Age differences in the neural basis of decision-making under uncertainty

Humans globally are reaping the benefits of longer lives. Yet, longer life spans also require engaging with consequential but often uncertain decisions well into old age. Previous research has yielded mixed findings with regards to life span differences in how individuals make decisions under uncertainty. One factor contributing to the heterogeneity of findings is the diversity of paradigms that cover different aspects of uncertainty and tap into different cognitive and affective mechanisms. In this study, 175 participants (53.14% females, mean age = 44.9 years, SD = 19.0, age range = 16 to 81) completed functional neuroimaging versions of two prominent paradigms in this area, the Balloon Analogue Risk Task and the Delay Discounting Task. Guided by neurobiological accounts of age-related changes in decision-making under uncertainty, we examined age effects on neural activation differences in decision-relevant brain structures, and compared these across multiple contrasts for the two paradigms using specification curve analysis. In line with theoretical predictions, we find age differences in nucleus accumbens, anterior insula, and medial prefrontal cortex, but the results vary across paradigm and contrasts. Our results are in line with existing theories of age differences in decision making and their neural substrates, yet also suggest the need for a broader research agenda that considers how both individual and task characteristics determine the way humans deal with uncertainty. Supplementary Information The online version contains supplementary material available at 10.3758/s13415-022-01060-610.3758/s13415-022-01060-6.


Power analyses and sample characteristics
For the larger research study we recruited a convenience sample of 200 healthy, right-handed adult human volunteers between 16 and 81 years of age. The original sample size was informed by power analyses in G*Power using standard methods under the assumption of using linear regression models to estimate age e ects on the primary outcomes of interest. A sample larger than 80 participants was determined to yield 80% power to detect medium e ect sizes in a cross-sectional analyses. The comparatively larger recruited sample reflects our interest in investigating individual di erences, as well as our initial intention to extend the study to a longitudinal design; both components require a su ciently large (initial) sample to achieve and retain su cient power. Simulation methods assuming the use of bivariate latent growth curve models suggested 200 individuals to be su cient to detect medium size e ects with 80% probability in longitudinal analyses.
To ensure participants' safety during the neuroimaging session, we conducted a thorough screening for any contraindications to MRI safety, and excluded individuals if they reported having permanent implants (e.g. pacemaker, cochlear implant, neurostimulator, insulin pump), claustrophobia, tinnitus, epilepsy, permanent metal in or on the body (e.g., surgical clip, metal splinter, metal prosthesis, copper coil, artificial heart valve), had previously had heart or brain surgery, reported su ering from any conditions which prevented them from lying (comfortably) still inside the scanner, were pregnant, or reported the use of prescribed medication which could interfere with cognitive and neural function. Figure A1 summarizes the study's e ective sample (N=175) with regards to its (socio)demographic characteristics.

Figure A1
Demographic and sociodemographic characteristics of the study sample (N=175).

BART reward functions
In this study we introduced two balloons with the same maximum capacity but for which the accumulation of reward was driven either by a linear or an exponential reward function ( Figure A2). We formalized the di erence between the linear and exponential reward balloons as follows: To get a better intuition about the exponential function describing these explosion probabilities, it is informative to start at the end: given all 15 previous pumps were successful and did not lead to an explosion, the balloon will definitely explode after the 16th pump (probability = 100%). In contrast, given all 14 previous pumps were successful and did not cause an explosion, the 15th pump has an explosion probability of 50% because the 15th pump (for a balloon with a maximum capacity of 16) can either explode and finish the trial, or not explode and result in the possibility for one last pump. Based on the conditional explosion probability, we computed the Expected Value ( Figure A2, right panel) for a given pump and balloon type as: where ntrials = 20 (the average number of trials per balloon type completed in previous studies with similar length and maximum pumps).

