CNP DDT

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Contents

Basic Task Description

Delay discounting is the tendency to reduce, or discount, the perceived value of a reward as a function of the amount of time delayed before receiving the reward. The more time elapsed before receiving a reward, the lower its present value with respect to current alternatives. For example, most people would ascribe a higher perceived value to $5 which could be received immediately relative to $5 received in one year. The discount rate describes the steepness of the reduction in the present value of a reward with increases in its delay. The higher the rate of delay discounting, the less relative value which is assigned to a reward as its availability is delayed. Although different measures of delay discounting have been developed (e.g., Petry and Casarella, 1999; Kirby, Petry, and Bickel, 1999), some of which involve actually experiencing delays before receiving rewards (Reynolds and Schiffbauer, 2004), we used a questionnaire-based measure which requires the examinee to determine his or her preference for various hypothetical monetary rewards available at different timeframes (Kirby, Petry, and Bickel, 1999). By evaluating an examinee’s preferences across the task, a discount rate can be estimated. The discount rate is referred to as the individual’s k value. K values have been shown to vary across individuals and have been associated with self-reported impulsivity and drug use (Kirby, Petry, and Bickel, 1999; Kirby and Petry, 2004; Audrain-McGovern et al., 2009).

Task Procedure

For general testing procedure, please refer to LA2K General Testing Procedure [here?].

Our version of the Kirby et al. (1999) delay discounting questionnaire was programmed in E-Prime 2.0. Participants must indicate their preference for one of two hypothetical options across 27 trials: one option consists of receiving an amount of money immediately (e.g., $24 today), and the other option consists of receiving a larger amount of money at a later point in time (e.g., $35 in 29 days). The discrepancy between the money amounts ($25 to $85) and the duration of the delay period (7 to 186 days) is varied across trials. Sampling of different monetary magnitudes and delay periods allows for calculation of the discounting rate (k value) most characteristic of an individual’s responding (see the Dependent Variables section for discussion of k value calculation).

The task begins with a title screen (displaying the acronym DDT in yellow on a black background in Arial size 45 font) which is advanced by a left mouse-click from the examiner. The next screen displays the instructions for the task as follows:

  • We would like you to imagine that someone is willing to give you different amounts of money. You could receive some of the amounts of money today, while other amounts you could only receive at a later point in time.
  • We would like you to make choices about different money options. Please respond as if the choices involved real money.
  • If you would prefer the money option on the LEFT, please press the LEFT key.
  • If you would prefer the money option on the RIGHT, please press the RIGHT key.
  • There are no right or wrong answers on this test. Just pick the option you would prefer if the money were real.
  • Place your hand on the table with your fingers extended and resting comfortably on the LEFT and RIGHT keys.


Following the instructions, the examinee is presented with the first trial of the task. At the top of each trial is a prompt which says “Would you prefer to receive:” (yellow Arial 16 font), followed by two choices presented below, one on the right, and one on the left (in yellow Arial size 16 font on a black background). One choice is the immediate option, and the other is the delayed option. Using the left and right keys, the participant selects the option he or she prefers (the selected option briefly [1 sec] turns green while the nonselected option turns white), and then the next trial is immediately presented on a subsequent screen. The order of the trials presented is fixed and is identical to that used by Kirby, Petry, and Bickel (1999, see Order on p. 81). The side of the screen on which the immediate and delayed option is presented varies by trial: trials 1-5, 9-14, 23, 24, 26, and 27 have the immediate option presented on the left side of the screen and the delayed option on the right side of the screen, and trials 6-8, 15-22, and 25 have the delayed option presented on the left side of the screen and the immediate option on the right side of the screen. The task concludes after 27 trials and ends with a screen which says “Thank you for participating” in yellow Arial size 16 font. Participants are not provided any feedback regarding their selections during the task, nor are they given any actual monetary rewards for their performance. For discussion of task scoring, please see the Dependent Variables section.

