Rapid, precise, and reliable measurement of delay discounting using a Bayesian learning algorithm

Abstract

Machine learning has the potential to facilitate the development of computational methods that improve the measurement of cognitive and mental functioning. In three populations (college students, patients with a substance use disorder, and Amazon Mechanical Turk workers), we evaluated one such method, Bayesian adaptive design optimization (ADO), in the area of delay discounting by comparing its test-retest reliability, precision, and efficiency with that of a conventional staircase method. In all three populations tested, the results showed that ADO led to 0.95 or higher test-retest reliability of the discounting rate within 10-20 trials (under 1-2 min of testing), captured approximately 10% more variance in test-retest reliability, was 3-5 times more precise, and was 3-8 times more efficient than the staircase method. The ADO methodology provides efficient and precise protocols for measuring individual differences in delay discounting.

Figure 1

Schematic illustration of adaptive design optimization (ADO) in the area of delay discounting. Unlike the traditional experimental method, ADO aims to find the optimal design that extracts the maximum information about a participant’s model parameters on each trial. In other words, ADO identifies the most informative or optimal design (d^*) using the participant’s previous choices (y), the mathematical model of choice behavior, and the participant’s model parameters ($\theta$). In our delay discounting experiment with ADO, y would be 0 (choosing smaller and sooner reward) or 1 (larger and later reward), the mathematical model would be the hyperbolic function (see “Methods”), $\theta$ would be k (discounting rate) and $\beta$ (inverse temperature), and d* would be the experimental design (a later delay and a sooner reward, which are underlined in the figure) that maximizes the integral of the local utility function, $u(d,\theta ,y)$, which is based on the mutual information between model parameters ($\theta$) and outcome random variable conditional upon design (y|d). For more mathematical details of the ADO method, see^,.

Figure 2

Comparison of ADO and Staircase (SC) within-visit test–retest reliability of temporal discounting rates when assessed cumulatively in each trial (ADO) or every third trial (SC) (Experiment 1, college students) at each of the two visits. Two visits were separated by approximately one month. In each visit, a participant completed two ADO sessions and two SC sessions (within-visit test–retest reliability). Test–retest reliability was assessed cumulatively in each trial (See “Methods” for the procedure). Shaded regions represent the 95% frequentist confidence interval of the concordance correlation coefficient (CCC).

Figure 3

Reliability and efficiency of the ADO method in Experiments 2 and 3 (A) Comparison of ADO and Staircase (SC) test–retest reliability of temporal discounting rates when assessed cumulatively in each trial (ADO) or every third trial (SC) (Experiment 2, patients with SUDs) (B) Test efficiency as measured by the cumulative test–retest reliability across trials (Experiment 3, Amazon MTurk workers). Dashed line = 0.9 test–retest reliability. Unlike Experiments 1 and 2, only ADO sessions were administered and each session consisted of 20 trials in Experiment 3. Shaded regions represent the 95% frequentist confidence interval of the concordance correlation coefficient (CCC).