Preprocessing of neuroimaging data
We processed the raw images from from the BART and the delay discounting task in the same way. First, we used a two pass procedure to spatially realign

Figure A2
Risk and reward in the fMRI version of the BART.
participants' functional volumes to the series' mean image, saving out realignment parameters for six directions (three parameters for translation, three parameters for rotation). Second, to account for the interleaved (bottom-to-top) acquisition of the functional volumes, we implemented a standard SPM12 slice time correction routine.
Third, we coregistered the spatially and temporally realigned functional volumes to the structural (T1-weighted) volume via maximization of a normalized mutual information objective function. Fourth, we segmented participants' structural volumes, and applied the information gained from the segmentation routine to the normalization of the functional volumes from native to MNI space via individuals' structural volumes. Fifth, we smoothed the realigned, coregistered and normalized functional volumes using a 4 mm full-width half-maximum Gaussian kernel (Sacchet & Knutson, 2013). To account for the heterogeneity of the current sample with regards to age and the impact this may have on automated preprocessing routines, we manually inspected all functional volumes of all participants, but found no evidence for suboptimal or failed normalization or misalignment. However, inspection of the realignment parameters saved out for each functional run identified two participants with excessive head motion, defined here as motion with >4 mm absolute volume-to-volume translational di erences; these were excluded from all further analyses. The e ective sample thus included 175 participants.

Individual-level contrast analyses for the BART
All contrast analyses were set up in the same general linear model by concatenating over the two BART runs. The structure of the BART allows for di erent ways of aggregation, e.g., over trials (i.e., over a sequence of balloon displays until the participant decides to cash out or the balloon explodes) or displays (i.e., individual displays and decisions within a trial). Looking at the top row in Figure 1, for a trial, we would aggregate and model activation over the entire row of events (e.g., across the first four balloons), whereas for a display, we would aggregate and model activation separately for each of the first four balloon display appearances. We specified a variable epoch model to capture neural activation over the course of one balloon display (that is, from balloon display onset to balloon display o set once a decision to pump or cash-out was recorded). We modeled each balloon display as a boxcar function, with the length being equal to the participant's balloon-specific reaction time (i.e., the time from display onset until a choice was recorded). In the general linear model, we included separate onset vectors for linear, exponential and control balloons (i.e., displays), as well as parametric modulation regressors for each of these balloon types, reflecting the demeaned pump number with regard to the entire trial. To explicitly model and thus remove other trial-relevant events from the implicit baseline activation, we also included onset vectors for explosions, as well as the six head motion parameters estimated during the spatial realignment procedure. Although the completion of the BART was self-paced, all participants completed a su cient number of linear (mean=20.50, median=20, range=15-25), exponential (mean=20.45, median=20, range=14-26), and control (mean=20.59, median=21, range=15-27) balloon trials for analysis.

Individual-level contrast analyses for the delay discounting task
Mirroring contrast analyses for the BART, we specified one general linear model for all analyses, and used boxcar functions with individuals' trial-specific reaction time to model activation di erences in the delay discounting task, from display (trial) onset to display (trial) o set. For delay discounting, we thus define a trial as the period from the onset of the display presenting a choice between a smaller-sooner and a larger-later option to the o set of the display once a choice is recorded (or five seconds have elapsed without a response being recorded). To specifically capture neural activation associated with the "temporal uncertainty" aspect of choices between smaller sooner and larger later rewards, we sorted and contrasted (a) trials with and without an immediate option, and (b) trials with shorter (two weeks) and longer (four weeks) delays. In other words, we did not focus our analyses on capturing age di erences in the neural representation of the subjective value of choice options, or, put di erently, in identifying age e ects on activation di erences tracking subjective value (cf. Seaman et al., 2018).

Volumes of Interest
In addition to selecting VOIs based on theoretical accounts of their involvement with particular pertinent decision processes and their potential role for driving age e ects therein (Samanez-Larkin & Knutson, 2015), we defined all VOIs structurally; that is, based on anatomical boundaries defined in the Harvard-Oxford probabilistic cortical and subcortical structural atlases (Desikan et al., 2006) to further circumvent arguments of circularity (Vul & Pashler, 2012). To create the binary VOI masks, we first saved out masks for "Frontal Medial Cortex", "Left Accumbens", "Right Accumbens", "Insular Cortex", "Left Thalamus" and "Right Thalamus" (as per atlas labels). All masks were then thresholded at 20 to exclude voxels with a less than 20% chance of belonging to the particular region of interest. As we had no hypothesis regarding laterality of age e ects, we combined the masks for left and right nucleus accumbens and thalamus. Given the theoretical focus on the anterior insular cortex

