Delay and probability discounting in cocaine use disorder: Comprehensive examination of money, cocaine, and health outcomes using gains and losses at multiple magnitudes

Abstract

Understanding factors associated with cocaine use disorder is important given its public health impact. One factor is delay discounting (devaluation of future consequences). Cocaine-users have shown greater delay discounting of money rewards than non-cocaine-users. But under-examined are factors known to affect discounting, such as sign (reward vs. loss), magnitude (e.g., $10 vs. $1000), and commodity (e.g., money vs. health) of the consequence. Also under-examined is probability discounting (devaluation of uncertain consequences). We conducted a comprehensive group-comparison study of discounting processes by comparing sign, magnitude, and commodity effects between demographically matched cocaine-users (n=23) and never-users (n=24) for delay discounting; and sign and magnitude effects for probability discounting. Participants completed delay and probability discounting tasks spanning: rewards and losses; money, cocaine, and health outcomes; and magnitudes of $10, $100, and $1000. Four primary findings emerged when controlling for other drug use. First, cocaine-users pervasively discounted delayed consequences more than never-users regardless of sign, magnitude or commodity, with the possible exception of delay discounting of $1000 health equivalences. Second, both groups discounted delayed rewards more than losses, with a similar trend for probability discounting. Third, magnitude effects in cocaine-users for delayed and probabilistic outcomes were similar to those previously observed in never-users and other-drug-users. Fourth, cocaine-users discounted cocaine-related outcomes more than money and health, with variable results comparing money and health. These data suggest the behavioral processes of delay and probability discounting are qualitatively similar for cocaine-users and never-users. However, quantitatively, cocaine-users generally show greater delay and similar probability discounting than never-users.

Cocaine use is associated with many health complications resulting from acute toxicity and chronic use (e.g., cardiac, pulmonary, and hepatic toxicities, and high risk of death; Reizzo et al., 2012). These many forms of negative consequences typically involve delay and/or uncertainty. Therefore, cocaine use has been studied through the lens of behavioral discounting processes.

Delay and probability discounting refer to observations that delayed or probabilistic (uncertain) outcomes have less value than immediate or certain outcomes, respectively. Researchers typically use choice procedures to determine the extent to which outcomes are devalued due to delay or probability, by pitting smaller immediate outcomes versus larger delayed outcomes, or pitting smaller certain outcomes versus larger uncertain outcomes (e.g., Rachlin, Raineri, & Cross, 1991). For example, many people would take $90 right now over $100 in one year even though $100 is more than $90, indicating the value of $100 is reduced as a function of the delay. Similarly, many people would prefer $90 for certain over a 50% chance at $100, indicating the value of $100 is reduced by uncertainty. Delay and probability discounting are pervasive, as they likely occur in all animal species (e.g., Adessi, Paglieri, & Focaroli, 2011; Budenberg, 2014; Dandy & Gatch, 2009; Green, Myerson, & Calvert, 2010; Mazur, 2006; Stevens, Hallinan, & Hauser, 2005; Stevens & Muhlhoff, 2012; Vanderveldt, Oliveira, & Green, 2016), and with many outcomes including receiving or losing commodities (e.g., Calvert, Green, & Myerson, 2010; Kirby, Petry, & Bickel, 1999; Odum & Rainaud, 2003) and other experiences (e.g., Johnson & Bruner, 2012; Lawyer, 2008). Despite this pervasiveness, the extent of discounting (i.e., the degree to which delay or uncertainty devalues an outcome) can vary strongly between individuals and situations.

Group Comparison Studies

One form of evidence linking cocaine use to discounting has been comparisons between cocaine users and controls. Group comparison studies have broadly found cocaine use to be associated with increased delay discounting. For example, compared to control groups, cocaine users show greater delay discounting of monetary rewards (e.g., Coffey, Gudleski, Saladin, & Brady, 2003; Heil, Johnson, & Higgins, & Bickel, 2006; Johnson, 2012; Kirby & Petry, 2004), preferred liquids (Mejia-Cruz et al., 2016), and condom-protected sex for a subset of potential sexual partners (Johnson et al., 2015b).

There are a few caveats to the broad group-based associations between cocaine use and discounting. For delay discounting, cocaine-users and non-users have not significantly differed in discounting delayed monetary losses or leisure activities (Mejia-Cruz et al., 2016). For probability discounting, cocaine-users and non-users have not significantly differed in discounting of monetary rewards (Johnson et al., 2015b; Mejia-Cruz et al., 2016), monetary losses (Mejia-Cruz et al., 2016), sexual outcomes (Johnson et al., 2015b), leisure activities (Mejia-Cruz et al., 2016), or preferred liquid rewards (Mejia-Cruz et al., 2016).

Aside from cocaine, studies have found greater monetary delay discounting in several drug using groups compared to controls. This suggests the possibility that a common predisposition toward frequent drug use or addiction accounts for group differences rather than, or in addition to, pharmacological effects of cocaine. This is been found for alcohol (MacKillop et al., 2010; Vuchinich & Simpson, 1998), methamphetamine (Hoffman et al., 2006), tobacco (e.g., Baker et al., 2003; Bickel, Odum, & Madden, 1999; Mitchell, 1999; Johnson et al., 2007), and opioids (e.g., Kirby et al., 1999; Madden, Petry, Badger, & Bickel, 1997), although cannabis may constitute an exception (Johnson et al., 2010; Strickland et al, 2017). Similar to cocaine use, monetary probability discounting does not consistently differ between smokers and nonsmokers (e.g., Bialaszek et al., 2017; Mitchell, 1999, Ohmura et al., 2005, but in contrast see: Reynolds et al. 2004; Yi, Chase, & Bickel, 2007) or between marijuana-dependent and non-dependent users (Mejia-Cruz et al., 2016).

Cocaine Administration Studies

Administering cocaine to cocaine users caused no significant change in delay or probability discounting of money (Johnson, Herrmann, Sweeney, LeComte, & Johnson, 2017). However, the same study found that cocaine administration increased delay discounting of condom-protected sex and increased probability discounting of sexual outcomes (i.e., the effect of sexually transmitted infection uncertainty on decreasing the likelihood of condom use) in a dose-dependent manner (Johnson et al., 2017). Interestingly, cocaine users continue to steeply discount monetary rewards at 14 (Kirby & Petry, 2004) and 30 days (Heil et al., 2006) after cocaine cessation. This suggests either persistent effects of cocaine use on delay discounting, or that a common predisposition, rather than a causal effect of cocaine, accounts for elevated monetary delay discounting among cocaine users.

Persistent preference for smaller-sooner over larger-later rewards has also been observed after chronic cocaine exposure in rats (e.g., Koffarnus & Woods, 2013; Logue et al., 1992; Roesch et al., 2007; Setlow et al., 2009). Additionally, the persistent effects of cocaine on delay discounting have lasted for 3 months after cocaine cessation (Mendez et al., 2010; Simon et al., 2007), and rats that self-administered cocaine at higher rates showed the greatest discounting changes from baseline (Dandy & Gatch, 2009; Mitchell, Weiss, Ouimet, Fuchs, Morgan, & Setlow, 2014). No significant effect of cocaine on probability discounting has also been observed with rats (Mendez et al., 2010).

