Investigating Associations Of Delay Discounting With Brain Structure, Working Memory, And Episodic Memory Part 2

Relationship between structural predictors and DD

We tested for associations between the variables of interest (subcortical volumes, gray matter and white matter components, EM, WM) and DD with linear models and nonparametric permutation tests as implemented in FSL’s PALM software version 1.11 (Winkler et al. 2014; Winkler, Webster, et al. 2016b) running on MATLAB R2017b. 

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We used 10,000 permutations, modeling the tail of the permutation distribution of P-values with a Pareto distribution (Winkler, Ridgway, et al. 2016a), and family-wise error rate (FWER) control for multiple tests using the distribution of the maximum statistic (Westfall and Young 1993). The HCP dataset contains subjects who were sampled along with their siblings (mostly their twins), which means that the measurements cannot be regarded as independent. 

To test for associations between variables of interest while accounting for the family structure in the dataset, we used multilevel block permutation testing (Winkler et al. 2015). These associations were corrected for linear and quadratic age terms, sex, education, income, and the cognitive function composite score of the NIH Toolbox (“CogTotalComp_Unadj”), a measure of general intelligence. We report 2-tailed P-values for the associations tested.

Vertex- and voxel-wise analyses

For comparison, we also performed separate univariate vertex-wise (cortical thickness, surface area) and voxelwise (GMV, FA, MD) analyses to test for associations with DD. These analyses were performed using nonparametric permutation tests as implemented in FSL’s PALM software, with 2,000 permutations, and threshold-free cluster enhancement (Smith and Nichols 2009). As in the previous analyses, we modeled the tail of the permutation distribution of P-values with a Pareto distribution, applied FWER control for multiple tests using the distribution of the maximum statistic, and accounted for family structure with multilevel block permutation testing. Like above, these analyses were controlled for linear and quadratic age terms, sex, education, income, and general intelligence.

Results

We excluded subjects with incomplete responses in the DD tasks (3), who chose either always immediate or delayed responses (9), or for whom the posterior probability of the pseudo-R2 statistic (Camerer and Ho 1999) being above zero was below 0.95, i.e. subjects for which the model fitted responses better than a chance model (166). These criteria led to the exclusion of 178 subjects from the HCP sample. Table 1 displays demographic information about the samples and the number of valid observations for the different cognitive tasks and imaging modalities that were analyzed about DD. The subjective value of rewards was on average 79% of their nominal value after a month and 23% after a year. Gender differences in DD were not significant (male (n = 473) > female (n = 545): t = 0.27, P = 0.80).

Relationship between DD and gray matter

After correcting for linear and quadratic age terms, sex, and total intracranial volume, the discount rate was not associated with total cortical volume or the volume of any of the subcortical structures investigated. Table 2 displays the statistics for these associations.

Cortical thickness, surface area, and GMV maps were decomposed jointly with linked-ICA in 50 components, each of them defining a spatial map reflecting the regions where gray matter structure covaried strongly across participants and individual scores indicating the magnitude of the component’s contribution. The scores of one of the gray matter components were significantly negatively associated with DD (Fig. 2A, r = −0.172, Pcorr < 1e−4, corrected for the 50 components tested, n = 946). 

Out of the 3 gray matter modalities, this component weighted most heavily (62%) on GMV (Fig. 2B), and its largest loadings were in the temporal pole and precuneus (Fig. 2C and D). Because ICA suffers from sign indeterminacy, the scores of a component have to be interpreted concerning its loadings (whose anatomical distribution is represented by the corresponding spatial map), i.e. a negative association with the scores of one component reflects a (partial) negative correlation with gray matter structure measurements in the areas where the values of its loadings are positive. These associations were corrected for linear and quadratic age terms, sex, education, and income. 

When decomposing the data in 100 components, similarly only one component was significantly associated with DD, showing a pattern very similar to the one retrieved with the 50-component decomposition (Fig. 2E–G, r = −0.158, Pcorr = 5e−4, corrected for the 100 components tested, n = 946). The univariate voxel-wise analysis also revealed a negative significant association between GMV and DD in bilateral temporal gray matter regions after controlling for linear and quadratic age terms, sex, education, and income (Supplementary Fig. 2). 