Group-level contrast analyses of brain activation di erences
Group-level activation maps are one way to visually display average activation di erences; that is, to show in which brain regions, on average, activation di erences can be observed for a given statistical (contrast) analysis. In this study we did not focus while controlling for varying combinations of covariates. By "packaging" all relevant and reasonable analytic specifications (i.e., unique models) with age as a predictor, we aimed to perform a principled yet exhaustive quantification of the e ect of age on di erent outcomes. For example, we opted to operationalize uncertainty with regards to two behavioral paradigms capturing di erent aspects of uncertainty, and for each paradigm we computed both behavioral and neural indices. We further distinguish between di erent behavioral indices, as well as between di erent contrast analyses of brain activation in response to the two paradigms, and between di erent theoretically justified brain structures (Samanez-Larkin & Knutson, 2015). Our main motivation behind performing a SCA was thus to increase methodological and outcome transparency via a multiverse approach (Steegen et al., 2016) to data analysis, allowing us to speak to the convergence or divergence of age e ects as a function of the measures we chose to capture individual di erences in decision-making under uncertainty.

Figure B1
Age-related di erences in BART performance, organized by reward balloon type.

Behavior in Delay Discounting
We performed descriptive and inferential analyses to examine behavior in the delay discounting task, in particular as a function of whether an immediate choice was presented (Immediacy), the delay between the sooner and the later option (Delay), as well as the di erence between the smaller and the larger option (Reward di erence).
The statistics reported in Table B2 correspond to Figure 4.

Table B2
Behavior in the delay discounting task (N=175).

Choice proportion (S-S) RT (sec)
Trial type M (SD) M (SD) f

Figure B3
Age-related di erences in the delay discounting task. , .
White points indicate the mean, with error bars extending to one standard deviation.

Group-level maps of activation di erences associated with decision-making under uncertainty
Group-level whole brain activation di erences for BART and delay discounting are shown in Figure B5. These group-level analyses did not inform our individual di erences analyses because we relied on theoretically defined VOIs instead of peak activation di erences observed as a result of the contrast analyses (Vul & Pashler, 2012). These analyses did not examine age e ects, as this was the focus of the individual di erences analyses using theoretically defined VOIs.

Reward balloons versus control balloons.
Average activation di erences for reward versus control balloon trials resulted in regional activation and deactivation patterns that were comparable to results reported in previous neuroimaging analyses (Rao et al., 2008;Schonberg et al., 2012;Yu et al., 2016) ( Figure B5, top panel). These included increased activation in ventral striatum, anterior insular cortex, and anterior cingulate cortex, as well as decreased activation in (ventromedial) prefrontal cortex (corrected using peak-level family-wise error correction, p<0.05).
Parametric risk. When we compared parametric modulation of activation di erences as a function of the number of pumps (i.e., number of balloon in current trial) on reward versus control balloons, we also obtained results in line with previous findings (Schonberg et al., 2012;Tisdall et al., 2020;Yu et al., 2016) ( Figure B5, second panel from the top). After controlling for multiple comparisons (via peak-level family-wise error correction, p<0.05), we specifically found that anterior insula activation di erences parametrically track number of pumps; the more pumps are administered on a given trial, the higher the insula activation di erences. Similar patterns were observed for nucleus accumbens and (ventromedial) prefrontal cortex, as well as anterior cingulate. As such, both the average reward versus control balloon contrast and the parametric modulation contrast pointed towards the involvement of a (largely overlapping) set of cortical and subcortical brain regions when participants made decisions under uncertainty in the BART. The regions we observed to show activation di erences in both BART contrasts are also in line with candidate regions postulated to be sources for age e ects by the AIM framework (Samanez-Larkin & Knutson, 2015), and thus are also regions we targeted with our VOI analyses.
Linear versus exponential rewards. The originality of the reward balloon conditions implemented in this study precluded us from making comparative statements regarding activation patterns observed in the current and in previous work. In contrast to the other two BART analyses, none of the observed voxel-wise activation di erences survived correction procedures (i.e., peak-level FWE correction, p>0.05); on average, when controlling for multiple comparisons, we found no activation di erences between reward balloons following a linear versus exponential reward function. At the level of uncorrected (p<0.001) voxel-wise activation di erences ( Figure B5, third panel from the top), we found increased (ventromedial) prefrontal cortex activation for linear versus exponential balloons, as well as a few clusters of increased activation in medial parietal cortical regions, including bilateral precuneus, as well as more lateral parietal regions (e.g., angular gyrus). However, given that none of these regional activation di erences survived correction procedures, it would be premature to conclude involvement of these regions for the contrast of interest. Moreover, the motivation for contrasting the di erent reward functions in the current analytical context was to examine whether the introduction of the exponential reward balloon would lead to di erent behavioral patterns (in particular for pumping and explosions), but behavioral analyses ( Figure 3, Table B1) yielded no evidence for behavioral di erences on the two reward balloons. We discuss potential reasons for the indi erence between the two balloon types, which could equally account for the lack of neural di erences between linear and exponential reward balloons.

