Demographics.

Participants first completed a demographic questionnaire, as used previously [12, 38].

Intertemporal choice.

Next, participants completed the five-trial, adjusting-delay task [39] to assess intertemporal choice at each of three different bundle-size conditions (1, 3, and 9). Participants were randomly assigned to complete these conditions in either ascending or descending bundle-size order. Prior to completing any of the bundle-size conditions, participants read the following instructions [adapted from those used previously; e.g., 39]

You will now be presented with a series of choices between receiving different amounts of money at different points in time. In some questions, the amounts will be delivered all at once in lump sums. For example, you may see a question like this:

Which would you rather receive?

A. $500 now

or

B. $1000 in 3 weeks

In other questions, the total amounts of each choice option will be the same as those above ($500 and $1000), but these amounts will be delivered in installments over time. For example, you may see a question like this:

Which would you rather receive?

A. $166.67 now, $166.66 in 3 weeks, and $166.67 in 6 weeks

or

B. $333.33 in 3 weeks, $333.34 in 6 weeks, and 333.33 in 9 weeks?

These questions are hypothetical, but please choose your answer as if you will receive the money in the time frame(s) selected. Please pay close attention to the amount and time frame(s) of each option, and choose accordingly. There are no right or wrong answers in this task. Please take your time.

Fig 2 depicts the choices presented in each of the bundle-size conditions. The bundle-size 1 (BS1) condition was identical to the five-trial adjusting-delay task developed by Koffarnus and Bickel [39]. Here, participants made repeated, hypothetical choices between receiving either $1000 after a single delay (D₁) or $500 immediately. The position of these LLR and SSR options on the screen (left or right) was randomized on every question. The value of D₁ started at three weeks and adjusted after each trial based on the previous choice until reaching an indifference delay (one of 32 possible values, ranging from 1 h—25 y, in approximately logarithmic intervals), at which point the subjective values of the LLR and SSR choice options are approximately equal.

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Fig 2. Choices presented in the bundle-size 1, 3, and 9 conditions.

The delay to the first LLR in all conditions was D₁, with additional rewards in the bundle (where applicable) delivered after D₂, D₃, etc. These additional delays were equal to D₁ multiplied by the order of that delay in the series (e.g., D₂ = D₁*2, D₃ = D₁*3, etc.). The first SSR in all conditions was delivered immediately, with additional rewards in the bundle (where applicable) delivered after D₁, D₂, D₃, etc. Note that with this method of arranging delays, the interval between any two rewards in a given bundle was equal to D₁. Likewise, any given SSR in a bundle was available D₁ units sooner than its paired LLR.

https://doi.org/10.1371/journal.pone.0259830.g002

The bundle-size 3 and 9 conditions (BS3 and BS9, respectively) were identical to the BS1 condition, with the following exceptions. Both the LLR and SSR choice options comprised either 3 (BS3) or 9 (BS9) rewards delivered over time. The delay to the first LLR in both conditions was D₁, as described above, with additional rewards in the bundle delivered after D₂, D₃, etc. These additional delays were equal to D₁ multiplied by the order of that delay in the series (e.g., D₂ = D₁*2, D₃ = D₁*3, etc.; see Fig 2). The first SSR in both conditions was delivered immediately, with additional rewards in the bundle delivered after D₁, D₂, D₃, etc. Note that with this method of arranging delays, the interval between any two rewards in either bundle (LLR or SSR) was equal to D₁. Likewise, any given SSR in a bundle was available D₁ units sooner than its paired LLR.

In these BS3 and BS9 conditions, the value of D₁ was adjusted across trials as described for the BS1 condition, with the values of additional delays in the bundle adjusted accordingly. In order to ensure that the total amounts available from the LLR and SSR choice options remained constant across bundle sizes, the monetary amounts of individual rewards in the bundle were equal to the amounts from the BS1 condition divided by the bundle size (e.g., $1000/3 = $333.33). Individual reward amounts were adjusted in $0.01 increments to correct for rounding errors, where needed (see Fig 2).

