Preference for Safe Over Risky Options in Binge Eating

Binge eating has been usually viewed as a loss of control and an impulsive behavior. But, little is known about the actual behavior of binging patients (prevalently women) in terms of basic decision-making under risk or under uncertainty. In healthy women, stressful cues bias behavior for safer options, raising the question of whether food cues that are perceived as threatening by binging patients may modulate patients’ behaviors towards safer options. A cross-sectional study was conducted with binging patients (20 bulimia nervosa (BN) and 23 anorexia nervosa binging (ANB) patients) and two control groups (22 non-binging restrictive (ANR) anorexia nervosa patients and 20 healthy participants), without any concomitant impulsive disorder. We assessed decisions under risk with a gambling task with known probabilities and decisions under uncertainty with the balloon analog risk taking task (BART) with unknown probabilities of winning, in three cued-conditions including neutral, binge food and stressful cues. In the gambling task, binging and ANR patients adopted similar safer attitudes and coherently elicited a higher aversion to losses when primed by food as compared to neutral cues. This held true for BN and ANR patients in the BART. After controlling for anxiety level, these safer attitudes in the food condition were similar to the ones under stress. In the BART, ANB patients exhibited a higher variability in their choices in the food compared to neutral condition. This higher variability was associated with higher difficulties to discard irrelevant information. All these results suggest that decision-making under risk and under uncertainty is not fundamentally altered in all these patients.

Gains and losses of gambles are computed according to the sure payoff. Indeed, if a participant has to choose between 1€ for sure and 4€ with 25% of chances to get it, choosing the gamble will lead to 0€ in 75% of cases and thus to a relative loss of 1€ compared to the sure payoff. Similarly, in 25% of cases, it will lead to a 3€ gain. We therefore computed gains as the difference between the gamble payoff in case of winning and the sure payoff. Losses were set to the amount of the certain payoff.
Participants would therefore choose the gamble if the perceived payoff computed by equation 1 is higher than the certain payoff proposed. We therefore fitted a logistic model over participants' choices following the same reasoning as for the hyperbolic discounting function: For each participant, parameters were estimated by maximizing the log likelihood (i.e. minimizinglog(likelihood)) with matlab fminsearch function the error between fit and participant's choice. In order to avoid to fall into a local minimum when running the fminsearch function, we run it for all combinations of initializations among a set of 3 different initializations for each parameter of equation 1: 0.1, 0.5 and 1. The fit with the highest log likelihood was selected.

Fitting Wallsten model over participants' choices at BART
Wallsten & al. proposed a derivative model of equation s1.1. This model includes the same parameters of aversion to losses, sensitivity to gains and losses as in equation s1.1 but also adds a learning parameter that take into account the learning of probabilities for each balloon to explode across balloons. However, compared to equation s1.1, perception of probabilities are replaced by a model of the estimation process made by participants of the probability of balloons to explode based on the number of inflates done in the previous balloons. This leads to equation s1.4: ) ) * ) 1 (( Where β+ and β-measures the sensitivity to the magnitude of the reward (either positive for gains or negative for losses), θ, aversion to losses, ρ, learning rate, i the number of pumps, x, the quantum of money won at each inflate, and pi represents the probability for the balloon to explode at pump i. As the learning process occurs across all balloons and we compared conditions between them, the estimate of pi by each participant based on the previous number of inflates done for the previous balloons and on participants a priori before the first balloon would be the same for each condition. Therefore, we replaced this model of probabilities estimate by the true probability for the balloon to explode at pump i. This limits non linearities in equation s1.4 and therefore leads to a more reliable estimation of parameters of equation s1 In order to avoid to fall into a local minimum when running the fminsearch function, we run it for all combinations of initializations among a set of 4 different initializations for each parameter of equation 1: 0.1, 1 and 2 for β+, β-and θ, and 0.1, 1 and 1.5 for ρ. The fit with the highest log likelihood was selected.

Reaction time at BART
A linear mixed model was carried out first within each group of binging participant. Reaction time was modeled as a function of the condition (Food/Neutral/Stress), type of choice (pump/save balloon), their interaction and participants as a random factor over the intercept. The stressful condition was added to improve the estimate of the variance of each condition. Second, a linear mixed model was carried out between binging participants and ANR.

Neutral condition
At the BART task, the rate of balloons saved (p=0.87, figure 1B), average number of pumps (p=0.55, supplementary figure 3) and standard deviation of the number of pumps per balloon (p=0.94, figure  1B) were similar. The rate of certain payoff when the gamble probability is at 50% at the gambling task (p=0.73, figure 1C), loss aversion in the gambling task (p=0.46, figure 3) and in the BART (p=0.46), perception of gains and losses in gambling task (p=0.63 and p=0.48 respectively, figure 3) and in the BART (p=0.33 and p=0.35 respectively), decision making duration computed by the DDM (p=0.87) and relative bias toward the sure option at gambling task (p=0.64) were also similar between the four groups.

Association between age and food specific parameters of the two tasks
Age did not correlate with the food specific rate of balloons saved, average number of pumps per balloon won, standard deviation of number of pumps per balloon won at the BART and rate of choices of the safe option at the gambling task in ANR and ANB patients (r ANR+ANB =0.1, p=0.58; r ANR+ANB =-0.13, p=0.47; r ANR+ANB =-0.08, p=0.64; r ANR+ANB =0.03, p=0.86; respectively).

BART task
BN and ANR patients were slower to inflate a balloon in food compared to neutral condition (mean difference (standard error of the mean (SEM)): 41ms (  Parameter estimates of the differences between food specific and stress specific differences within patients for the parameters of the BART and the gambling tasks that exhibited differences between neutral and food conditions. Mean (Standard Error of the Mean, (SEM)) are reported for the estimates of the difference between stress specific (difference between stressful and neutral conditions) and food specific (difference between food and neutral conditions) differences for the dependant variable after regressing out the magnitude of the anxiety. A positive value means that the difference is stronger for the stress specific difference.