Delay Discounting
Immediacy. Following previous work, we first contrasted trials that included an immediate option with trials that did not include an immediate option (Eppinger et al., 2012;McClure et al., 2004;Samanez-Larkin et al., 2011). When examining voxel-wise activation di erences that were not corrected for multiple comparisons ( Figure B5, second panel from the bottom), we obtained main e ects of increased activation in brain regions similar to those reported previously (Eppinger et al., 2012;McClure et al., 2004;Samanez-Larkin et al., 2011), including middle frontal gyrus, medial prefrontal cortex and medial orbitofrontal cortex, anterior cingulate gyrus, inferior frontal gyrus, bilateral anterior insula, bilateral caudate, as well as in more regionally extensive clusters including posterior cingulate cortex, precuneus and angular gyrus. However, mainly posterior regions including posterior cingulate gyrus, precuneus, and angular gyrus survived corrected for multiple comparisons (peak-level FWE, p<0.05) at the level of the whole brain. We also obtained a bilateral cluster of activation decreases for immediate versus delayed option trials in the occipital pole (peak-level FWE, p<0.05; not shown). To summarize, we did not find the same level of strong group-level activation di erences in frontal and (ventral) striatal regions implicated in the processing of immediate choices found in the literature (Eppinger et al., 2012;McClure et al., 2004;Samanez-Larkin et al., 2011), despite choice-compatible incentivization.
Delay. We ran a final contrast to examine whether the brain tracks the actual length of the delay, i.e., whether a di erence between the sooner and later option of four weeks may be processed di erently (e.g., as less rewarding) compared to trials involving a shorter delay of two weeks. While we distinguished between trials with and without an immediate option for the first contrast analysis, for the delay contrast we did not distinguish trials based on the respective starting points, and included 32 trials which included options that were two weeks apart in one onset vector (regressor), and specified another onset vector for the 32 trials that included a four-week delay between the sooner and later option. Assessing patterns of uncorrected activation di erences ( Figure B5, bottom panel), we observed a few small clusters of voxels with increased activation for two-relative to four-week delays, including in bilateral putamen, bilateral superior temporal gyrus, and left central operculum. We also found clusters with decreased activation patterns, most prominently in bilateral superior frontal gyrus.

Figure B5
Group-level whole brain contrast activation maps for neural correlates of decision-making under uncertainty (N=175). Summary of permutation testing analysis. The majority of SCAs on the shu ed data sets did not yield more significant (positive or negative) e ects than observed in the unshu ed data, but yielded more null e ects than observed in the unshu ed data. Note: N_null, N_pos, N_neg = null, positive, and negative age e ects obtained from the 500 shu ed data sets; dotted lines represent the number of null, positive, and negative age e ects observed in the unshu ed data.