Outcome Specificity and Discounting

Robust evidence indicates the extent of discounting will change for most people depending on the specific details of the choice. For example, Baker and colleagues (2003) comprehensively examined delay discounting in current- and never-smokers across gains and losses of money, health, and cigarettes (smokers only), and at outcome amounts of $10, $100, and $1000. They observed pervasively steeper delay discounting in smokers compared to non-smokers, but also found that discounting was steeper for gains compared to losses, for smaller amounts compared to larger amounts, and for cigarettes compared to money (Baker et al., 2003). These results were subsequently replicated with light smokers (10 or fewer cigarettes per day; Johnson et al., 2007) who did not differ significantly from the heavy smokers in Baker et al. (2003). Intriguingly, all three groups did not differ significantly in the extent they discounted health outcomes and both smoking groups (light vs. heavy) discounted cigarettes similarly.

In some cases, aberrant discounting has been observed only with outcomes related to the problem behavior. Shallower probability discounting has been observed for food in people with elevated percent body fat, but no differences for probability discounting for money (e.g., Rasmussen et al., 2010; but in contrast also see: Hendrickson & Rasmussen, 2013). Administration of cocaine and alcohol, two drugs that are associated with risky sexual behavior, cause increases in the delay and probability discounting of sexual consequences previously mentioned, but had no significant or minimal effects on delay and probability discounting of money (Johnson, Sweeney, Herrmann, & Johnson, 2016; Johnson et al., 2017). Although only money was studied, several studies indicate that problem gamblers aberrantly discount money, the outcome typically at play with gambling. Compared to control groups, greater delay discounting of monetary rewards has been observed with pathological gamblers (e.g., Madden, Francisco, Brewer, & Stein, 2011) and shallower probability discounting has been observed for monetary outcomes in gamblers (e.g., Holt, Green, & Myerson, 2003; Madden, Petry, & Johnson, 2009; Shead, Callan, and Hodgins, 2008). Together, these data suggest that delay and probability discounting are not monolithic constructs, and that relations and effects often depend on a number of factors, including sign, magnitude, and commodity of the discounted outcome.

Sign Effect.

The sign effect describes the observation that both delayed and uncertain gains (or rewards) are discounted more than losses (or punishments) (e.g., Kahneman & Tversky, 1979, 1984; Thaler, 1981; Thaler, Tversky, Kahneman, & Schwartz, 1997). For example, a $100 reward delayed by a year might be subjectively equivalent to $60 now (a 40% reduction). But for the same person, a $100 loss delayed by a year might be subjectively equivalent to a $80 loss now (only a 20% reduction). Similarly, a 50% chance at $100 reward might be subjectively equivalent to a certain $60 reward (40% reduction). But for the same person, a 50% chance at $100 loss might be subjectively equivalent to a certain $80 loss (20% reduction). The sign effect has occurred with delayed monetary outcomes (e.g., Estle, Green, Myerson, & Holt, 2006; Murphy, Vuchinich, & Simpson, 2001; Thaler, 1981), probabilistic monetary outcomes (e.g., Estle et al. 2006; Shead & Hodgins, 2009), delayed health outcomes (e.g., Baker et al., 2003; Chapman, 1996), delayed cigarettes (Baker et al., 2003), and delayed cocaine (Johnson, Bruner, & Johnson, 2015).

Magnitude (Amount) Effect.

The magnitude effect describes the observations that smaller amounts (e.g., $10) are discounted to a different extent than larger amounts (e.g., $1000), with the direction differing between delay and probability discounting. For delayed rewards, small amounts are discounted more than large amounts (e.g., Green, Myerson, & McFadden, 1997; Kirby, 1997; Thaler, 1981). For example, a $100 reward delayed by a year might be subjectively equivalent to a $60 reward now (a 40% reduction). But for the same person, a $1000 reward delayed by year might be subjectively equivalent to a $800 reward now (only a 20% reduction). A magnitude effect for delayed rewards has occurred with real money (e.g., Johnson & Bickel, 2002), hypothetical money (e.g., Green, Myerson, & McFadden, 1997), hypothetical health (e.g., Chapman, 1996; Chapman & Elstein, 1995), and even hypothetical vacations and rental cars (Raineri & Rachlin, 1993). For probabilistic rewards, the opposite occurs as small amounts are discounted less than large amounts (e.g., Myerson, Green, & Morris, 2011). The opposite effect that changing magnitude has on discounting delayed and probabilistic outcomes is the strongest evidence that delay and probability discounting are fundamentally different processes. Shallower probability discounting of larger amounts has occurred with hypothetical money (e.g., Estle, Green, Myerson, & Holt, 2006; Myerson, Green, & Morris, 2011) and points in a computer game (e.g., Greenhow, Hunt, Macaskill, & Harper, 2015). Lastly, a magnitude effect is typically not observed for delayed or uncertain losses (e.g., Green, Myerson, Oliveira, & Chang, 2014; Miranda, Drabek, & Cox, 2018; but in contrast also see: Cox & Dallery, 2016).

Domain / Commodity Effect.

The commodity effect occurs when the extent of discounting differs depending on the commodity under consideration (e.g., Chapman & Elstein, 1995; Madden et al., 1997, 1999). Generally, delayed and probabilistic consumable commodities and events (e.g., alcohol, cigarettes, cocaine, food, heroin) are discounted more steeply than money (e.g., delay: Baker et al., 2003; Bickel et al., 1999; Coffey, Gudleski, Saladin, & Brady, 2003; Madden et al., 1997, 1999; probability: Rasmussen et al., 2010). Steeper discounting appears to result from the consumable nature of tangible outcomes, rather than anything particular about drug reinforcers, because food is also discounted more than money (Estle, Green, Myerson, & Holt, 2007; Odum & Rainaud, 2003). Interestingly, mixed results exist for less tangible commodities (health outcomes) which have been discounted less than money (e.g., Baker et al., 2003; Cairns, 1992; Friedel et al., 2016; Baker et al., 2003) and more than money (Chapman, 1996; Chapman & Elstein, 1995). Other relevant outcomes for cocaine-users are access to cocaine and health outcomes which have not been comparatively examined.

Comprehensive Comparison of Discounting.

Outcome specificity has emerged as a general theme in the discounting literature. That is, the extent of discounting may differ depending on sign, magnitude, and commodity of the outcomes being considered. Several of these outcome characteristics have been compared in cocaine-users (e.g., sign effect, Johnson et al., 2015a; magnitude effect Kirby & Petry, 2004) or between cocaine-users and never-users (e.g., delay and probability discounting of multiple commodities, Johnson et al., 2015b). However, we are not aware of any research that has comprehensively examined both delay and probability discounting across multiple signs, magnitudes, and commodities in demographically matched cocaine- and never-users. This is the purpose of the current study.

