Tolerance for risk

Risk preferences were assessed using a well-validated, incentive-compatible procedure4,9,10,11,12,13. Fifty-two participants (18–88 years old, mean: 54.7, s.d.:22.1; 30 females) made 60 binary choices between a certain gain of $5 and a lottery whose monetary value and probability of payout were systematically manipulated (Fig. 1). We modelled the expected utility (EU) of each option using the functional form:

Figure 1: Experimental design. (a) Example lotteries representing a 25, 50, 75% chance of gaining $15, $7, $30, respectively. (b) Example trial sequence. Full size image

where v=value (amount), p=probability, and α (alpha)=the risk preference parameter, with larger alpha values indicative of increased risk tolerance (that is, risk aversion increases as alpha decreases). Choice data were fit, and alpha estimated, using maximum likelihood, with the probability of choosing the lottery (P lottery ) given by a logistic function:

where EU safe (EU lottery ) indicates the EU of the certain (lottery) option, and σ indicates the slope of the choice function. To account for within and between participant variabilities in an assumption-free and statistically rigorous manner, we fit choice data from all participants simultaneously, clustering the standard errors to account for participant-level correlations7,14,15.

rPPC grey matter volume

Using voxel-based morphometry (VBM), we sampled GMV in the rPPC region-of-interest, which was defined independently based on an earlier study (Fig. 2a; MNI coordinates 27, −78, 48; spatial extent, 1,232 mm3; from ref. 7, Study 1; mask download available at https://yale.box.com/v/levylab-gilaie-dotan-etal-2014). In Fig. 2b, rPPC GMV is plotted as a function of age and confirms that GMV in our parietal region-of-interest does indeed decrease with age in our lifespan sample (Pearson correlation, n=52, r=–0.66, P=1.1–07).

Figure 2: rPPC grey-matter volume accounts for risk tolerance after controlling for age. (a) A priori defined region of interest: right posterior parietal cortex (rPPC). (b) rPPC grey matter volume plotted as a function of age for individual participants (n=52). (c) rPPC grey matter volume plotted as a function of risk tolerance for individual participants. (d) Risk tolerance as a function of age, controlling for rPPC grey matter volume, plotted for individual participants. (e) Risk tolerance as a function of rPPC grey matter volume, controlling for age, plotted for individual participants. Full size image

Brain-behaviour relationships

To assess the relationship between risk preferences and our variables of interest we allowed alpha, the risk preference parameter, to vary during the estimation procedure as a linear function of age (Model 1: α=β 1 × age+β 0 ) and rPPC GMV (Model 2: α=β 1 × rPPC GMV+β 0 ). As predicted by previous research4,7, we found a significant negative relationship between alpha and age (Z-test, n=3,077, s.e.’s clustered on 52 participants, z=–2.58, P=0.01; Table 1, Model 1) and a significant positive relationship between alpha and rPPC GMV (Z-test, n=3,077, s.e.’s clustered on 52 participants, z=3.51, P=0.0004; Table 1, Model 2). Controlling for gender in each model revealed no effect of gender on risk tolerance and did not qualitatively change the relationship between risk tolerance and age/rPPC grey matter (Table 2). To illustrate the positive correlation between risk tolerance and parietal grey matter, choice data were modelled at the individual level and the risk tolerance parameter derived from those fits (alpha) is plotted as a function of each individual participant’s rPPC GMV in Fig. 2c.

Table 1 Estimated coefficients and Bayesian Information Criteria values for each model. Full size table

Table 2 Estimated coefficients for each model. Full size table

Does the decline of rPPC GMV in fact account for the age-related increase in risk aversion? To answer this question we employed a standard econometric approach to obtain an unbiased estimate of the degree to which age-related variation in risk attitude can be attributed more parsimoniously to GMV: we allowed alpha to vary with both age and rPPC GMV (Model 3: α=β 1 × age+β 2 × rPPC GMV+β 0 ) and again found a significant positive relationship between alpha and rPPC GMV (Z-test, n=3,077, s.e.’s clustered on 52 participants, z=2.13, P=0.033). Critically, however, when the linear regression was computed in this manner, age no longer had any influence on alpha (Z-test, n=3,077, s.e.’s clustered on 52 participants, z=–0.24, P=0.81), indicating that rPPC GMV, and not age per se, modulates risk preferences (Table 1, Model 3). To illustrate this effect for individual participants, we plot the independent contributions of these two factors on risk preferences: alpha as a function of age after regressing out the contribution of rPPC GMV (Fig. 2d) and as a function of rPPC GMV after regressing out the contribution of age (Fig. 2e). A schematic of the main results is presented in Fig. 3.

Figure 3: Overview. Schematic presentation of results. Full size image

Two additional models confirmed that these results are specific to local grey matter decline in the rPPC, rather than global, age-related changes in grey matter thickness. When global GMV (Model 4: α=β 1 × rPPC GMV+β 2 × global GMV+β 0 ) and global GMV+age (Model 5: α=β 1 × age+β 2 × rPPC GMV+β 3 × global GMV+β 0 ) were included, increased rPPC GMV still predicted increased risk tolerance (Z-tests, n=3,077, s.e.’s clustered on 52 participants, z=2.09, P=0.037, Model 4; z=1.95, P=0.051, Model 5), whereas neither global GMV nor age did (Table 1). Bayesian Information Criteria16 values indicate that these final two neurobiologically comprehensive models best characterize the choice process, despite the penalties incurred for additional parameters (Table 1). Finally, to ensure that our results do not depend on the functional form of the model, we used multiple regression to determine if individual age and rPPC GMV can predict the proportion of lottery choices that each participant made, with fewer lottery choices indicative of greater risk aversion: proportion of lottery choice=β 1 × age+β 2 × rPPC GMV+β 0 . We found converging evidence that rPPC GMV, but not age, accounts for changes in risk preferences using this model-free approach (T-tests, n=52, β 1 =0.00, t=0.77, P=0.78; β 2 =1.31, t=1.85, P=0.035; ps one-tailed in predicted directions).

While the primary aim of the current study was to test a specific hypothesis regarding the rPPC’s role in modulating age-related changes in risk tolerance, we also conducted an exploratory whole-brain VBM analysis to evaluate whether GMV is predictive of risk tolerance in any additional brain regions. In a voxel-wise manner, multiple regression was used to compute the linear relationship between risk tolerance and GMV, controlling for age, gender and global GMV. No clusters showed a significant relationship between GMV and risk tolerance after the stringent corrections needed to combat false discoveries in exploratory whole-brain analyses. Given that this is the third independent data set showing a significant relationship between rPPC GMV and risk tolerance, the likelihood that we are reporting a repeated false discovery is extremely low. While we cannot definitively rule out the possibility that additional regions’ structure and function contribute to age-related changes in risk tolerance, our a priori hypothesis-driven ROI analyses point to a clear role of the rPPC in these processes.

Choice data were collected in a magnetic resonance imaging (MRI) scanner during the acquisition of functional scans (manuscript in preparation). Although in theory the scanner environment may affect individual risk attitudes, we note that age-based estimates of risk tolerance derived from Model 1 are comparable to those obtained outside the scanner: the risk tolerance parameter (alpha) is predicted to drop slowly with each passing year, from 0.61 at 21 years of age to 0.42 by 90 years old. These estimates of risk tolerance fall within the 95% confidence intervals for age-specific alpha values reported previously by our group4 in a task where choices were made on a desktop computer.