Figure 1
Sample balloons for the computerized Balloon Analogue Risk Task (BART) used in the present study. Participants earned 100 points to a temporary account with each pump made (balance at bottom of screen) and ‘banked’ points were saved to a permanent account (balance at top of screen). Balloons were programmed to burst at unknown breakpoints. A) Example of trial in which the participant successfully banked points and earned a reward. B) Example of trial in which the balloon burst.
Table 1
Overview of models tested.
| MODEL | PARAMETERS | ESTIMATED VIA |
|---|---|---|
| Exponential-Weight Mean-Variance (EWMV) Model Park et al. (2021) | ψ = Prior belief of burst ξ = Learning rate ρ = Risk preference τ = Behavioral consistency λ = Loss aversion | Equation 1 Equation 1 Equation 2 Equation 3 Equation 2 |
| Bayesian Sequential Risk-Taking (BSR) Model Park et al. (2021); Wallsten et al. (2005) | φ = Prior belief of success η = Learning rate γ = Risk propensity τ = Behavioral consistency | Equation 4 Equation 4 Equation 6 Equation 7 |
| 3-Parameter No Learning (3par) Model Park et al. (2021) | θ = Prior belief of success γ = Risk propensity τ = Behavioral consistency | Equation 8 Equation 8 Equation 9 |
| 2-Parameter No Learning (2par) Model Adapted – van Ravenzwaaij et al. (2011) | γ = Risk propensity τ = Behavioral consistency | Equation 10 Equation 9 |
Table 2
Model comparison: Leave-one-out (LOO) information criterion.
| Group | Model | LOO | SE | ΔLOO |
| BD+ | EWMV | 1774.00 | 82.68 | 0 |
| BSR | 1799.72 | 87.02 | 25.72 | |
| Par2 | 1935.07 | 76.89 | 161.07 | |
| Par3 | 1938.79 | 75.99 | 164.79 | |
| BD– | EWMV | 1497.36 | 70.89 | 0 |
| BSR | 1512.64 | 73.54 | 15.28 | |
| Par3 | 1612.30 | 77.64 | 114.94 | |
| Par2 | 1614.21 | 78.27 | 116.85 | |
| HC | BSR | 2854.09 | 114.28 | 0 |
| EWMV | 2855.26 | 107.53 | 1.17 | |
| Par2 | 3119.08 | 129.02 | 264.99 | |
| Par3 | 3121.87 | 128.22 | 267.78 |
[i] Note: Lower LOO values are indicative of better model performance. LOO = Leave-one-out Information Criterion; SE = LOO standard error; BD+ = bipolar disorder (BD) with prior substance use disorder (SUD); BD– = BD without prior SUD; HC = healthy comparisons; EWMV = Exponential-Weight Mean-Variance model; BSR = Bayesian Sequential Risk-Taking Model; Par2 = 2-parameter (no learning) model; Par3 = 3-parameter model (no-learning; estimates prior belief).
Table 3
Characteristics of the sample.
| BD+ (n = 18) | BD– (n = 15) | HC (n = 33) | GROUP DIFFERENCES | |||
|---|---|---|---|---|---|---|
| M (SD) | M (SD) | M (SD) | F/t/χ2 | p | Post-hoc | |
| Demographic | ||||||
| Age (years) | 36.5 (10.9) | 29.7 (9.5) | 33.5 (10.3) | 1.76 | 0.180 | |
| Sex (% female) | 38.9 | 66.7 | 57.6 | 2.79 | 0.248 | |
| Education (years) | 14.9 (2.6) | 15.4 (4.2)a | 16.0 (1.9) | 0.96 | 0.390 | |
| Clinical | ||||||
| Psych Meds (%) | 77.8 | 93.3 | 1.54 | 0.215 | ||
| Antidepressant (%) | 27.8 | 46.7 | 1.26 | 0.261 | ||
| Antipsychotic (%) | 44.4 | 26.7 | 1.12 | 0.291 | ||
| Benzodiazepine (%) | 38.9 | 20.0 | 1.38 | 0.240 | ||
| Mood Stabilizer (%) | 61.1 | 73.3 | 0.55 | 0.458 | ||
| Stimulant (%) | 11.1 | 6.7 | 0.20 | 0.658 | ||
| Diagnosis | 0.55 | 0.761 | ||||
| BD I (%) | 83.3 | 73.3 | ||||
| BD II (%) | 11.1 | 20.0 | ||||
| BD NOS (%) | 5.6 | 6.7 | ||||
| YMRS | 2.8 (2.1) | 1.7 (1.9) | –1.48 | 0.149 | ||
| HAM-D | 3.4 (2.9) | 2.7 (2.5) | –0.76 | 0.455 | ||
| Self-report | ||||||
| BIS | 20.4 (3.3) | 20.9 (4.0) | 18.2 (3.8) | 3.61 | 0.033* | HC < BD– |
| BAS-Reward | 17.2 (2.2) | 17.9 (2.2) | 17.5 (1.6) | 0.54 | 0.587 | |
| BAS-Fun | 11.1 (3.1) | 11.1 (3.2) | 11.0 (2.2) | 0.02 | 0.984 | |
| BAS-Drive | 11.2 (3.3) | 11.4 (2.5) | 10.7 (2.8) | 0.35 | 0.705 | |
| SSS-Disinhibit | 5.2 (2.9) | 5.1 (2.3) | 3.8 (2.6) | 1.95 | 0.151 | |