Data quality.

Within the survey, data quality was monitored using four quality control questions. One was embedded in the demographics questionnaire, in which participants were instructed, as follows: “Most of the options below are colors. Please select the option that is not a color.” Response options included “red”, “yellow”, “blue”, “purple”, and “winter”, with the location of the latter randomized among the other response options. Choice of any response except “winter” was interpreted as inattention. Three additional questions were specific to the choice tasks. Because the five-trial task does not allow use of standardized diagnostic criteria to assess orderliness of obtained data [e.g., 40], these quality control questions were appended to the five-trial, adjusting-delay task, as has been done previously [12, 38]. Specifically, in each of three bundle-size conditions, a sixth trial asked participants to choose between $500 now and $1000 now. In the BS3 and BS9 conditions, these monetary amounts were framed as separate rewards, as described above for these conditions; however, all delays were removed (e.g., $333.33 now, $333.34 now, and $333.33 now). Choice of the smaller option in these questions was interpreted as inattention or atypical valuation of monetary rewards.

Data analysis.

All analyses were performed in MINITAB statistical software version 20.1 (MINITAB Inc., State College, PA). The approximate sample size was informed by a power analysis in which 260 participants provides 95% statistical power to detect at least a small (f = .10) within- and between-subjects factors interaction in repeated-measures ANOVA, assuming an alpha value of .05, two groups, three repeated measures, and a correlation between repeated measures of .50.

Participant characteristics. Participant characteristics were compared between the ascending and descending bundle-size orders using t tests and Fisher’s Exact tests, as appropriate.

Dependent measures of intertemporal choice. The dependent measure of intertemporal choice was indifference delay (in days), calculated as the adjusted value of D₁ after the final trial of the five-trial adjusting-delay task. This is similar to measures of indifference delay used and validated previously with discrete rewards [12, 39, 41, 42]. Longer values of indifference delay reflect greater willingness to wait for LLRs. Indifference delay was used as the measure of intertemporal choice, rather than the more commonly used discount rate, k [21], because choice bundling was not expected to alter discount rate directly; indeed, Eq 2 assumes a constant value of k for all rewards. Rather, choice bundling was expected to alter the cumulative discounted values of choice options, thus increasing willingness to wait for the LLR option. Indifference values were non-normally distributed (positive skew) and were thus log transformed prior to analysis.

Effects of bundle size on intertemporal choice. Effects of bundle size on intertemporal choice were examined using repeated-measures ANOVA, including bundle size (1, 3, and 9) as a within-subjects factor, order (ascending and descending) as a between-subjects factor, and a Bundle Size x Order interaction term. In the primary analysis, participants who failed one or more quality control questions were excluded. In a sensitivity analysis, ANOVA was repeated when including all participants. In both analyses, ANOVA was followed by planned within-subjects comparisons between individual bundle-size conditions, and planned between-subjects comparisons between order groups at individual bundle-size conditions. Bonferroni correction was used to maintain family-wise Type 1 error rate of .05.

Comparing model predictions to observed data. To estimate the accuracy of Eq 2 in predicting choice with bundled rewards, observed and model-predicted data were compared. Specifically, to derive predicted indifference delays in the BS3 and BS9 conditions, we input individual participants’ k values [i.e., 1/indifference delay; 41] from the BS1 control condition into Eq 2 and solved for the value of D₁ at which LLR V_bundle = SSR V_bundle. The delay value in the five-trial adjusting-delay task nearest to this calculated value was the predicted indifference delay. All LLR and SSR amount parameters in these calculations were as described in Fig 2. Next, observed log indifference delays in the BS3 and BS9 conditions were subtracted from predicted values. Difference scores greater than or less than zero would indicate that Eq 2 over- or underestimated, respectively, the effects of bundling on log indifference delay. One-sample t tests were used to determine whether these scores differed significantly from zero.