Task Structure Detail

  • Task Structure
    • The Delay Discounting Task has one instructional screen, followed by 27 trials.
      • Instructional screen. Advanced with a right mouse click from the examiner.
      • Experimental trials 27 trials).
        • Presentation of immediate and delayed options (no time limit on either side of screen.
          • Participant selects preferred option, and the selected option briefly turns green for 1 sec and the nonselected option turns white, and then the next trial is immediately presented.
      • End. Thank you screen presented.
    • Timing
      • Instruction screen is static until advanced by examiner with a right mouse click.
      • Presentation of trial with immediate and delayed options (no time limit).
      • Selected option turns green for 1 sec, and then immediately advances to next trial.
      • The ending thank you screen is static until advanced by the examiner with right mouse click.
  • Stimulus Characteristics
    • sensory modality: Visual text. All screens have a black background. Instructions and trials are presented in yellow Arial 16 point font. Trial text briefly turns green to indicate when a particular option is selected (and the nonselected option turns white).
    • functional modality: Visual linguistic (understanding of text).
    • presentation modality: computer display, no audio, directions are assisted by examiner.
  • Response Characteristics
    • responses required: left or right key press to select the right or left option on the screen.
      • effector modality: Manual button press.
      • functional modality: Manual button press.
    • response options (e.g., yes/no, go/no-go, forced choice, multiple choice [specify n of options], free response): multiple choice between two options.
    • response collection (e.g., examiner notes, keyboard, keypad, mouse, voice key, button press): Button press and recording of responses in Eprime 2.0.

Task Schematic

Example appearance of Delay Discounting trial.

DDTslide2.PNG

Task Parameters Table

DDTtaskparameterstable.PNG

Stimuli

Stimuli consist of visual text in a two-choice multiple choice format. Trials use yellow Arial size 16 text. This text briefly turns green to indicate when a particular option is selected.

Dependent Variables

The primary dependent variable for the Delay Discounting task is the k value. The k value is an estimate of the degree to which future rewards are discounted relative to immediate rewards, and is defined by the following hyperbolic statistical function (Kirby, Petry and Bickel, 1999) :

V =A / (1 + kD)


Where V is the present value of the delayed reward A at delay D, and k is a free parameter that determines the discount rate. If an individual were indifferent between the immediate and delayed reward on any given trial, V in the above equation can be assumed to be the smaller, immediate option, and k would thus represent a discounting rate which is indifferent between the immediate and delayed reward on that trial. Thus, each trial on the task can be assigned a k value which represents the point at which an individual would be indifferent between the immediate and delayed options. The indifference k values for the trials on the task have one of the following k values:

  • 0.00016
  • 0.00040
  • 0.0010
  • 0.0025
  • 0.0060
  • 0.016
  • 0.041
  • 0.10
  • 0.25


Each of the above indifference k values is represented by 3 items on the task (3 items by 9 indifference k values = 27 total items). One of the 3 items for each k value uses small sums of money ($25 to $35), one uses medium sums of money ($50 to $60), and one uses large sums of money ($75 to $85). Different magnitudes of reward were used because discount rates typically decrease as the magnitude of rewards increase (Kirby et al., 1999).

Now, although the indifference k value for each item is known, the participant’s actual k value when responding to any individual item is NOT known. When responding to the trials, participants indicate their preference for either the immediate or delayed option on any given trial. If they select the immediate option, their actual k value can be assumed to be higher than the indifference k for that item; if they select the delayed option, their actual k value can be assumed to be lower than the indifference k for that item. In order to estimate the individual’s actual k value, the participant’s responding across trials is mapped onto a range of possible k values. This range consists of the highest (.25) and lowest (.00016) possible k values described above, with intermediate k values which consist of the geometric mean between the adjacent indifference k values of the list above (e.g., in the preceding list, 0.00016 was followed by 0.00040. The geometric mean of these values is 0.000253, which is shown below). The geometric mean is used rather than the arithmetic mean to avoid underweighting the smaller of the two values. I will call this range of k values the “placeholder” k values, and the placeholder range is as follows:

