Attention-Deficit/Hyperactivity Disorder (ADHD) is characterized by a persistent pattern of developmentally inappropriate levels of inattention, hyperactivity, and impulsivity (American Psychiatric Association, 2000). The high rates of heritability for ADHD suggest a genetic contribution, leading to investigations of cognitive endophenotypes in ADHD (Castellanos and Tannock, 2002, DiMaio et al., 2003 and Faraone and Doyle, 2001). However, the search for an elementary, behaviorally identifiable marker of ADHD that is not part of the symptomatology used in the DSM-IV definition has been elusive.
Past attempts to identify cognitive endophenotypes have almost exclusively focused on dysfunctions in the prefrontal cortex, namely executive functioning. In explicating these dysfunctions, however, both past theoretical and empirical work (for a review see Barkley (1997), and recent work by Rommelse and colleagues (Rommelse et al., 2008), suggest an endophenotypic component in ADHD related to time estimation and production. Individuals with ADHD and their non-affected siblings exhibited motor timing deficits compared to participants from families with no formally diagnosed or suspected ADHD behaviors or symptoms. Other studies, however, have failed to show differences in time estimation when comparing children with and without ADHD (see Toplak, Dockstader, & Tannock (2006) for a review).
Luman et al. (2009) examined timing variance of children with ADHD as well as children with ADHD and Oppositional Defiant Disorder (ODD) in a 1000 millisecond (ms) timed interval tapping task. The notion that ADHD is primarily a difficulty in response inhibition (Barkley, 1997) was supported by the observation that children with ADHD and children with ADHD + ODD underestimated the 1000 ms interval compared to typically developing children. Furthermore, children with ADHD exhibited a much larger timing variance than typically developing children.
Valera et al. (2010) utilized a timed tapping task and demonstrated that along with increased timing variability of adults with ADHD compared to adults without ADHD, neuro-anatomical areas of the central nervous system such as the cerebellum and basal ganglia, known to be motor timing areas, showed less activity for adults with ADHD compared to adults without ADHD. This result provides initial evidence that a tapping timing task can be used to capture fundamental neurological differences in ADHD.
Valera et al. (2010) and Luman et al. (2009) employed the most widely used and useful analytical model of time-keeping by Wing and Kristofferson (1973). However, in both studies, there was not a detailed analysis of what might be called Wing and Kristofferson behavior. For example, Luman et al. (2009) did not compute the classic motor and clock variances. Furthermore, Valera et al. did not report whether participants obeyed the fundamental assumptions of the Wing and Kristofferson model. Thus, in the current study, we examined timing in children with ADHD within the timing framework of Wing and Kristofferson. Furthermore, we fully explored how child participants with and without ADHD produce temporal intervals in a tapping task when the interval time series obeys the Wing and Kristofferson assumptions, compared to not obeying these assumptions.
In the Wing and Kristofferson (1973) model, it is assumed that timing is open-loop; participants are not basing the production of the next interval upon evaluating the duration of the previous interval(s). Wing and Kristofferson show how the variance of the time series can be decomposed into two additive components, the variance attributed to a central time-keeping process (clock), and the variance attributed to an implementation process (motor variance). Motor variance is computed from the covariance of adjacent intervals, termed the lag one covariance. The model computations require that the lag one covariance be negative. Furthermore, the lag one autocorrelation must be bounded between 0.0 and −.05. In other words, a long interval is followed by a short interval and vice versa, and the covariance cannot be greater than half of the total variance. Once the motor variance is calculated, the clock variance can be estimated by subtracting twice the implementation variance from the total variance.
One caveat is in order. The interval time series might drift from the prescribed rate. This “drift” increases the total variance and of course reduces the negativity of the lag one covariance. Thus, a time series is first detrended, on a trial by trial basis, to remove this unwanted source of variance and then the total detrended variance is partitioned into clock and implementation (motor) components (Keele et al., 1985 and Wing and Kristofferson, 1973).
