Control program, with the same functional characteristics but without the targeted cognitive functions.

For the control program (comparator), we will use a software solution from the same company, but dedicated to stimulating and training auditory functions (AUDITICO® software). The advantage of this solution is that, like PRESCO®, it offers training exercises that are not aimed at re-educating cognitive functions. These include, for example, sound identification and discrimination activities. This tool can also be used by anyone, and is accessible for follow-up by the practitioner. It also offers levels of increasing difficulty, making it stimulating for users.

To evaluate the efficacy of cognitive remediation versus the control program, alongside MPH treatment, in reducing ADHD symptoms in patients with comorbid addictions, at the end of treatment and 6 months post-treatment

The evaluation criterion will be the proportion of patients who achieved symptom improvement (at least 30% improvement in the ASRS score (Adult ADHD Self-Report Scale Symptom Checklist, higher scores mean a worse outcome, the minimum and maximum values for each score are 0 and 36 respectively) for the dominant ADHD subtype, or either in case of combined type) in each group, estimated at treatment end or 6 months later.

To compare the efficacy of cognitive remediation versus the control program in addition to MPH treatment, at the end of treatment and 6 months after the end of treatment, in improving neuropsychological deficits.

Neuropsychological deficits will be evaluated using performance scores on a series of neurocognitive tasks assessing key cognitive functions (all performance scores will be standardized to be comparable, i.e. Z-scores):

• D2-R (selective attention),
• Digit memory test (short-term memory and working memory),
• Stroop test (inhibition),
• Verbal fluency test (spontaneous flexibility)
• Zoo test (planning)

To compare the efficacy of cognitive remediation versus the control program in addition to MPH treatment, at the end of treatment and 6 months after the end of treatment, in reducing the severity of comorbid addictive disorders

The severity of comorbid addictive disorders will be assessed based on the number of diagnostic criteria met in the diagnostic interviews, including:

• MINI-S (alcohol and substance use disorders),
• NODS (gambling disorder),
• Diagnostic interview adapted from NODS for sexual addiction,
• Diagnostic interview adapted from NODS for gaming disorder,
• YFAS for food addiction,
• Mc Elroy for compulsive buying.

Compare the efficacy of cognitive remediation versus the control program, in addition to MPH treatment, at the end of treatment and 6 months later, in alleviating psychopathological features associated with ADHD-addiction(s) comorbidity. Psychopathological characteristics associated with ADHD-addiction(s) comorbidity will be assessed by (all scores will be standardized to be comparable, i.e. Z-scores):

• UPPS-P (Urgency, Premeditation (lack of), Perseverance (lack of), Sensation seeking impulsivity behavior scale, higher scores mean a worse outcome, the minimum and maximum values for each score are 4 and 16 respectively), (impulsivity): 5 scores,
• DERS-16(Difficulties in Emotion Regulation Scale, higher scores mean a worse outcome, the minimum and maximum values are 16 and 80 respectively), (emotional dysregulation): 5 scores,
• RSES (Rosenberg Self-Esteem Scale, higher score mean a better outcome, the minimum and maximum values are 10 and 40 respectively), (self-esteem): 1 score.

To compare the efficacy of cognitive remediation versus the control program in addition to MPH treatment, at the end of treatment and 6 months after the end of treatment, in enhancing adherence to MPH treatment through CRT.

Adherence to treatment will be evaluated based on:

• Compliance with and tolerance to medication (structured interview, vital signs, and weight checks at follow-up visits)
• The number of CRT sessions completed relative to the number of planned sessions.

To analyze the short- and medium-term evolution of functional impairment based on ADHD subtype (predominantly inattentive, predominantly impulsive/hyperactive, or combined type).

Functional impairment will be assessed using the WFIRS (Weiss Functional Impairment Rating Scale, A score of more than 1.5 points is considered to be representative of an impairment in the area concerned. Higher scores mean a worse outcome, the minimum and maximum values for each score are 0 and 3 respectively), (improvement of at least 30% in the functional impact score between post- and pre-treatment assessment), and the ADHD subtype will be determined using the DIVA-5 diagnostic interview.