These regions matched closely the spatial pattern for the gray matter component identified (Fig. 2C and G). There was no cortical region where the association between DD and cortical thickness or area was significant after FWER correction for multiple tests in the surface-based vertex-wise analysis for these measures.

To ensure that the association with gray matter scores was specific to DD and not merely reflecting general cognitive function, we repeated these analyses adding a measure of general intelligence to the set of covariates of no interest. The same component was still the only one that was significantly associated with DD (50-component decomposition: r = −0.145, Pcorr = 0.001; 100-component decomposition: r = −0.138, Pcorr = 0.123), and the result of the univariate voxel-wise analysis remained largely unchanged (Supplementary Fig. 2).

Relationship between DD and white matter

We decomposed the FA and MD data jointly into 50 components. None of the components were associated with the discount rate after controlling for multiple tests and covarying for linear and quadratic age terms, sex, education, and income. Using 100 components or controlling additionally for general intelligence yielded similar results. Correspondingly, there was no region where the association between DD and FA or MD was significant after FWER correction for multiple tests in the voxel-wise analysis.

Discussion

After examining behavioral and neuroimaging data from a large sample of healthy adults, our findings show that greater DD was predicted by smaller anterior temporal GMV. The size of the HCP dataset sample, larger than that from most previous studies linking DD and brain structure, granted us the power to reliably capture effects of a small magnitude. However, in contradiction with former reports, we found no evidence of a reliable association between DD and cortical volume, subcortical volumes, white matter microstructural organization, and scores in WM or EM tasks.

Greater discounting was associated with smaller GMV in anterior temporal regions. This result was robust to changing the number of linked ICA components and controlling for a measure of general intelligence. Owens et al. (2017) analyzed cortical volume from T1-weighted scans in the HCP dataset and reported associations between cortical volume and DD in temporal regions corresponding to the areas in the gray matter component identified by our analysis. 

The association with anterior temporal gray matter is expected (as we used the same dataset), but our study extends the previous one by also examining cortical thickness and surface area and GMV for subcortical regions, as well as measures of white matter structure. Beyond the fact that we have included a more thorough set of structural measures, we respected the family structure of the data in computing the associations between brain structure measures and DD to avoid biased estimates that may ensue from incorrectly assuming independence of the observations (Winkler et al. 2015). 

We also performed a more stringent selection of subjects, excluding those who were performing at the chance, and decomposed the data in structural covariance networks (Pehlivanova et al. 2018), a method that affords greater sensitivity to detect associations with DD by averaging together (in a weighted manner) values of the structural images across brain regions and combining several modalities to produce more robust estimates. Indeed, an important advantage of using ICA to decompose imaging data in covariance networks over a voxel-wise approach for analysis of structural data is that it yields scores that should be less noisy than voxel-based values because they are obtained as a weighted average of the signal in all voxels across the brain, implementing dimensionality reduction that may decrease the risk of type II errors, albeit at the expense of a vaguer anatomical delineation.

anatomical delineation. In contrast to the study by Owens et al. (2017), in our analysis, the relationship between cortical volume and DD did not reach significance. This divergence is likely to be the product of our more stringent analysis choices (removal of subjects responding at random, nonparametric tests accounting for data family structure, stricter control for confounds) and indicates that the previously reported association between cortical volume and DD corresponds possibly to a spurious rather than a robust finding. It seems plausible that an association of DD with a measure of global cortical volume should be mediated by variables that reflect more general aspects of cognition than DD.

Despite the large sample size of the HCP dataset, we found no evidence of a significant association between white matter structure and DD. Previous studies showing tractographic reconstructions in smaller samples have reported negative associations between DD and structural connectivity strength measures (e.g. number of streamlines) in specific white matter tracts to the PFC (van den Bos et al. 2015; Hänggi et al. 2016; Hampton et al. 2017). 

In contrast with those studies investigating connectivity strength, we analyzed FA maps processed with TBSS, a technique that enables a wide-ranging analysis of white matter regions and is more suitable for exploratory analysis of large-scale datasets, due to the computational and labor costs associated with performing comprehensive tractography mapping on a large number of subjects. To our knowledge, the sample in our analysis is substantially larger than in previous studies linking white matter to discounting. We note, however, that a recent study employing TBSS on 302 older subjects without dementia (Han et al. 2018) (mean age = 81.38 years, SD = 7.57 years, 75.5% female) reported widespread negative associations between temporal discounting and FA in bilateral frontal, frontostriatal, and temporoparietal tracts. The disagreement with our results may respond to demographic differences in the samples. 

