A simulated maximum likelihood procedure for analyzing imprecise trade-off thresholds between the benefits and harms of medicines.

Stated preference studies in which information on the willingness to trade-off between the benefits and harms of medicines is elicited from patients or other stakeholders are becoming increasingly mainstream. Such trade-offs can mathematically be represented by a weighted additive function, with the weights, whose ratios determine how much an individual is willing to trade-off between the treatment attributes, being the response vector for the statistical analysis. One way of eliciting trade-off information is through multi-dimensional thresholding (MDT), which is a bisection-based approach that results in increasingly tight bounds on the values of the weights ratios. While MDT is cognitively less demanding than other, more direct elicitation methods, its use complicates the statistical analysis as it results in weights data that are region censored. In this article, we present a simulated maximum likelihood (SML) procedure for fitting a Dirichlet population model directly to the region-censored weights data and perform a series of computational experiments to compare the proposed SML procedure to a naive approach in which a Dirichlet distribution is fitted to the centroids of the weights boundaries obtained with MDT. The results indicate that the SML procedure consistently outperformed the centroid-based approach, with the centroid-based approach requiring three bisection steps per trade-off to achieve a similar precision as the SML procedure with one bisection step per trade-off. Using the newly proposed SML procedure, MDT can be applied with smaller sample sizes or with fewer questions compared to the more naïve centroid-based approach that was applied in previous applications of MDT.