PMC

A generic ROC curve is shown along with lines of iso-utility as defined in . The iso-lines partition the domain into regions of higher utility (upper left) from lower utility (lower right). The relative utility (U_Rel) and the odds ratio for disease prevalence (Q_π) define the slope of iso-utility lines. The optimal operating point on the ROC curve is tangent to an iso-utility line.

Value Function Ratio vs. Consumption Ratio. This figure depicts the ratio and for different EIS and risk aversion. In all graphs, the solid lines represent the results for time-additive utility (CRRA) where the EIS is and . In the upper graphs, we vary the risk aversion and fix the EIS at . The dashed lines are the results for recursive utility (Rec1) with and . The dashed-dotted lines are the results for recursive utility (Rec2) with and . In the lower graphs, we vary the EIS and fix the risk aversion at . The dashed lines are the results for recursive utility (Rec3) with and . The dashed-dotted lines are the results for recursive utility (Rec4) with and .

Estimating riskless utilities from the stochasticity in safe–safe choices. a Measuring stochasticity in choices between safe two reward options. Example visual stimuli (top) representing choices between safe rewards (A: low, B: high) resulting in different percentage of choices for the high option (bottom; black dots). This was repeated for different reward option sets, centered at different increments (midpoints). For each midpoint, the likelihoods were fitted with a softmax curve (dashed), used to estimate the probability of choosing the larger option for a gap of 0.03 ml (gray dot). b Choice ratios as differences in utility. The likelihoods that monkeys would pick the better reward were transformed using the inverse cumulative distribution function (iCDF) of a logistic distribution. The utility of different rewards took the form of equally noisy distributions centered at the true utilities. The output of iCDFs is the distance between these random utilities (i.e. the marginal utility). c From marginal utilities to utility. The cumulative sum of marginal utilities approximated a direct utility measure for each midpoint. These measurements were normalized whereby the utility of the highest midpoint was 1, and the starting midpoint had a utility of 0. d Daily strength of preference estimates. Each point represented the temperature of the softmax curve fitted on the choice ratios (blue points: average across days). The lower the temperature parameter, the steeper was the softmax curve and the more separable were the random utilities. Lower values meant higher marginal utility measurement (steeper utility function), higher ones meant lower marginal utility (flatter function). e Daily choice ratio estimates from softmax fits. Estimates from the same day are linked by grey lines. Ratios of 0.5 meant that the random utility of the two options were fully overlapping (i.e. flat utility function); choice ratios closer to 1 meant random utilities that were fully dissociated and non-overlapping. f Utility functions. Utilities estimated in single days (grey lines) and averages (blue), normalized relative to the minimum and maximum midpoint

Fraction correct of carcinoembryonic antigen, carbohydrate antigen, neutrophil-to-lymphocyte ratio, platelet-to-lymphocyte ratio and systemic immune-inflammation index. ¹Fraction correct (FC) overall utility good; ²FC overall utility acceptable; ³FC overall utility poor. CEA: Carcinoembryonic antigen; CA19-9: Carbohydrate antigen; NLR: Neutrophil-to-lymphocyte ratio; PLR: Platelet-to-lymphocyte ratio; SII: Systemic immune-inflammation index.