Comparing exponential and exponentiated models of drug demand in cocaine users.

Abstract

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model, but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use), whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values impact demand parameters and their association with drug-use outcomes when using the exponential model, but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency, in addition to demonstrating construct validity and generalizability.

Clinical models of decision making in addiction

“…The only difference between the two is that we raised each side of the equation to a power of 10 so the untransformed consumption ( Q ) data can be fit without log transformation. We found that this modification allows for the same interpretation of the fitted parameters and, if anything, improved fits to the data (Koffarnus et al, 2015), as did an independent follow-up evaluation (Strickland et al, 2016).…”

The condom purchase task: A hypothetical demand method for evaluating sexual health decision‐making

“…Data from the condom purchase task were analyzed using the exponentiated demand equation (Koffarnus, Franck, Stein, & Bickel, 2015;Strickland, Lile, Rush, & Stoops, 2016):…”

“…Data from the condom purchase task were analyzed using the exponentiated demand equation (Koffarnus, Franck, Stein, & Bickel, ; Strickland, Lile, Rush, & Stoops, ): where Q = consumption; Q 0 = derived demand intensity; k = a constant related to consumption range ( a priori set to 2); C = commodity price; and α = derived demand elasticity. Demand intensity reflects theoretical consumption of a commodity at zero cost and demand elasticity reflects the sensitivity of consumption to changes in price.…”

Unique prediction of cannabis use severity and behaviors by delay discounting and behavioral economic demand

“…Price elasticity and intensity were generated using the exponentiated demand equation: $$Q=Q_0\ast {10}^{k\ast (e^{(-\alpha \ast Q_0\ast C)}-1)}$$ where Q = consumption; Q 0 = derived intensity of demand (consumption at zero price); k = a constant that denotes consumption range in log units ( a priori set to 2); C = the price of the commodity; and α = derived elasticity of demand. The exponentiated model is a recently developed and validated equation that allows for the inclusion of zero consumption values (Koffarnus et al, 2015; Strickland et al, 2016b). Area under the curve (AUC) values were also generated as described previously (Amlung et al, 2015b; Aston et al, 2016).…”