Delay discounting and probability discounting as related to cigarette smoking status in adults
Introduction
People will typically discount the value of rewards when the rewards are coupled with a long delay or low probability of occurrence (e.g. Rachlin, 2000). For example, virtually everyone would prefer a larger amount of money over a smaller amount. However, most would at some point shift their preference to the smaller amount of money (thus receiving less total money) if a delay to the larger amount were added and gradually increased. This shift to a smaller amount of money would represent a decrease in subjective value for the larger amount of money as a function of it being delayed. An individual whose preference shifts to smaller rewards due to relatively short delays would be considered more “impulsive” than another individual who shifts preference only after longer delays (e.g. Bickel et al., 1999, Green et al., 1994). In addition to delay discounting (DD), the same generalized predisposition towards discounting has been demonstrated in a number of human studies with probabilistic rewards (e.g. Mitchell, 1999, Richards et al., 1999). The current paper is an examination of the relation between both delay and probability discounting (PD) as they relate to cigarette smoking status in adults.
Delay discounting as described above is the extent to which an individual discounts the value of a reward (e.g. money, food, weight loss, etc.) as a function of having to wait for it. Procedures for assessing delay discounting in humans, most of which present participants with hypothetical choice options that require them to imagine receiving differing monetary amounts after certain delays, involve determining indifference points between larger reinforcers delivered after different delays and smaller more immediate reinforcers. An indifference point is the point at which two reinforcers (i.e. a large reinforcer delivered after a delay and a smaller more immediate reinforcer) are of equal subjective value for an individual.
Indifference points obtained across a series of different delay lengths can be used to plot discount curves. The curve represents the rate of reinforcer discounting that occurs as a function of increasing the delay to its delivery. Discount curves for delayed reinforcers have been characterized most accurately in humans, rats, and pigeons by Mazur’s (1987) hyperbolic functionwhere V represents the value of the delayed reinforcer, and A and D are the amount of reinforcer and length of delay to its delivery, respectively and k is a free parameter that indicates the steepness of the discount curve. Higher k values indicate more rapid discounting, which has been defined to represent greater impulsivity (e.g. Evenden, 1999, Logue, 1988, Monterosso and Ainslie, 1999, Richards et al., 1999). Higher k values reflect a preference for more immediate smaller reinforcers at the expense of larger but delayed reinforcers.
Similarly, the outcome measure in probability discounting is the extent to which an individual discounts a larger reinforcer as a function of a decreasing probability of its delivery. Indifference points and discount curves can be derived from PD procedures just as they are for DD procedures. The pattern of discounting as a function of probability is best characterized by a hyperbolic model (Rachlin et al., 1991). The hyperbolic discount functions for probability discounting are calculated as followswhere p and O are inversely related. The p represents the probability of receiving the reinforcer, the O stands for odds against receiving the reinforcer, and the h represents the rate of discounting as a function of decreasing probability of receiving the larger reinforcer. Higher h values represent a more rapid rate of discounting and thus greater impulsivity. The h value of Eq. (2) is analogous to the k value of Eq. (1).
Measures of DD and PD are typically correlated with one another (e.g. Mitchell, 1999, Richards et al., 1999); however, correlations between these discounting measures and well recognized self-report personality questionnaires with impulsivity scales are typically low or non-existent (e.g. Crean et al., 2000, Mitchell, 1999). However, relations have been found between excessive alcohol consumption (Vuchinich and Simpson, 1998), opioid dependence (Madden et al., 1997, Petry and Casarella, 1999), and the clinical diagnoses of substance abuse and dependence, borderline personality disorder, and bipolar disorder (Allen et al., 1998, Crean et al., 2000) and higher rates of DD. Similarly, research with adult smokers has shown that those who smoke cigarettes clearly discount money by delay more on average than those who have never smoked or those who have quit smoking (e.g. Bickel et al., 1999). Such findings point to the “real-life” validity of DD as a measure of impulsivity. However, even with the typically observed correlations between DD and PD, the relation between PD and cigarette smoking in adults is less clear, with PD not differentiating between adult smokers and non-smokers in the one published study examining PD and smoking status (Mitchell, 1999). In another study with adolescent participants, PD differentiated between those adolescents who had recently tried smoking versus those who had never tried smoking, with those who had tried smoking being significantly more impulsive. In the same participants, DD did not differentiate between the groups (Reynolds et al., submitted for publication).
Given the lack of correspondence between adult and adolescent findings regarding PD and cigarette smoking, and also the lack of corroborating research in the literature examining PD and cigarette smoking in adults, the present study sought to further examine the relation between PD and smoking in adults. Measures of both DD and PD were compared between adult smokers and non-smokers. It was hypothesized that DD would differentiate between these two groups, as it has in other studies with this population (e.g. Bickel et al., 1999, Mitchell, 1999). However, given the lack of observed relation between PD and smoking in adults (Mitchell, 1999), it was hypothesized that PD would not differentiate between smokers and non-smokers, which would be consistent with the earlier finding with adults.
Section snippets
Participants
The participants were 54 (25 females) adults between 19 and 21 years of age (M=20.04; S.D.=0.78). Twenty-five of the participants (10 females) were regular smokers who reported smoking at least 20 cigarettes a day. The remaining 29 participants (15 females) were non-smokers who reported having never smoked. To biochemically validate the self-reported smoking status, a breath sample was taken to measure level of carbon monoxide (CO). Regular smokers were required to have a score ≥9 to
Results
Fig. 1, Fig. 2 are graphs made from the median indifference point values for DD and PD functions, respectively. Median values were used for Fig. 1, Fig. 2 because the data are necessarily skewed due to limits on potential variability imposed by the nature of the choice options during the task (Myerson and Green, 1995). The R2 values for the different discount functions for DD (0.82 for non-smokers and 0.75 for smokers) and PD (0.99 for both) represent the variance accounted for by , . These
Discussion
Results of the present study are consistent with past research that has shown DD differentiates between smokers and non-smokers (e.g. Bickel et al., 1999). Also PD differentiated between smokers and non-smokers, which is a new finding. Surprisingly, DD and PD were not significantly correlated with each other or with any of the questionnaire measures of personality. However, past research with these questionnaire measures of personality have shown only modest correlations with DD/PD measures (
Acknowledgements
We are grateful to Ryan Schiffbauer, Megan Dillow, and Tara Williams for their technical assistance.
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