To comprehensively examine discounting in cocaine-users and never-users, we analyzed unpublished data that was collected from participants in a previously published study (Johnson et al., 2015b) in conjunction with the $100 monetary gain delay discounting and $100 monetary gain probability discounting data published in that same study (Johnson et al., 2015b). The previous publication by Johnson et al. (2015b) was focused on the differences between cocaine-users and never-users in discounting of sexual outcomes. The $100 monetary delay and probability gain tasks were included as comparators to determine if any differences were specific to sexual outcomes. For the present analysis, we were interested in broadly examining discounting characteristics that were not directly relevant to the previous analysis. Specifically, we compared sign, magnitude, and domain commodity effects between cocaine-users and never-users for delay discounting; and sign and magnitude effects for probability discounting. The present study constitutes the most robust examination of discounting processes in human cocaine users to date.

Methods

Participants

Participants were cocaine-using (n=23) or never-using (n=24) individuals recruited from the Baltimore area using flyers, internet, newspaper, and radio advertisements. All participants were 18 years of age or older and had an 8^th grade reading level or higher. Participants in the Cocaine group also met Diagnostic and Statistical Manual of Mental Disorders (4th edition, DSM-IV) criteria for cocaine abuse or dependence. Control participants reported no lifetime use of cocaine. Participants in both groups could meet criteria for abuse of drugs other than cocaine, but could not meet dependence criteria for drugs other than nicotine and caffeine. Exclusion criteria for both groups were self-reported head trauma, dementia, significant cognitive impairment, or a diagnosis of major psychiatric disorder other than substance abuse/dependence.

Procedure

Following a telephone screen, potentially-qualified participants came to a laboratory for an in-person screen. During the in-person screen, participants completed: informed consent, demographic questionnaire, lifetime drug use questionnaire, assessment of current and past drug abuse and dependence, and gave a urine sample to test for recent presence of cocaine, amphetamine, methamphetamine, morphine, and cannabinoids. Participants also completed two standardized assessments for matching purposes. These were the Quick Test for verbal intelligence (Ammons, & Ammons, 1962) and the Wide Range Achievement Test for reading comprehension (Wilkinson, 1993). Participants completed the discounting tasks after completing intake.

Monetary Delay Discounting.

We assessed monetary delay discounting using a computerized task published previously (e.g., Johnson, 2012; Johnson, Baker, & Bickel, 2007; Johnson et al., 2015a; Johnson & Bickel, 2002). All outcomes were hypothetical. On each trial participants chose between an immediate, small amount of money and a delayed, large amount of money for one of three larger delayed reward magnitudes ($10, $100, and $1,000). For each trial, participants were asked to treat the outcomes as real and to consider their current finances. A computer-algorithm adjusted the magnitude of the smaller, immediate option across trials for each larger, delayed magnitude reward (see -Richards, Zhang, Mitchell, & Wit, 1999 – for a description of the algorithm). The algorithm resulted in an indifference point for each participant at each of 7 delays: 1 day, 1 week, 1 month, 6 months, 1 year, 5 years, and 25 years. The order in which delays was assessed (ascending or descending) was counterbalanced across participants. Each participant completed six monetary delay discounting tasks – one each for gaining the above amounts and one each for losing the above amounts. For each loss trial, participants chose between losing an immediate, smaller amount of money and a delayed, larger amount of money. For money and all other loss conditions, the algorithm differed from gains such that choosing the smaller outcome increased the value of the smaller outcome across trials (rather than decrease as in the gains conditions), and choosing the larger outcome decreased the value of the smaller outcome across trials (Baker et al., 2003).

Monetary Probability Discounting.

We assessed monetary probability discounting using a previously published task analogous to the above monetary delay discounting task (Yi, Johnson, & Bickel, 2005). All outcomes were hypothetical. Participants chose between a small, certain amount of money and a large, uncertain amount of money across three magnitudes ($10, $100, or $1,000). Participants were asked to treat the outcomes as real and to consider their real-life finances. Each participant’s pattern of responding led to an indifference point at each of 7 probabilities: 99%, 90%, 75%, 50%, 25%, 10%, and 1%. The order that probability values were assessed for each participant (ascending or descending) was the same as they experienced in the delay discounting task. All participants completed six probability discounting tasks – one each for gaining the above amounts and one each for losing the above amounts.

Delay Discounting Health Outcomes.

To assess discounting of health outcomes, participants first provided an estimate of health value (see – Baker et al., 2003 – for full description). Briefly, participants estimated a duration of 10% improved health that was subjectively equivalent to getting $100 immediately. The duration provided was then used as the larger amount in the health-gains of $100 discounting task. For example, a participant may state that 3 months of 10% better health was equivalent to getting $100 immediately. A trial of delay discounting health-gains would have them choose between a shorter duration of improved health now and 3 months of 10% better health after a delay. The shorter-immediate duration would adjust based on each choice using the same computer algorithm as above. Indifference points were obtained at the same 7 delays used in the monetary delay discounting tasks. The process of estimating health values for use in health-discounting tasks was repeated for health-gains equivalent to $1,000, health-loss equivalent to $100, and health-loss equivalent to $1,000. For losses the word “improved” was replaced by “worse.”

Delay Discounting Cocaine-Related Outcomes.

Participants completed two delay discounting tasks of cocaine gains (amounts of $100 and $1,000). Participants first indicated whether they typically consume cocaine in powdered or rock (crack) form. Their stated preference was then used in the delay discounting cocaine gains and losses tasks. The choice options in cocaine-related tasks were framed is nickel quantities ($5 worth) of cocaine sold in the Baltimore area. The delay discounting tasks asked participants to choose between a smaller quantity of nickel rocks/vials of powder immediately and 20 ($100 worth of cocaine) or 200 ($1,000 worth of cocaine) after a delay. The delays and adjusting algorithm used were similar to the discounting tasks above.

Participants also completed two delay discounting tasks of cocaine-related losses in a manner similar to health-discounting. Each participant estimated two durations of cocaine abstinence that were subjectively equivalent to losing $100 and losing $1,000 immediately. Estimated durations were used in delay discounting tasks where participants chose between a shorter duration of cocaine abstinence starting immediately or the longer duration of abstinence starting after a delay. Calculation of indifferences points and the delays used were identical to the discounting tasks above.

All participants completed the discounting tasks in the following order: money delay discounting gains, money delay discounting losses, health delay gains, health delay losses, money probability discounting gains, money probability discounting losses, cocaine delay discounting gains (cocaine participants only), and cocaine delay discounting losses (cocaine participants only). The order of magnitudes that each different participant experienced was randomly set to either ascending ($10, $100, $1000) or descending ($1000, $100, $10). However, each participant completed the same order across all tasks.