  • 0.00016
  • 0.000253
  • 0.000632
  • 0.001581
  • 0.003873
  • 0.009798
  • 0.025612
  • 0.064031
  • 0.158114
  • 0.25

Now, for each item on the task, the participant either chooses the immediate or the delayed option. If the immediate option was chosen, all the placeholder k values above the indifference k value of the item are considered to be consistent with that selection (all these placeholders get value of 1), while all the k values below the indifference k value of the item are considered to be inconsistent with that selection (all these placeholders get a value of 0). Conversely, if the delayed option was chosen, all the placeholder k values below the indifference k value of the item are considered to be consistent with that selection (all these placeholders get value of 1), while all the placeholder k values above the indifference k value of the item are considered to be inconsistent with that selection (all these placeholders get a value of 0). So for each item on the measure, the placeholder k values shown above receive a score of 0 or 1 depending on how the participant responds. This process is achieved with a looping function in the scoring program.

In order to determine the participant’s final actual k value, the tally of the placeholder k values is evaluated to determine which placeholder value had the most selections across the task which were consistent with it. Because of possible reward magnitude effects, this process is done in the small, medium, and large sums of money separately. When two or more placeholder values were equally consistent in a given magnitude, the geometric mean of the placeholder values was taken to provide the final k value. Lastly, to get the total k value for the participant, the geometric mean of the k values for the small, medium, and large magnitudes was obtained. Because k value data are typically skewed, the variables are typically normalized with the natural log function prior to implementation in research (Kirby et al., 1999).

Before using the obtained k values, it is important to determine whether the participant responded consistently enough across trials for the derived k value to be meaningful. Kirby and Petry (2004) defined inconsistent responding as the selection of 3 or more response options within a given magnitude that are inconsistent with the assigned k value. Variables for inconsistent responding have been created for each reward magnitude, and it is recommended that the Delay Discounting data not be used for any subject with inconsistent responding in any magnitude.

In addition to the k values for the small, medium, large, and total sums of money, the mean, median and standard deviation of reaction times are derived for all button presses during the task. These reaction time variables are exploratory.

Because there is a typo on item 7 of our version of the task, we recommend the use of the LOGGED REVISED TOTAL K VALUE as the primary variable of interest. The small k value, in particular, should be used with caution given potential unreliability (see History of Checking Scoring section for details).

Table of all available variables

DDTvariables2.png

Cleaning Rules

The algorithm to score the DDT does not work if the task was not completed in its entirety, so all available data should be comprised of complete administrations. The primary consideration in cleaning the data lies in checking the INCONSISTENCY variables for each money magnitude. We recommend excluding all subjects who have an inconsistency in ANY reward magnitude; one or more inconsistencies suggest that the hyperbolic function does not fit the data accurately.

Because there is a typo on item number 7, we recommend using the REVISED inconsistency measure for the small k magnitude (DDT_R_SMALL_INCON), rather than the original measure. Similarly, we recommend using the REVISED logged total k value as the primary variable of interest (DDT_R_LOG_TOTAL_K).

In addition to excluding participants with inconsistent responding, researchers can consider excluding participants who always selected the delayed option throughout the task (DDT_TOTAL_K = .00016), or those who always selected the immediate option (DDT_TOTAL_K = .25).

Given the skewness of the data, we generally recommend using the logged, versus the raw, data.

Code/Algorithms

The following is a DDT scoring script in Visual Basic language. This script was provided by Stone Shih, and is based on a script developed by Cody Ashe-McNalley, Andy Dean, and John Monterosso.