Given the extensive nature of their associations, their findings may be reflecting aging-related degenerative mechanisms, as opposed to the more confined pattern that would be expected for a specific measure such as DD. Besides, Han et al. did not control for income level. Indeed, when only adjusting for age and sex in our analysis, we identified further gray and white matter components that had scores significantly correlated with discount rates (see Supplementary Material). While large samples are capable of detecting smaller effects, there is also a higher risk of detecting associations merely produced by confounding variables, which makes it key to adjust for the appropriate covariates.

Recent work (Marek et al. 2022) has emphasized the importance of using large samples in brain-wide brain–behavior association studies and shown that typical sample sizes for these studies should lead to irreproducible effects and inflated effect sizes. Assuming that the true effect is about 0.15 (comparable to the effect size for the gray matter component, we identified and compatible with the results from Marek et al. 2022), over 250 subjects would be needed to achieve a power of 80%. Most previous studies in the area of DD have thus been underpowered, which explains the literature inconsistencies mentioned in Section 1. Please note that this conclusion applies to brain–behavior associations only and not too functional brain mapping studies on DD, which should require smaller sample sizes to detect true effects, and therefore, there is no contradiction between our results and findings from those studies.

We could did not find an association between a preference for immediate rewards and any of the WM tests (LSWMT and 2-back). Similarly, there was no association of DD with either verbal or nonverbal EM in the HCP data. These results are in line with a recent study (Yeh et al. 2021), which we complement by including the 2-back task and a more strict statistical treatment, for the analysis of brain structural data. Although Shamosh et al. (2008) reported a link between lower WM and a preference for immediate rewards, this correlation was not specific to WM, as in their data this ability did not explain variance in DD beyond that explained by general intelligence. When correcting the associations for age and sex only, DD was significantly negatively correlated with LSWMT, 2-back, and verbal EM scores (see Supplementary Material), but this correlation was no longer significant when adjusting for socioeconomic status variables (which should already account partly for general cognitive function). Thus, our considerations above regarding spurious associations due to nuisance variables and irreproducible findings when using small samples also apply to these analyses.

A limitation of our study is that our analyses were not preregistered, and therefore, the reported associations cannot be regarded as confirmatory. Nevertheless, we believe that an important contribution of these results is in providing more precise estimates of effect size for relationships between cognitive measures, structural imaging, and intertemporal choices due to the considerably larger sample size of previous studies. Another limitation is the low reliability of discount rates. Task parameters have been criticized for their low test–retest reliability (Enkavi et al. 2019) and, in the related domain of risk preferences, for lacking consistency across experimental paradigms (Pedroni et al. 2017). These reasons may partly explain the paucity of associations with brain structure we found and the low reproducibility of findings across studies. A crucial future avenue should then be to design novel paradigms to measure DD with improved reliability. A possible way forward may lie in deriving summary scores combining several task parameters to achieve higher reliability and using multivariate methods to increase the chances of finding brain–behavior associations (Moutoussis et al. 2021).

Considering the importance of DD in the study of psychopathology, it is fundamental to robustly determine its underlying neurobiological scaffolding. By leveraging a large neuroimaging dataset, the present study helps reconcile disparities in the literature on gray and white matter correlates of DD. This behavioral trait was negatively associated with GMV in anterior temporal regions and, importantly, the structural effect identified was small, such that it would be unlikely to be detected in samples with a size comparable to that found in many related studies. All in all, associations with cognitive abilities and brain structure may be feebler than previous reports suggest. Our results call for the development of more robust measures of DD and the implementation of neuroimaging studies of larger sample sizes than what has been common in the field as well as appropriate control for possible confounders.

Acknowledgments

We thank Mats Erikson and Kajsa Burström for collecting the data. We are grateful for the open-access dataset provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657).

Supplementary material

Supplementary material is available at Cerebral Cortex online.

Funding

This work was supported by the Swedish Research Council (grant number VR521-2013-2589 to MG-M), an Alexander von Humboldt Research Award (LB), and a donation from the AF Jochnick Foundation (LB).

Conflict of interest statement: Dr Zeb Kurth-Nelson is employed by DeepMind. The remaining authors declare no conflict of interest.

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