Study procedures were approved by the Johns Hopkins Medicine Institutional Review Board 3 (Office for Human Research Protections Registration #00001656). The study was conducted in accord with the principles expressed in the Declaration of Helsinki and written informed consent was obtained from all participants. Collection of these data were part of a larger study (see Johnson et al., 2015b) and participants received $250 in total compensation for their participation.

Data Analysis

Data were examined for orderliness using previously published criteria for nonsystematic patterns of responding (Johnson & Bickel, 2008; Johnson, Herrmann, & Johnson, 2015c). The first criterion was whether, beginning with the second indifference point, the indifference point exceeded the preceding indifference point by more than 20% of the larger outcome (e.g., more than $200 if the larger-later outcome was $1000; Johnson & Bickel, 2008). The second criterion was that the final indifference point could not exceed the first indifference point by more than 10% (e.g., more than $100 if the larger-later outcome was $1000; Johnson et al., 2015c). These criteria were used to characterize the data rather than to identify data for elimination. All data were retained for subsequent analyses.

The shape of a delay discounting curve is often well described by a hyperbolic equation (Mazur, 1987), written as:

$$I=\frac{1}{1+kD}.$$ Equation 1

Here, I is the indifference point expressed as a proportion of the delayed reward amount, D is the delay to receiving the reward, and k is a discounting parameter that estimates the extent of discounting. Probability discounting uses the same equation with the exception of odds against (calculated as (1-p)/p) where p is probability) instead of delay, and the letter h used to represent the extent of probability discounting. Greater preference for immediate/certain alternatives is represented by higher k/h values. Greater preference for delayed/uncertain alternatives is represented by lower k/h values.

Nonlinear regression was used to fit Equation 1 was fit to the seven indifference points for each participant and for each outcome condition (i.e., for a single magnitude of delayed/uncertain reward, and for a single valence (gain or loss)). This resulted in a best-fit estimate of the discounting parameter k for delay tasks and h for probability tasks. We did not remove any participants from the data analysis given the comprehensive nature of the comparisons being made. All parametric statistical tests were performed on the natural log transform of k/h as the raw distribution of estimated k and h values were positively skewed (average Pearson’s Coefficient of Skewness = 1.06 for k and 0.86 for h).

A planned series of five analyses of variance (ANOVA) were conducted (Table 1). ANOVA 1 focused on delay discounting of money where cocaine status was the between-subjects variable (cocaine user or non-user), sign was one within-subject variable (gain or loss), and money amount was the second within-subject variable ($10, $100, or $1000). ANOVA 2 was identical to ANOVA 1 with the exception that it analyzed probability, rather than delay, discounting. ANOVA 3 focused on delay discounting of health where cocaine status was the between-subjects variable, sign was one within-subject variable, and health amount was the second within-subject variable ($100 or $1000 equivalencies). ANOVA 4 focused on the sign, magnitude, and commodity effects for delay discounting where cocaine status was the between-subjects variable, sign was one within-subjects variable, outcome amount was a second within-subject variable (only $100 or $1000 equivalencies), and commodity was the third within-subject variable (money or health). Finally, ANOVA 5 focused on cocaine users only examining the sign (gain or loss), magnitude ($100 or $1000 equivalencies), and commodity effect (money, health, or cocaine). Any significant interaction in the above ANOVAs was followed up by simple effect analyses (ANOVAs or t-tests) exploring the nature of the interaction. We used Greenhouse-Geiser corrections wherever Mauchly’s test of sphericity was significant indicating unequal variance across within-subject conditions (denoted by non-integer degrees of freedom).

Table 1.

Summary of planned ANOVAs.

ANOVA Number	Focus	Between Subjects Variable	Within Subjects Variable 1	Within Subjects Variable 2	Within Subjects Variable 3
1	Delay Discounting Money	Cocaine Status (User or Non-User)	Sign (Gain or Loss)	Money Amounts ($10, $100, $1000)	---
2	Probability Discounting Money	Cocaine Status (User or Non-User)	Sign (Gain or Loss)	Money Amounts ($10, $100, $1000)	---
3	Delay Discounting Health	Cocaine Status (User or Non-User)	Sign (Gain or Loss)	Health Amounts ($100, $1000)	---
4	Delay Discounting All Effects	Cocaine Status (User or Non-User)	Sign (Gain or Loss)	Amounts ($100, $1000)	Commodities (Money or Health)
5	Cocaine Users All Effects	---	Sign (Gain or Loss)	Amounts ($100, $1000)	Commodities (Money, Health, Cocaine)

RESULTS

Demographic Characteristics

Demographic descriptions of the cocaine group (n=23) and healthy controls (n=24), which were previously published (Johnson et al., 2015b), are presented in Table 2. Groups did not significantly differ across age, race, sex, marital status, income, education, or intelligence. Participants did not differ in cigarette or opiate use in the year prior to the study, but individuals in the cocaine group reported greater consumption of alcohol and cannabis relative to the healthy controls. The number of participants who tested positive for cocaine, amphetamine, methamphetamine, morphine, and cannabinoids in the cocaine group were 14, 0, 0, 1, and 7, respectively. In the control group, 3 participants were positive for cannabinoids but no participants were positive for any other drugs.

Table 2:

Sample Demographic and Substance-Use Characteristics

Characteristic	Cocaine (n=23)	Control (n=24)	Test Statistic	p value
Demographics
Age in years, mean (SD)	46.3 (10.9)	40.0 (15.3)	t(45) = 1.62	0.11
Sex, count (%)
Male	13 (57)	15 (63)		0.77
Female	10 (43)	9 (38)
Race, count (%)b,c				0.76
African-American/Black	14 (61)	17 (71)
Caucasian/White	8 (35)	7 (29)
More than one race	1 (4)	0 (0)
Marital Status, count (%)				1.00
Non-married (single/separated/divorced/widowed)	20 (87)	21 (88)
Married	3 (13)	3 (13)
Education in years, mean (SD)	13.1 (1.7)	13.8 (1.6)	t(45) = 1.49	0.14
Monthly income in US dollars, mean (SD)	1186 (826)	1369 (1222)	t(45) = 0.59	0.55
Quick Test intelligence score, mean (SD)	43.2 (3.4)	41.6 (4.1)	t(45) = 1.44	0.16
Substance Use
Cocaine
Number reporting use in past year (%)	23 (100)	—
Frequency of use (days per month), mean (SD)	16.0 (9.1)	—
Number meeting DSM-IV criteria for current abuse (%)	23 (100)	—
Number meeting DSM-IV criteria for current dependence (%)	20 (87)	—
Alcohol
Number reporting use in past year (%)	22 (96)	17 (71)		0.048
Frequency of use (days per month), mean (SD)	10.2 (10.4)	1.5 (3.3)	t(45) = 3.90	<0.0001
Number meeting DSM-IV criteria for current abuse (%)	7(30)	1 (4)		0.02
Cannabis
Number reporting use in past year (%)	16 (70)	6 (25)		<0.01
Frequency of use (days per month), mean (SD)	5.2 (9.9)	2.0 (7.0)	t(45) = 1.30	0.20
Number meeting DSM-IV criteria for current abuse (%)	5 (22)	0 (0)		0.02
Opiates
Number reporting use in past year (%)	6 (26)	2 (8)		0.14
Frequency of use (days per month), mean (SD)	1.0 (3.2)	0.007 (0.02)	t(45) = 1.53	0.13
Number meeting DSM-IV criteria for current abuse (%)	1 (4)	0 (0)		0.49
Cigarettes smoked per day, mean (SD)	6.9 (5.4)	4.3 (7.6)	t(45) = 1.39	0.17