Dim aryScore(10) for s = 1 to ubound(aryScore) aryScore(s) = null next

' Modification based on Cody Ashe-McNalley 11/12/08 dim slots(9), Trial_Data(9,3), Discount_Rates(10) Trial_Data(1, 2) = 0.00016 Trial_Data(5, 3) = 0.006 Trial_Data(5, 1) = 0.006 Trial_Data(9, 3) = 0.25 Trial_Data(7, 1) = 0.041 Trial_Data(2, 2) = 0.0004 Trial_Data(8, 1) = 0.1 Trial_Data(8, 2) = 0.1 Trial_Data(1, 3) = 0.00016 Trial_Data(5, 2) = 0.006 Trial_Data(9, 1) = 0.25 Trial_Data(3, 3) = 0.001 Trial_Data(1, 1) = 0.00016 Trial_Data(7, 2) = 0.041 Trial_Data(4, 3) = 0.0025 Trial_Data(4, 2) = 0.0025 Trial_Data(2, 3) = 0.0004 Trial_Data(6, 1) = 0.016 Trial_Data(8, 3) = 0.1 Trial_Data(2, 1) = 0.0004 Trial_Data(6, 2) = 0.016 Trial_Data(4, 1) = 0.0025 Trial_Data(7, 3) = 0.041 Trial_Data(3, 2) = 0.001 Trial_Data(6, 3) = 0.016 Trial_Data(3, 1) = 0.001 Trial_Data(9, 2) = 0.25

' These values are the endpoints and geometric means of the k indifference values Discount_Rates(1) = 0.00016 Discount_Rates(2) = 0.000253 Discount_Rates(3) = 0.000632 Discount_Rates(4) = 0.001581 Discount_Rates(5) = 0.003873 Discount_Rates(6) = 0.009798 Discount_Rates(7) = 0.025612 Discount_Rates(8) = 0.064031 Discount_Rates(9) = 0.158114 Discount_Rates(10) = 0.25


Dim rank Dim Choice_Counts(10,3) Dim TopScores() Dim Inconsistencies(3) 'Indicator for inconsistent results Dim Delayed_Choice(10,3)

strSQL = "SELECT * FROM " & TableName & " where [Subject]=" & SubjectID Set ers = Server.CreateObject("ADODB.Recordset") ers.Open strSQL, DataConn, adOpenStatic

if ers.eof or ers.recordcount <> 27 then exit sub end if

do while not ers.eof

       select case ucase(ers("R_Size"))

Case "S"

               m = 1
           Case "M"
               m = 2
           Case "L"
               m = 3

case else m = ers("R_Size")

       End Select

response.flush If ((right(ers("choice2"),4) = "days" and ers("ChoiceResp") = "{RIGHTARROW}") or (right(ers("choice2"),4) <> "days" and ers("ChoiceResp") = "{LEFTARROW}")) Then

           Delayed_Choice(ers("k_rank"), m) = True
       Else
           Delayed_Choice(ers("k_rank"), m) = False
       End If
   	ers.movenext

loop

For m = 1 To 3

   	aryScore(m) = 1

For i = 1 To 9 For a = 1 To 10 'Debug.Print "Trial_Data = " & Trial_Data(i, m) & " DiscountRate = " & Discount_Rates(a) & " DelayedChoice = " & Delayed_Choice(i, m) If a <> 1 And Trial_Data(i, m) < Discount_Rates(a) And Delayed_Choice(i, m) = False Then Choice_Counts(a, m) = Choice_Counts(a, m) + 1

           	ElseIf a <> 10 And Trial_Data(i, m) > Discount_Rates(a) And Delayed_Choice(i, m) = True Then
               	Choice_Counts(a, m) = Choice_Counts(a, m) + 1
           	ElseIf a = 1 And Trial_Data(i, m) = Discount_Rates(a) And Delayed_Choice(i, m) = True Then
             	  Choice_Counts(1, m) = Choice_Counts(1, m) + 1
           	ElseIf a = 10 And Trial_Data(i, m) = Discount_Rates(a) And Delayed_Choice(i, m) = False Then
              	 Choice_Counts(10, m) = Choice_Counts(10, m) + 1

End If

       	Next
   	Next
   	' Determine the most consistent choice
   	Top_Choice = -1
   	For i = 1 To 10

If Choice_Counts(i, m) > Top_Choice Then Top_Choice = Choice_Counts(i, m) end if

   	Next

' debug.print "Top Choice = " & Top_Choice

   	' Determine all discount rates that are equally consistent (if more than one)
   	ReDim TopScores(1)
   	For i = 1 To 10