In an exploratory analysis, one-sample equivalence tests were also used to evaluate whether difference scores were equivalent to zero [43]. Specifically, in one-sample equivalence tests, the equivalence interval was defined as zero plus or minus 0.1 standard deviations in difference scores, considered a negligible effect size [44]. The one-sample equivalence test evaluates the null hypothesis that observed data are not equivalent to zero (i.e., are ≤ or ≥ the lower and upper bounds, respectively, of the equivalence interval) against the alternative hypothesis that data are equivalent to zero (i.e., are within the lower and upper bounds). In the case of significant equivalence, the 95% confidence interval of observed difference scores would fall entirely within the equivalence interval.

These one-sample t tests and equivalence tests were repeated twice: once in a primary analysis in which participants who failed one or more quality control questions were excluded, and once in a sensitivity analysis in which all participants were included.

Potential limitations and future directions.

Investigating potential moderators of bundling effects in future research may help to explain observed heterogeneity. For example, studies may be designed to examine interactions between choice bundling and various behavioral, psychological, and sociodemographic factors that are commonly associated with delay discounting [e.g., cigarette smoking; 38, 45] or moderate effects of interventions that reduce delay discounting [e.g., working memory; 20, 46]. The present study had limited statistical power to conduct such analyses because recruitment of a general sample yields relatively few cigarette smokers or members of other clinical populations. Likewise, sociodemographic diversity in this online sample was limited, with college-educated adults overrepresented and minorities underrepresented compared to prevalence in the general U.S. population [47].

Additional research may instead seek to reduce heterogeneity in choice bundling effects by using behavioral tasks that provide greater resolution in measurement. Specifically, the five-trial adjusting-delay task used here allows measurement of only 32 possible indifference delay values, ranging from 1 h to 25 years in approximately logarithmic intervals. In future research, use of the adjusting-amount [48] or other tasks that offer more granularity may increase precision of measurement, reduce heterogeneity, and facilitate comparisons of observed bundling effects to model-predicted values. Nonetheless, the five-trial task was used in the present study because it provides rapid and generally accurate estimates of choice, thus facilitating the use of statistically powerful within-subjects designs in brief online studies. Estimates of discounting from this task also show strong concordance with those from the more common, but also more time-consuming, adjusting-amount task (e.g., r=.67-.86 for monetary rewards; [20, 39, 49]). Moreover, both tasks are sensitive to the same experimental manipulations [12, 20, 39, 50, 51] and cross-sectional associations with maladaptive health behavior [12, 38, 52].

Use of alternative behavioral tasks, however, would allow determination of whether other delay discounting models [52–55] would more precisely predict observed effects. The five-trial adjusting-delay task used here generates only a single value of indifference delay, from which estimates of k from the hyperbolic model can be derived [39]. Use of this task prohibits examination of quasi-hyperbolic models that add a scaling parameter (s) to Eq 1 [54, 56], which would require methods of assessment that allow application of nonlinear regression to estimates of discounted value across a range of delays. Nonetheless, the simple hyperbolic model used here tends to account for the most variance in observed data with the fewest free parameters [42, 57–59], which supports its application in the present study. We note, however, that predicted effects of choice bundling are theoretically unique to hyperbolic or hyperboloid models of discounting [22, 24].