^aAll participants identified as non-Hispanic

^bRace categorized as white/Caucasian vs Other

All participants in the cocaine group met DSM-IV criteria for cocaine abuse, and 20 (87%) met criteria for cocaine dependence. Self-reported preferred cocaine administration methods were inhalation (smoking crack) for 18 participants (78%), intranasal for 4 participants (17%) and intravenous for 1 participant (4%).

Data Orderliness

Participants completed the discounting tasks in a mean (standard deviation) of 98 (43) trials which equates to a mean (standard deviation) of approximately 14 (6) trials per indifference point. Appendix A provides the box-and-whisker distribution values for each the total trials required per discounting task. Table 3 shows the number of participants from each group that met criteria for nonsystematic patterns of responding (Johnson & Bickel, 2008; Johnson et al., 2015c). For the criteria, in all conditions, the majority of data sets did not violate the criteria. Data were generally more orderly for money compared to other commodities, and for gains compared to losses. The median (mean) number of indifference points that violated criterion 1 were 1.00 (1.14) and 1.00 (1.11) for the cocaine and control groups, respectively.

Table 3.

Number (percentage) of participants meeting orderliness criteria. n = 23 for cocaine group and n = 24 for control group.

Task	Cocaine Group		Control Group
	Criterion 1	Criterion 2	Criterion 1	Criterion 2
$10 Delayed Monetary Gain	1 (4%)	0 (0%)	1 (4%)	0 (0%)
$100 Delayed Monetary Gain	1 (4%)	0 (0%)	1 (4%)	0 (0%)
$1000 Delayed Monetary Gain	1 (4%)	0 (0%)	2 (9%)	0 (0%)
$10 Delayed Monetary Loss	4 (17%)	0 (0%)	1 (4%)	0 (0%)
$100 Delayed Monetary Loss	5 (22%)	0 (0%)	4 (17%)	1 (4%)
$1000 Delayed Monetary Loss	3 (13%)	0 (0%)	5 (22%)	2 (8%)
$100 Delayed Health Gain	3 (13%)	0 (0%)	5 (22%)	0 (0%)
$1000 Delayed Health Gain	4 (17%)	0 (0%)	1 (4%)	0 (0%)
$100 Delayed Health Loss	2 (9%)	0 (0%)	5 (22%)	0 (0%)
$1000 Delayed Health Loss	2 (9%)	0 (0%)	8 (35%)	1 (4%)
$100 Delayed Cocaine Gain	2 (9%)	0 (0%)	---	---
$1000 Delayed Cocaine Gain	3 (13%)	0 (0%)	---	---
$100 Delayed Cocaine Loss	10 (48%)	2 (9%)	---	---
$1000 Delayed Cocaine Loss	10 (48%)	4 (17%)	---	---
$10 Probability Monetary Gain	0 (0%)	0 (0%)	3 (13%)	0 (0%)
$100 Probability Monetary Gain	0 (0%)	0 (0%)	1 (4%)	0 (0%)
$1000 Probability Monetary Gain	2 (9%)	0 (0%)	2 (9%)	0 (0%)
$10 Probability Monetary Loss	3 (13%)	0 (0%)	4 (17%)	2 (8%)
$100 Probability Monetary Loss	5 (22%)	1 (4%)	2 (9%)	1 (4%)
$1000 Probability Monetary Loss	5 (22%)	1 (4%)	1 (4%)	0 (0%)

Discounting Tasks

Figure 1 shows the median, untransformed discount rates for participants in the cocaine and control groups across discounting tasks of varying sign, magnitude, commodity, and process (delay and probability). Table 4 shows the results of ANOVA 1 focused on delay money discounting (corresponding to Panel A, Fig. 1). We observed a main effect of cocaine use status as cocaine-users discounted more than never-users. We also observed main effects for sign and magnitude with gains being discounting more than losses overall, and smaller amounts being discounted more than larger amounts overall, but there was an interaction between sign and magnitude. Follow-up analyses showed that small gains were discounted more than large gains (i.e., statistically significant simple effect of magnitude for gains; F(1.68, 75.72) = 14.92, p < 0.001, pη²= 0.249), but magnitude did not influence discounting for losses (i.e., no statistically significant simple effect of magnitude for losses F(1.76, 79.03) = 0.98, p = 0.88, pη²= 0.002). Also, gains were discounted more than losses at $10 (t₉₁ = 3.00, p = 0.004) and $100 (t₉₁ = 1.95, p = 0.05), but not at $1000 (t₉₁ = 1.58, p = 0.12). Appendix B shows the results of the same ANOVA when controlling for alcohol and cannabis use as covariates.

Figure 1.

Median (untransformed) discount rates for delay discounting of hypothetical money (panel A), probabilistic money (panel B), and delayed health outcomes (panel C) using a logarithmic y-axis. Panel D juxtaposes delay discounting of money, health- and cocaine-related outcomes in the cocaine group for easy comparison of discounting across different signs, magnitudes, and commodities.

Table 4:

Results of ANOVA 1 for delay money discounting.

Effect	dfs	F	p	pη2
Cocaine Use (A)	1,45	7.928	0.007*	0.15
Sign (B)	1,45	4.988	0.031*	0.10
Magnitude (C)	2,90	3.202	0.045*	0.07
A × B	1,45	0.035	0.853	0.00
A × C	2,90	0.498	0.609	0.01
B × C	2,90	3.529	0.033*	0.07
A × B × C	2,90	0.318	0.729	0.01

^*p<.05

Table 5 shows the results of ANOVA 2 focused on probability money discounting (corresponding to Panel B, Fig. 1). We observed a main effect of magnitude as larger amounts were generally discounted more than smaller amounts (magnitude effect). We did not observe a main effect of cocaine use status or sign on probability discounting of money, but a nonsignificant trend was present suggesting greater discounting of gains than losses (sign effect). However, we also observed group by magnitude, and sign by magnitude interactions. Follow-up analyses for the group by magnitude interaction found that cocaine-users discounted $1000 more than $10 (t₄₅ = 2.63, p = 0.012) and $1000 more than $100 (t₄₅ = 3.23, p = 0.002); but there were no differences between cocaine-users’ discounting of $10 and $100 (t₄₅ = 0.03, p = 0.98) nor for any magnitude comparisons within the control group (all p ≥ 0.19). Additionally, there were no differences in probability discounting between cocaine-users and the control group at any magnitudes (all p ≥ 0.37). Follow-up analyses for the magnitude by sign interaction found that $1000 gains were discounted more steeply than $10 gains (t₄₆ = 2.36, p = 0.023) and $100 gains (t₄₆ = 2.95, p = 0.005); $100 gains were discounted more than $100 losses (t₄₆ = 2.31, p = 0.025); and $1000 gains were discounted more than $1000 losses (t₄₆ = 2.95, p = 0.005). All other pairwise comparisons for the magnitude by sign interaction were not significant (p > 0.08).