' debug.print "i = " & i ' debug.print "Choice_Counts(" & i & "," & m & ") = " & Choice_Counts(i,m)

       	If Choice_Counts(i, m) = Top_Choice Then

' debug.print "TopScores contains " & ubound( TopScores ) & " items"

           	If TopScores(1) > 0 Then
               	ReDim Preserve TopScores(UBound(TopScores) + 1)
               	TopScores(UBound(TopScores)) = i
           	Else
               	TopScores(1) = i
           	End If
       	End If
   	Next
   	' Calculate the assigned discount rate
   	If UBound(TopScores) > 1 Then
       	For i = 1 To UBound(TopScores)
           	aryScore(m) = aryScore(m) * CDbl(Discount_Rates(TopScores(i)))
       	Next
       	aryScore(m) = aryScore(m) ^ (1 / UBound(TopScores))
   	Else

' debug.print TopScores(1) aryScore(m) = Discount_Rates(TopScores(1))

   	End If
   	
   	' Check if the most common choice is not actually consistent (according to Kirby criteria)
   	If Top_Choice < 7 Then Inconsistencies(m) = True

Next

   aryScore(4) = (aryScore(1) * aryScore(2) * aryScore(3)) ^ (1 / 3)

for i = 1 to 4 aryScore(i) = formatnumber(aryScore(i),6) next

Dim Distribution

for i = 1 to 3 if (len(Inconsistencies(i))=0) then aryScore(4+i)="N" else aryScore(4+i)="Y" end if next kk = 8 ' =============================================================================================== ' Mean RT ' =============================================================================================== strSQL = "SELECT avg(cast(ChoiceRT as float))as MeanValue FROM " & TableName & " where [Subject]=" & SubjectID Set ers = Server.CreateObject("ADODB.Recordset") ers.Open strSQL, DataConn, adOpenStatic TotalRec = ers.RecordCount if ers.eof then aryScore(kk) = null else aryScore(kk) = ers("MeanValue") end if kk = kk + 1

' =============================================================================================== ' Median RT ' =============================================================================================== sSQL = "SELECT * FROM " & TableName & " where [Subject]=" & SubjectID & " and ChoiceRT is not null order by ChoiceRT" aryScore(kk) = RunSQL_MEDIAN(sSQL,"ChoiceRT") kk = kk + 1

' =============================================================================================== ' SD Reaction Time for 1 repeat ' =============================================================================================== strSQL = "SELECT STDEV(ChoiceRT) as STDDEV FROM " & TableName & " where [Subject]=" & SubjectID Set ers = Server.CreateObject("ADODB.Recordset") ers.Open strSQL, DataConn, adOpenStatic if ers.eof then aryScore(kk) = Null else aryScore(kk) = ers("STDDEV") end if