If a time series of intervals is not consistent with the Wing and Kristofferson (1973) model, then time keeping might not be attributable to an open-loop central clock-like timing process (see Zelaznik, Spencer, & Ivry, 2008). In the present study we examined timing behavior across groups when the Wing and Kristofferson model was obeyed and not obeyed, respectively. By examining how timing precision differs for children with ADHD compared to children without ADHD in these conditions, we are able to examine various sources of timing precision.
Finally, timing variance is composed of other sources outside of the Wing and Kristofferson (1973) model. People can change strategies across trials, as well as within trials. Small alterations in behavior (a sneeze or a yawn) can produce large changes in timing variance. Because in the present work we are interested in clock-like timing, we want to have a maximum likelihood of capturing the variability due to the inherent nature of an unadorned clock-like timing process. Thus, we also report on the best eight trials in terms of timing precision. It is possible that children without ADHD are not better timekeepers than children with ADHD once these unwanted sources of variability have been removed. Zelaznik and colleagues have used this technique for over a decade, with great success, to examine timing precision (see Zelaznik et al., 2008).
Thus, we now re-examine the Valera et al. (2010) and Luman et al. (2009) work relative to the tenets of the Wing and Kristofferson (1973) model. Valera et al. found that in a timed tapping task, at a 500 ms goal interval, adults with ADHD exhibited a greater clock variance but not a greater motor variance compared to adult participants without ADHD. This result was interpreted as supporting a central time keeping deficit associated with ADHD, but not a motor output deficit. Luman et al. discussed the Wing and Kristofferson model, but did not conduct the classic and expected analyses. Instead they reported what appears to be trial to trial variability, not an interval time series variance.
Although the recent work of Valera et al. (2010) and Luman et al. (2009) supports the idea of a timing deficit in people with ADHD, the overall research literature offers conflicting messages. Timing in the millisecond range has been investigated in children and adolescents with ADHD with visual synchronized tapping (Rubia et al., 1999, Rubia et al., 1999 and Rubia et al., 2001), auditory synchronized tapping (Pitcher, Piek, & Barrett, 2002), simultaneous visual and auditory synchronized tapping (Ben-Pazi, Gross-Tsur, Bergman, & Shalev, 2003), visual synchronized tapping followed by a continuation phase (Toplak & Tannock, 2005), and auditory synchronized tapping followed by a continuation phase (Tiffin-Richards et al., 2004 and Toplak and Tannock, 2005) (see Toplak et al., 2006, for a review). Because the current study focused on the continuation phase of tapping, it is of interest that, to our knowledge, only four of the above studies (Luman et al., 2009, Tiffin-Richards et al., 2004, Toplak and Tannock, 2005 and Valera et al., 2010) included a continuation phase. One of these studies compared 10- to 13-year-old children with or without an ADHD diagnosis and reported no differences in timing (average inter-response interval or inter-response interval variability) in the continuation phase (Tiffin-Richards et al., 2004). The second study reported a significantly greater coefficient of variation in the continuation phase of a visually-defined 1000-ms interval for 13- to 18-year-old children with an ADHD diagnosis (Toplak & Tannock, 2005). Notably, neither of these studies employed the Wing and Kristofferson (1973) analysis.
Valera et al. (2010) conducted the Wing and Kristofferson (1973) analysis on the continuation portion of the time series (the Wing and Kristofferson decomposition should not be conducted on the synchronization portion of the trial). Given the importance of the Valera study in examining timekeeping in a principled and theoretical fashion, we present a comparable behavioral study that examines children with ADHD and typically developing children. In pursuing this aim, we extend Valera et al. and Luman et al. (2009) by reporting on key details of the Wing and Kristofferson analysis. Accordingly, we provide the first detailed Wing and Kristofferson analysis of timing in tapping for children with and without ADHD. Furthermore, we examined timing variability as a function of the child performing their best, or not. By providing detailed analyses of timing, we hope to be able to begin to delineate a behavioral marker of ADHD that is not part of the diagnostic symptomology.
