Heterogeneous D-Error Designs for Discrete Choice Experiments Using Prior Beliefs

Rationale: Whilst recent applications have advanced the econometric modeling of discrete choice experiments (DCEs) in health care, little research has examined the statistical efficiency of their experimental design (ED). ED is a combinatorial problem of specifying the profiles of the choice sets. Statistically efficient provide as much information as possible on the model parameters, which enables a reduction in the number of respondents needed to achieve a given level of accuracy. DCEs in health typically focus on design criteria enforcing orthogonality, level balance, and minimum level overlap. For non-linear choice models, such criteria may not produce efficient designs, and claims of D-error efficiency assume the expected coefficients are zero. Assuming zero priors is conservative and possibly inappropriate. More efficient designs may be obtained using non-zero priors, the D-error criterion to summarize efficiency, and algorithms to search over the design space. Objective: To investigate the gains in statistical efficiency accrued from employing D-error heterogeneous designs using the mixed logit (MXL) behavioural model and non-zero prior coefficients. Methodology: The designs were structured around a DCE investigating preferences for diagnosing genetic causes of developmental delay. Three attributes were included: likelihood of genetic diagnosis, time waiting for results, and cost. The base design was constructed using orthogonal arrays, and 16 choice sets were generated using the foldover technique to ensure level balance and minimum level overlap; for non-demanders, an opt-out alternative was also included. To search for more efficient designs, choice sets were generated using two design algorithms - swapping and cycling - and the efficiency of each design was summarized using the D-error criterion. D-error is a scaled measure of the determinant of the Fisher Information Matrix (IM). Prior coefficients obtained from the pilot study were used to estimate the IM. Because these coefficients were based on a small sample, heterogeneous designs were constructed to help mitigate the potential effects of misspecified priors. The heterogeneous design approach produces several subdesigns to be administered across study participants, which allows for greater variability in the attribute levels. The theoretical gains from these procedures were evaluated using Monte Carlo analysis; real-world gains in efficiency were examined by directly evaluating the IM of the base design versus the heterogeneous design. The relative efficiency of the design approaches was derived as the ratio of the D-errors. Results: The homogeneous design with informative priors was expected to be 30% more efficient when compared to the base design. The heterogeneous approach with two subdesigns resulted in theoretical efficiency gains of 35% compared to the base; Monte Carlo analysis confirmed that the heterogeneous approach produced greater efficiency gains if the priors were misspecified. The real-world D-error statistics revealed the single and heterogeneous designs were respectively 19 and 23% more efficient than the base design. Conclusions: The statistical efficiency of the ED for the MXL specification can be improved using informative priors and the heterogeneous design approach. The degree of improvement, however, may be overestimated in theoretical applications because of issues such as complexity.

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