| SSS-Thrill | 5.7 (3.5) | 5.2 (2.9) | 5.7 (2.8) | 0.18 | 0.838 | |
| SSS-Bored | 3.8 (1.8) | 2.8 (2.0) | 2.0 (1.4) | 6.82 | 0.002** | HC < BD+ |
| SSS-Exper | 6.3 (1.7) | 5.6 (2.3) | 5.5 (1.6) | 1.18 | 0.313 | |
| Neuropsychological | ||||||
| Exec Func | –0.5 (1.1)b | 0.2 (1.0) | 0.2 (0.9) | 2.97 | 0.059 | |
[i] Note: BD+ = bipolar disorder (BD) with prior substance use disorder (SUD); BD– = BD without prior SUD; HC = healthy comparisons; M = mean; SD = standard deviation; Psych Meds = taking psychotropic medication; BD NOS = BD not otherwise specified; YMRS = Young Mania Rating Scale; HAM-D = Hamilton Depression Rating Scale; Exec Func = measure of executive function from Principal Components Analysis on Trail-Making Test (Part-B; TMT-B), Category Verbal Fluency (CVF), Stroop, Tower of London (ToL), and Digit Span Backward (DSB) scores; BIS = behavioral inhibition; BAS = Behavioral Activation Scale (reward sensitivity, fun-seeking, drive); SSS = Sensation Seeking Scale (disinhibition, thrill/adventure seeking, boredom susceptibility, experience seeking). a Based on 14 participants due to missing data. b Based on 17 participants due to missing data. * p < .05 ** p < .01.
Figure 2
Group differences in EWMV parameters indexing the mechanisms of risk-taking.
Note: Violin plots are based on 8000 post warm-up MCMC samples of the posterior distributions. Horizontal bars at top indicate credible differences between two groups based on 90% HDI of posterior differences for the given parameter. Dots indicate the mean of the posterior. BART = Balloon Analogue Risk Task; EWMV Model = Exponential-weight mean-variance model; ψ = prior belief of burst; ξ = learning rate; ρ = risk preference; τ = behavioral consistency; λ = loss aversion; BD+ = bipolar disorder with lifetime substance use disorder (SUD); BD– = bipolar disorder without lifetime SUD; HC = healthy comparisons.
Table 4
Post-hoc simulation results.
| OBSERVED DIFFERENCES | SIMULATIONS | ||||
|---|---|---|---|---|---|
| DIRECTION | MEAN DIFFERENCE | GROUP | ADJUSTMENT (ΔPARAMETER VALUE) | OUTCOME (ΔADJ. PUMPS) | |
| Prior Belief (ψ) | BD+ > BD– | 0.008 | BD– | Increased ψ by 0.008 | Decreased 3 pumps |
| BD+ | Decreased ψ by 0.008 | Increased 4 pumps | |||
| BD+ > HC | 0.008 | HC | Increased ψ by 0.008 | Decreased by 15 pumps | |
| BD+ | Decreased ψ by 0.008 | Increased by 4 pumps | |||
| Learning Rate (ξ) | BD+ > HC | 0.006 | HC | Increased ξ by 0.006 | Decreased by 6 pumps |
| BD+ | Decreased ξ by 0.006 | Decreased by 5 pumps | |||
| Behavioral Consistency (τ) | BD+ < HC | –4.034 | BD+ | Increased τ by 4.034 | Increased by 8 pumps |
| HC | Decreased τ by 4.034 | Decreased by 11 pumps | |||
| BD– < HC | –3.749 | BD– | Increased τ by 3.749 | Increased by 2 pumps | |
| HC | Decreased τ by 3.749 | Decreased by 12 pumps | |||
| Loss Aversion (λ) | BD+ < BD– | –0.849 | BD– | Decreased λ by 0.849 | Increased by 21 pumps |
| BD+ | Increased λ by 0.849 | Decreased by 11 pumps | |||
| BD+ < HC | –0.772 | HC | Decreased λ by 0.772 | Increased by 17 pumps | |
| BD+ | Increased λ by 0.772 | Decreased by 8 pumps | |||
[i] Note: Mean difference = to calculate the ‘mean difference’ we took the difference between the mean posterior distributions for both groups (for a given parameter) and determined the mean of the resulting distribution of differences; Adjustment (Δ Parameter Value) = indicates the direction and magnitude the parameter was changed for simulations; Outcome (Δ Adj. Pumps) = change in the overall adjusted average number of pumps that resulted from the change in parameter value shown in the ‘adjustment’ column (relative to adjusted pumps using true parameter values), averaged across 50 simulations.