Ahead of the (ROC) Curve: A Statistical Approach to Utilizing Ex-Gaussian Parameters of Reaction Time in Diagnosing ADHD Across Three Developmental Periods

Ex-Gaussian vector metric and similarity index applied to reaction time analysis

In psychology and cognitive neuroscience, reaction time (RT) series and their ex-Gaussian distributions are commonly used as scalar quantities to explore the time course of attentional processes. However, we propose that such attentional processes can also be analyzed using an "ex-Gaussian vector", defined by successive triads of ex-Gaussian sigma, tau, and mu parameters from RT series. This geometrical object may help characterize interindividual differences between congruent and incongruent stimuli in the attentional Stroop task within a group of participants. To test these hypotheses, we calculated the similarity index of these geometrical objects in young adults without detectable neurological disorders. Our findings show that during two weeks of continuous Stroop task application, each participant displayed distinct ex-Gaussian RT vectors in a Cartesian 3D plot. Furthermore, our study found that the similarity index between ex-Gaussian RT vectors was significantly higher for incongruent stimuli than for congruent stimuli.

Differences in Ex-Gaussian Parameters from Response Time Distributions Between Individuals with and Without Attention Deficit/Hyperactivity Disorder: A Meta-analysis

Attention Deficit Hyperactivity Disorder (ADHD) is one of the most prevalent neurodevelopmental disorders in childhood and adolescence. Differences in reaction times (RT) in cognitive tasks have been consistently observed between ADHD and typical participants. Instead of estimating means and standard deviations, fitting non-symmetrical distributions like the ex-Gaussian, characterized by three parameters (µ, σ, and τ), account for the whole RT distributions. A meta-analysis is performed with all the available literature using ex-Gaussian distributions for comparisons between individuals with ADHD and controls. Results show that τ and σ are generally greater for ADHD samples, while µ tends to be larger for typical groups but only for younger ages. Differences in τ are also moderated by ADHD subtypes. τ and σ show, respectively, quadratic and linear relationships with inter-stimulus intervals from Continuous Performance Test and Go/No Go tasks. Furthermore, tasks and cognitive domains influence the three parameters. Interpretations of ex-Gaussian parameters and clinical implications of these findings are also discussed. Fitting ex-Gaussian distributions to RT data is a useful way to explore differences between individuals with ADHD and healthy controls.

ADHD Adults Show Lower Interindividual Similarity in Ex-Gaussian Reaction Time Vectors for Congruent Stimuli Compared to Control Peers

OBJECTIVE

Interindividual similarity refers to how similarly individuals respond when receiving the same stimulus or intervention. In this study, we aimed to examine interindividual similarity in adults with ADHD.

METHOD

We used the cosine similarity index of ex-Gaussian reaction time (RT) vectors of mu, sigma, and tau parameters during a Stroop task.

RESULTS

Our results demonstrate that the ADHD group exhibits a reduced interindividual similarity index in their ex-Gaussian RT vectors for congruent stimuli compared to the healthy control group. Importantly, we did not find significant differences in the interindividual similarity index to incongruent stimuli between both groups, thus suggesting that this reduced index was selective for congruent stimuli.

CONCLUSION

Our findings highlight that ADHD adults exhibit more significant interindividual differences in cognitive functioning when processing congruent stimuli than healthy controls. These results provide new insights into the selective mechanisms underlying ADHD and may contribute to developing new targeted interventions for this disorder.