Table 5:

Results of ANOVA 2 for probability money discounting.

Effect	dfs	F	p	pη2
Cocaine Use (A)	1,43	0.007	0.934	0.01
Sign (B)	1,43	3.982	0.052	0.09
Magnitude (C)	2,86	3.706	0.029*	0.08
A × B	1,43	0.039	0.845	0.00
A × C	2,86	3.674	0.029*	0.08
B × C	2,86	3.459	0.036*	0.07
A × B × C	2,86	1.52	0.224	0.03

^*p<.05

Table 6 shows the results of ANOVA 3 for delay health discounting (corresponding to Panel C, Fig. 1). We observed main effects for outcome sign and outcome magnitude. Health-related gains were discounted more than losses, and smaller health-related outcomes were discounted more than larger health-related outcomes. We did not observe a main effect of cocaine use status, although a non-significant trend was present suggesting greater discounting in the cocaine group.

Table 6:

Results of ANOVA 3 for delay health discounting.

Effect	dfs	F	p	pη2
Cocaine Use (A)	1,44	3.283	0.077	0.07
Sign (B)	1,44	12.203	0.001*	0.22
Magnitude (C)	1,44	13.846	0.001*	0.24
A × B	1,44	0.199	0.658	0.01
A × C	1,44	0.008	0.927	0.00
B × C	1,44	0.078	0.781	0.00
A × B × C	1,44	1.156	0.288	0.03

^*p<.05

Table 7 shows the results of ANOVA 4 for delay discounting across money and health at $100 and $1000 equivalencies for both groups. We observed significant main effects showing greater delay discounting for: cocaine-users compared to never-users; gains compared to losses (sign effect); and small amounts compared to large amounts (magnitude effect). We found no statistically significant difference between discounting money compared to discounting health (no commodity effect). But we did observe sign by commodity, and magnitude by commodity interactions. Follow-up analyses for the sign by commodity interaction showed that money losses were discounted more than health losses (F(1, 44) = 4.61, p = 0.037, pη²= 0.093), and there was no difference between discounting health gains and money gains (F(1, 44) = 0.77, p = 0.385, pη² = 0.017). Gains were discounted more than losses for health (F(1, 44) = 12.20, p < 0.001, pη²= 0.217), but no difference in discounting gains or losses for money (F(1, 44) = 2.88, p = 0.097, pη² = 0.060). Follow-up analyses for the magnitude by commodity interaction showed: health-related $100 equivalence was discounted more than health-related $1000 equivalence (F(1, 44) = 13.85, p < 0.001, pη²= 0.239), but there was no difference between $100 money and $1000 money (F(1, 44) = 2.22, p = 0.143, pη²= 0.047). Also, money was discounted similarly to health-related equivalence at both $1000 (F(1, 44) = 3.16, p = 0.082, pη²⁼ 0.066) and at $100 (F(1, 44) = 0.03, p = 0.854, pη² = 0.001).

Table 7:

Results of ANOVA 4 for delay money and health discounting.

Effect	dfs	F	p	pη2
Cocaine Use (A)	1,44	7.51	0.009*	0.15
Sign (B)	1,44	7.81	0.008*	0.15
Magnitude (C)	1,44	14.02	0.001*	0.24
Commodity (D)	1,44	0.95	0.336	0.02
A × B	1,44	0.15	0.704	0.00
A × C	1,44	0.10	0.759	0.00
A × D	1,44	0.84	0.364	0.02
B × C	1,44	0.05	0.829	0.00
B × D	1,44	4.70	0.036*	0.10
C × D	1,44	5.22	0.027*	0.11
A × B × C	1,44	0.39	0.533	0.01
A × B × D	1,44	0.05	0.827	0.00
A × C × D	1,44	0.03	0.864	0.00
B × C × D	1,44	0.37	0.547	0.01
A × B × C × D	1,44	1.35	0.252	0.03

^*p<.05

Finally, Table 8 shows the results of ANOVA 5 comparing delay discounting across sign, magnitude ($100 or $1000), and the commodities of money-, health-, and cocaine-related outcomes in cocaine-users only (corresponding to Panel D, Fig. 1). We observed a main effect of commodity. Follow-up analyses found that cocaine-related outcomes were discounted more than health-related outcomes (F(1, 21) = 21.89, p < 0.001, pη² = 0.510) and money outcomes (F(1, 21) = 16.47, p < 0.001, pη² = 0.440); but there was no difference between discounting money and health-related outcomes (F(1, 21) = 1.94, p =0.177, pη² = 0.081). We also observed a non-for gains to be discounted more than pη losses, and no significant trend in the main effect of sign main effect for magnitude. However, there was a significant magnitude by commodity interaction. Follow-up analyses showed that, at $1000 equivalences, cocaine-related outcomes were discounted more than money (t₄₄ = 3.44, p = 0.001); and cocaine-related outcomes were discounted more than health-related outcomes (t₄₄ = 4.32, p < 0.001). Follow-up analyses also showed that, at $100 equivalences, cocaine-related outcomes were discounted more than health related outcomes (t₄₄ = 2.04, p = 0.047). All remaining pairwise comparisons within magnitudes, but across commodities, were not significantly different (all p ≥ 0.10). Finally, follow-up analyses showed that the only within commodity, but across magnitude, difference was greater discounting of $100 health-related outcomes than $1000 health-related outcomes (t₄₄ = 3.12, p = 0.003). All remaining pairwise comparisons within commodities, but across magnitudes, were not significantly different (p ≥ 0.12).

Table 8:

Results of ANOVA 5 for cocaine users’ delay discounting of money, health, and cocaine.

