian two-stage procedures; Bias; Data; Design; GD-optimality; Information; Lack-of-fit; Model; Model-robustness; Model-sensitive; Models; Planning; Posterior probabilities; Precision; Prior probabilities; Probability; Simulation; Strategy; Studies; Uncertainty;

On optimal designs for clinical trials: An updated review

Optimization of clinical trial designs can help investigators achieve higher qualityresults for the given resource constraints. The present paper gives an overviewof optimal designs for various important problems that arise in different stages ofclinical drug development, including phase I dose–toxicity studies; phase I/II studiesthat consider early efficacy and toxicity outcomes simultaneously; phase IIdose–response studies driven by multiple comparisons (MCP), modeling techniques(Mod), or their combination (MCP–Mod); phase III randomized controlled multiarmmulti-objective clinical trials to test difference among several treatment groups;and population pharmacokinetics–pharmacodynamics experiments. We find thatmodern literature is very rich with optimal design methodologies that can be utilizedby clinical researchers to improve efficiency of drug development