A final limitation regarding use of the five-trial task in the present study is that unrealistic delays are possible at large bundle sizes, particularly in the BS9 condition. For example, the two longest possible delays on the final trial in this task are 12 years and 25 years. When multiplied by the total number of delayed rewards in the BS9 condition, these would produce delays to the final reward of 108 and 225 years, respectively, in the LLR option; and 96 and 200 years, respectively, in the SSR option. Thus, the more distal rewards in the chosen bundle may exceed participants’ expected lifespan and impact choice in an unpredictable manner. Despite this potential limitation, we note that these unrealistic delays (if contacted) are determined by participants’ own choices and would appear simultaneously for the LLR and SSR options; therefore, they are unlikely to systematically influence choice for one option over the other. Moreover, we note that the mean log indifference delay in the BS9 condition (2.85) corresponded to a raw value of 715.30 days (1.96 years), producing a realistic maximum delay to the final reward of 17.64 years. Most importantly, we note that the BS3 condition is far less prone to unrealistic delays, with maximum delays to the final reward of 36 years and 75 years. In post-hoc tests, choice bundling in this condition significantly increased indifference delays compared to the BS1 control condition, which mitigates concern over unrealistic delays in the BS9 condition. Nonetheless, in future studies using the five-trial task to manipulate choice bundling, we recommend limiting the bundle size to 3 or fewer rewards. This should not pose a substantial restriction, as both the predicted and observed relationships between bundle size and indifference delay are negatively accelerating functions (see Fig 3), with the largest incremental effects at small bundle sizes.

Potential clinical utility of choice bundling.

Given the robust covariance between delay discounting and maladaptive health behavior [e.g., 3, 4, 60], identifying and developing methods to reduce delay discounting and increase preference for LLRs may provide therapeutic benefit in the treatment and prevention of lifestyle-related disease. That is, as many have suggested, a bias for immediate gratification may play an etiological role in lifestyle-related disease through a mechanism in which the reinforcing outcomes of many maladaptive health behaviors (e.g., cigarette smoking, consumption of obesogenic foods) are immediate and are therefore more highly valued than more beneficial, but delayed, health outcomes [e.g., avoidance of lung cancer, type 2 diabetes; 3, 7, 61, 62]. Thus, interventions that reduce bias for immediate gratification may improve health behavior.

In clinical interventions, the magnitude of observed shifts in willingness to wait may be sufficient to increase the value of long-term health consequences and improve health behavior. However, observed effects in the present and prior studies required manipulation of the timing of behavioral consequences. In contrast, most clinical interventions (e.g., for the prevention and treatment of obesity) cannot directly manipulate the consequences of health behavior in this way. For example, a treatment provider cannot control when and how often individuals at risk for diabetes will experience the health benefits of diet and exercise. As a result, adaptation of laboratory choice procedures for clinical use is required. In this regard, framing naturally occurring rewards as a bundled series of choices and consequences may hold clinical promise. For example, in addition to a condition in which the consequences of choices were bundled programmatically (as in the present study), Hofmeyr et al. [30] also showed that merely suggesting to cigarette smokers that their current choices were predictive of future choices significantly increased preference for monetary LLRs. Kirby and Guastello [25] replicated the significant effect of the suggested condition on choice for food rewards, although this effect for monetary rewards fell short of significance. These effects entail the bundling of not just consequences (as in the present study), but individual choices into a temporally extended pattern (bundle) of behavior [63].

Future research might build on these prior and present findings by developing framing or motivational interventions that emphasize that the outcomes of maladaptive health behavior are not discrete, but are chronic (and therefore bundled) conditions in which negative consequences are experienced over time (e.g., COPD, type 2 diabetes). For example, with every urge to smoke, individuals could be guided using ecological momentary intervention [64] to evaluate the bundled value of sustained, long-term good health against the value of continuing to smoke cigarettes.

Such attempts to adapt choice bundling for clinical use, however, may first benefit from a more thorough understanding of its effects in more controlled laboratory studies, particularly in clinical samples (e.g., smokers, overweight/obese participants). For example, as mentioned previously, identification of moderators of choice bundling effects may provide the ability to identify subpopulations likely to show optimal and suboptimal responses. Moreover, in order to be effective in clinical settings, choice bundling should be able to exert its effects across a wide range of choice contexts. Thus, examination of the effects of bundling on choice for monetary losses (as opposed to gains, in the present study), health gains and losses, and other commodities may provide insight into the generality or specificity of observed effects [for review, see 32]. Here, we note that the predictions of Eq 2 remain consistent regardless of the outcome examined (e.g., money, health) or its sign (gain vs. loss); however, future research is necessary in order to evaluate these predictions.