Effect	dfs	F	p	pη2
Sign (A)	1,42	3.891	0.062	0.16
Magnitude (B)	1,42	0.058	0.812	0.00
Commodity (C)	2,42	15.239	< 0.001*	0.42
A × B	1,42	2.612	0.121	0.11
A × C	2,42	0.74	0.439	0.03
B × C	2,42	4.674	0.028*	0.18
A × B × C	2, 42	0.896	0.416	0.04

^*p<.05

DISCUSSION

A few previous studies had found that cocaine-dependent individuals discount delayed hypothetical monetary gains more than non-using controls (e.g., Coffey et al., 2003; Heil et al., 2006; Kirby & Petry, 2004). However, a comprehensive comparison of variables known to impact discounting had not been conducted with cocaine-users. Therefore, by examining gains (rewards) and losses, and multiple magnitudes for delay and probability discounting, and by examining multiple commodities for delay discounting, in both cocaine users and matched controls, the present study constitutes the most comprehensive assessment of discounting processes in relation to cocaine use to date. There were four primary findings. First, cocaine-users pervasively discounted delayed consequences more steeply than never-users regardless of sign, magnitude, or commodity, with the possible exception of delay discounting of $1000 health equivalences. Second, both groups significantly discounted delayed rewards more than losses, with a similar trend for probability discounting. Third, magnitude effects in cocaine-users for delayed and probabilistic outcomes were similar to those previously observed in never-users and other-drug-users. Fourth, cocaine-users discounted cocaine-related outcomes most steeply, with variable results comparing money and health. Each of these findings will be discussed in turn.

This is the first study to show that cocaine-users discount delayed rewards more steeply than never-users regardless of magnitude or commodity (with the exception of $1000 health-related outcomes). This provides evidence of remarkably robust differences in delayed reward discounting associated with cocaine use. Previously published results from the present sample of participants also showed steeper delay and probability discounting of condom use in casual sexual scenarios in cocaine-users which complements this evidence of robustness (Johnson et al., 2015b). These results are also similar to previous research comparing magnitude and commodity effects between current- and non-smokers. Smokers in one study showed higher discount rates across all magnitudes and commodities (Baker et al., 2003). Johnson et al. (2007) examined a light smoking group in relation to these previous two groups, finding that light and heavy smokers did not significantly differ in discounting cigarettes or money. Cocaine use appears similar to cigarette smoking in showing robust relations to discounting processes. Assessments of such robustness have not been examined for other drugs.

This study more comprehensively extends previous research examining the sign effect in cocaine-users. Previous research found a consistent sign effect for cocaine-users with delayed money and cocaine outcomes (Johnson et al., 2015a). The current study extended the robustness of the sign effect in cocaine-users to health outcomes. The sign effect for delay discounting in the current study is consistent with non-users (e.g., McKerchar et al., 2013; Myerson et al., 2017). For cocaine-users, gains were discounted more steeply than losses regardless of commodity (money, health, cocaine), magnitude ($10, $100, $1000), or process (delay or probability). This finding is also consistent with smokers who have demonstrated the sign effect for money (Baker et al., 2003; Johnson et al., 2007; but in contrast also see: Bickel et al., 2008), health (Baker et al., 2003; Johnson et al., 2007), and cigarettes (Johnson et al., 2007). Interestingly, previous studies on the sign effect with money in heroin users did not detect differences in discount rates between monetary gains and losses (Cheng et al., 2012). However, it is unknown whether this is due to a difference between drugs (or the groups that use them), parametric differences between studies, or other demographics (e.g., China vs. USA study locations).

This is the first study to comprehensively examine magnitude effects in cocaine-users. Cocaine-users showed magnitude effects consistent with previous research on delayed and probabilistic outcomes with non-users (e.g., Green et al., 2013; Myerson et al. 2011) and other substance-abusers (e.g., Bickel et al., 2008; Cheng et al., 2012; Mejia-Cruz et al., 2016). Delay discounting systematically decreased as amount increased for money and health gains; and, probability discounting increased as amount increased for monetary gains. Lastly, no trend was observed in discount rates over increasing amounts of delayed or probabilistic monetary loss. In total, these data suggest the magnitude of an outcome influences discount rates similarly for cocaine-users and never-users.

This study more comprehensively extends previous research on the commodity effect in cocaine-users. Outcome commodity significantly influenced discount rate. Consistent with previous research (single-commodity tasks in Bickel et al., 2011; Coffey et al., 2003), cocaine gains were discounted more steeply than money gains at both $100 and $1000 equivalents. A novel finding is that cocaine was discounted more steeply than health at the $1000 outcome equivalents, but similarly at $100 outcome equivalents. Another novel finding was that money gains and health gains were discounted similarly at $100 and $1000 equivalents in cocaine-users. This finding is consistent with previous research studying discounting across commodities in heavy smokers (Baker et al., 2003). However, light smokers were found to discount money less than health in a different study (Johnson et al., 2007) suggesting relative rates of drug use may be associated with differential discounting of health and money outcomes. Also novel to this study were the loss comparisons in cocaine-users. Cocaine was discounted most followed by money then health. This is the same order observed by Baker et al. (2003) with heavy smokers, but different from the order observed by Johnson et al. (2007) with light smokers where cigarette-related losses were discounted least followed by money and health. In total, these data suggest that cocaine-related outcomes are devalued most quickly as a function of delay in cocaine-users, and differences in devaluation of money and health were specific to the unique combination of sign and magnitude in the choice context. It should be noted that steeper discounting of cocaine is likely due to the consumable nature of cocaine rather than anything particular about cocaine as a reinforcer, because food and other consumable primary reinforcers are also discounted more than money (Estle, Green, Myerson, & Holt, 2007; Friedel et al., 2016; Odum & Rainaud, 2003; Odum et al., 2006).

One limitation to this study is a potential decreased quality of responding due to the large number of discounting questions. Reduced quality of participant responding can be estimated in two ways. One way is to examine how many participants met established criteria suggesting nonsystematic discounting (Johnson & Bickel, 2008; Johnson et al., 2015c). Rates of nonsystematic responding were generally favorable compared to a recent meta-analysis of nonsystematic responding for delay and probability discounting of gains (Smith, Lawyer, & Swift, 2018). All 3 tasks that exceeded previously reported proportions of participants meeting one or more criteria for nonsystematic discounting involved criterion 1, and the 3 tasks were health-related losses of $1000 equivalencies for the control group and both cocaine-related loss tasks for the cocaine group. A second way to estimate quality of responding is to examine sign, magnitude, and commodity effects in control participants. Control participants showed the expected sign, magnitude, and commodity effects found in previous research. One exception was the absence of a magnitude effect for probability discounting monetary gains. Post hoc examination of participant data failed to uncover why the magnitude effect was not observed. Nevertheless, that 96% of the tasks resulted in a proportion of participants meeting criteria consistent with past literature, and sign, magnitude, and commodity effects were mostly consistent with past literature in the control group suggests the large number of discounting tasks likely did not negatively affect responding.

A second potential limitation was the inclusion criteria for cocaine-users. Cocaine-users showed significantly higher rates of alcohol and cannabis use relative to non-users. Poly-substance use reduces the association between patterns of discounting and cocaine-use alone. Nevertheless, high rates of alcohol and cannabis use are expected in cocaine-users and suggest face-validity in terms of participants being representative of individuals with cocaine-use disorder (e.g., Booth, Walters, & Chitwood, 1993; Coffey et al., 2003; Kirby & Petry, 2004; McCoy, Lai, Metsch, Messiag, & Zhao, 2004).

