A bayesian hierarchical modeling approach for the estimation of demand curves from hypothetical purchase tasks administered in an experimental setting

The reinforcing efficacy of a product, characterized by its demand curve, is an important construct for understanding a product's potential to cause addiction. Hypothetical purchase tasks (HPTs) are used to measure demand for addictive products because they are cost-efficient, ethical, and safe to administer. However, statistical methods used to estimate demand curves from HPTs are often flawed. We introduce a Bayesian hierarchical modeling strategy for estimating the intensity and elasticity of demand from HPT data collected in an experimental setting. The approach addresses several recurring challenges in the analysis of HPT data by accommodating count outcomes, repeated measures, and individual-level heterogeneity, while allowing demand curves and treatment effects to be estimated jointly within a single inferential framework. When applicable, the hierarchical model allows us to simultaneously estimate baseline demand quantities and include them as covariates to better inform the relationship of treatments to demand. Further, uncertainty in the span of the population demand curve is explicitly modeled, rather than treated as a fixed quantity. We fit the model using Bayesian techniques supported by simulations. The approach is applied to data from a randomized crossover study comparing the intensity and elasticity of demand for flavored little cigars/cigarillos (LCCs) to unflavored LCCs.