History of Checking Scoring and Program Changes

  • Before November 2009, the Delay Discounting Task required that the participant hit the left or right key twice to confirm the selection on any given trial (the first entry highlighted the option, and the second entry confirmed the selection). Some time slightly before November 2008 the task was changed by Bob Bilder and Fred Sabb so that the participant did not need to hit the left or right key twice to confirm their selection. Only one key press is now required for each trial.
  • In November 2008 Andy Dean checked the Delay Discounting Program and found an error. The variable named “DelayedChoice” within the eprime program is incorrect after item 19 (i.e., the option designated as the delayed choice was in fact the immediate choice). The scoring subsequently used to extract the k values was altered so that the DelayedChoice variable was no longer used. This error did not affect the running of the task, nor the accuracy of scoring after the alteration was made.
  • In July 2009 Andy Dean checked the results of the Delay Discounting Task and found them to be accurate.
  • In July 2011 Andy Dean found a typo on trial number 7 of the task. The delayed option on the trial should read “$35 in 13 days”, but instead it reads “$35 in 136 days”. Because of this error, the indifference k value for this item is 0.0098, rather than the intended 0.10. This item is part of the calculation for the small magnitude k value. Andy Dean worked with Stone Shih to reprogram the scoring method for the small magnitude so that the item was excluded from the scoring. When the scores for the small magnitude k were compared with and without the item in 680 healthy participants, the scores were highly similar when using the logged data (r = .96, p = .000), but were less similar when using the raw (skewed) data (r = .83, p = .000). When the total k values (for all sums of money) were compared with and without the item, the scores were all highly similar (raw data r = .98, p = .000; logged data r = .99, p = .000). In sum, we first recommend that the logged, rather than the raw, data from the task be used in analyses. With respect to the logged total k value, it should not make much difference if the original (with item 7) or revised (without item 7) k values are used. However, if using the small k value in analyses, we recommend using the revised logged k value (without item 7) rather than the original. However, it should be noted that the revised logged small k value is comprised of fewer items than the original small k value (8 rather than 9), and is thus less reliable than as originally intended. We generally recommend using the revised logged total k values as the primary variable of interest.
  • Because of the typo on item 7, we also developed measures of inconsistency with and without the item. However, when excluding the item, the inconsistency measure needs to be revised because of the item change in the subscale (8 vs. 9 items). In sum, we recommend using the REVISED measures of inconsistency and k value in the small magnitude, as well as the revised total logged k value as the primary variable of interest.

Data Distributions

Data below EXCLUDED participants who were flagged for any reason and those who were not completers. Participants who were not healthy controls (e.g., ADHD, schizophrenia) were also excluded.

The following data did NOT exclude item number 7 from calculations

Evaluation of Inconsistent Responding: Frequencies

DDTinconsistencies.png

Histograms and frequencies (excluding inconsistent responders from any magnitude)

Small magnitude raw k values

Smallkrawhistogram.png

Smallkfreq.png

Small magnitude logged k values

Smallklog.png

Medium magnitude raw k values

Mediumkrawhistogram.png

Mediumkfreq.png

Medium magnitude logged k values

Mediumklog.png

Large magnitude raw k values

Largekrawhistogram.png

Largekfreq.png

Large magnitude logged k values

Largeklog.png

All magnitudes raw k values

Allkrawhistogram.png

All magnitudes logged k values

Allklog.png

Relationship between demographics and logged total k value

No relation with age

Age.png


No relation with gender

Gender.png

p = .15
Negative relationship between education and delay discounting

Education.png


Relationship between Hispanic ethnicity and delay discounting

Ethnicity.png

p =.004
Modest to no relationship between Barratt Impulsiveness subscales and delay discounting

BIS.png


Comparison of calculations which included or excluded item number 7 (inconsistencies were not excluded)

Correlation between small k value and REVISED small k value, raw and logged

Revisedsmallk.png

Correlation between total k value and REVISED total k value, raw and logged

Revisedtotalk.png

Inconsistencies with and without item 7

Frequency of inconsistencies in the ORIGINAL small k magnitude (including item 7)

Originalsmallkinconsistencies.png

Frequency of inconsistencies in the REVISED small k magnitude (excluding item 7 but NOT revising inconsistency rule)

Wrongsmallkinconsistencies.png

Frequency of inconsistencies in the REVISED small k magnitude (excluding item 7 AND revising inconsistency rule)

Revisedsmallkinconsistencies.png

References

Audrain-McGovern J, Rodriquez D, Epstein LH, Cuevas J, Rodgers K, Wileyto EP (2009) Does delay discounting play an etiological role in smoking or is it a consequence of smoking? Drug Alcohol Dep 103: 99-106.

Kirby KN, Petry NM (2004) Heroin and cocaine abusers have higher discount rates for delayed rewards than alcoholics or non-drug-using-controls. Addiction 99: 461-471.

Kirby KN, Petry NM, Bickel WK (1999) Heroin addicts have higher discount rates for delayed rewards than non-drug-using controls. J Exp Psychology: General 128: 78-87.

Reynolds B, Schiffbauer R (2004) Measuring state changes in human delay discounting: An experiential discounting task. Behavioural Processes 67: 343-356.