A third limitation of this study was the use of hypothetical, rather than real, outcomes. Previous research has shown generally similar results when using real and hypothetical money (e.g., Baker et al., 2003; Green & Lawyer, 2014; Johnson, 2012; Johnson & Bickel, 2002; Johnson, Bickel, & Baker, 2007; Lagorio & Madden, 2005; but in contrast also see: Hinvest & Anderson, 2010; Jikko & Okouchi, 2007) and cigarettes (Green & Lawyer, 2014; Lawyer Schoepflin, Green, & Jenks, 2011). Thus, the observed patterns of preference for money gains in this study are likely to coincide with choices made with potentially real outcomes, and it is unclear it is ethically or legally possible to examine anything other than hypothetical health or cocaine outcomes, respectively. Nevertheless, no known research has compared real and hypothetical money losses, delayed health outcomes, or delayed cocaine outcomes. Thus, it is possible that our results were impacted by using hypothetical health and cocaine outcomes instead of potentially real outcomes.

In conclusion, this study comprehensively and precisely described ways that cocaine-users devalue outcomes. Cocaine and control groups showed similar sign, magnitude, and commodity effects for discounting tasks suggesting that outcome devaluation is not qualitatively different between the groups. However, pervasively greater delay discount rates by cocaine-users suggest that outcome devaluation as a function of delay differs quantitatively between the groups. For a current cocaine-user, the moment of choice to use cocaine involves a unique interaction between a variety of contingencies that include money, health, and cocaine-related outcomes. Cocaine use involves a reduction in money from cocaine purchase (loss), a negative impact to health (loss), and physiological effects of cocaine consumption (gain). Abstaining from cocaine use involves an opportunity to spend that money on something else (gain), an incremental positive health impact (gain), and the negative physiological effects of abstinence (loss). Thus, the relative preference between drug, health, and monetary gains and losses are important when considering choices made by cocaine-dependent individuals. This is particularly important for decisions to seek treatment to achieve and maintain abstinence from cocaine.

Public Significance Statement.

This is the most comprehensive within-subject comparison of discounting processes between cocaine-users and never-users spanning: rewards and losses; money, cocaine, and health outcomes; and magnitudes of $10, $100, and $1000. This study suggests that discounting processes are qualitatively similar for cocaine-users and never-users, but cocaine-users generally show quantitatively greater delay, and similar probability discounting, than never-users.

Appendix A.

75^th percentile, median, mean, 25^th percentile, and minimum number of trials needed to complete each discounting task. D = Delay; P = Probability; G = Gains; L = Loss; M = Money; H = Health; C = Cocaine. The top table is from participants in the control group. The bottom table is from participants in the cocaine group. The reported number of trials for each task are the trials needed to obtain all 7 indifference points for the specified task.

Control Group	DMG $10	DMG $100	DMG $1000	DML $10	DML $100	DML $1000	PMG $10	PMG $100	PMG $1000	PML $10	PML $100	PML $1000	DHG $100	DHG $1000	DHL $100	DHL $1000
Max	118	144	109	124	138	131	117	127	123	162	125	138	114	293	99	301
75th	94	98	98	99	109	104	96	105	100	100	95	95	82	165	85	175
Median	84	84	89	78	99	84	88	97	92	82	86	89	67	119	75	131
Mean	87	87	88	83	92	88	86	94	90	88	84	87	72	139	73	144
25th	78	80	80	66	72	70	76	83	82	70	71	69	61	102	60	100
Min	56	57	58	53	50	59	58	59	56	56	57	54	45	49	48	67

Cocaine Group	DMG $10	DMG $100	DMG $1000	DML $10	DML $100	DML $1000	PMG $10	PMG $100	PMG $1000	PML $10	PML $100	PML $1000	DHG $100	DHG $1000	DHL $100	DHL $1000	DCG $100	DCG $1000	DCL $100	DCL $1000
Max	144	166	141	144	171	176	141	156	126	187	113	150	113	340	124	458	256	301	124	346
75th	110	109	104	99	102	112	106	101	100	95	95	99	86	178	88	238	123	193	76	150
Median	104	97	90	93	93	88	98	91	94	89	86	92	73	141	75	137	107	145	67	105
Mean	96	95	90	89	89	91	96	89	89	89	82	89	74	161	77	177	115	158	70	131
25th	75	74	73	70	66	62	86	71	72	68	63	68	59	107	63	91	92	115	58	97
Min	53	56	64	50	57	54	47	51	56	52	53	57	48	82	56	82	64	75	50	87

Appendix B.

Results from each ANOVA when controlling for alcohol abuse or dependence and cannabis abuse or dependence as covariates. *p < 0.05

ANOVA 1: Delay discounting of money.
Effect	dfs	F	p	pη2
Cocaine Use (A)	1,45	7.557	0.009*	0.15
Sign (B)	1,45	9.59	0.003*	0.18
Magnitude (C)	2,90	2.299	0.107	0.05
A × B	1,45	0.566	0.456	0.01
A × C	2,90	0.654	0.522	0.02
B × C	2,90	2.911	0.060	0.06
A × B × C	2,90	0.266	0.767	0.01
ANOVA 2: Probability discounting of money.
Effect	dfs	F	p	pη2
Cocaine Use (A)	1,43	0.096	0.758	0.00
Sign (B)	1,43	4.204	0.047*	0.09
Magnitude (C)	2,86	2.023	0.139	0.05
A × B	1,43	0.000	0.983	0.00
A × C	2,86	2.756	0.069	0.06
B × C	2,86	2.503	0.095	0.06
A × B × C	2,86	1.350	0.265	0.03
ANOVA 3: Delay discounting of health.
Effect	dfs	F	p	pη2
Cocaine Use (A)	1,44	2.932	0.065	0.07
Sign (B)	1,44	18.493	< 0.001*	0.31
Magnitude (C)	1,44	12.487	0.001*	0.23
A × B	1,44	1.050	0.311	0.02
A × C	1,44	0.105	0.747	0.00
B × C	1,44	0.199	0.658	0.01
A × B × C	1,44	0.884	0.352	0.02
ANOVA 4: Delay discounting of money and health
Effect	dfs	F	p	pη2
Cocaine Use (A)	1,44	7.05	0.011*	0.14
Sign (B)	1,44	13.92	0.001*	0.25
Magnitude (C)	1,44	13.24	0.001*	0.24
Commodity (D)	1,44	1.10	0.301	0.03
A × B	1,44	0.96	0.333	0.02
A × C	1,44	0.36	0.549	0.01
A × D	1,44	0.95	0.335	0.02
B × C	1,44	0.02	0.904	0.00
B × D	1,44	3.82	0.057	0.08
C × D	1,44	4.33	0.044*	0.09
A × B × C	1,44	0.20	0.660	0.01
A × B × D	1,44	0.08	0.776	0.00
A × C × D	1,44	0.01	0.927	0.00
B × C × D	1,44	0.34	0.562	0.01
A × B × C × D	1,44	1.17	0.285	0.03