Inclusion Criteria:

• - Diagnosis of MS, received ≥3-months pre-enrolment (allowing for acute adjustment, as per other trials of cognitive rehabilitation) - Age 18-89 (to meet the standardisation criteria of psychometric assessments) - Cognitive difficulties as assessed by Perceived Deficits Questionnaire (PDQ) self-report (≥27) and Repeatable Battery for the Assessment of Neuropsychological Status (RBANS) testing (≤1 standard deviation below normative reference-value) - Able to read and speak English to standard necessary for completing assessment and intervention procedures.

• - Able and willing to access a computer/tablet/smart-phone with internet connection throughout the study.

• - Able and willing to give informed consent.

Exclusion Criteria:

• - Currently receiving cognitive rehabilitation.

• - Previously received SMART training.

- Vision or hearing problems precluding completion of procedures

Background: Cognitive deficits have been identified as the most debilitating impact of MS. These deficits interfere with daily living, manifesting as inattention (e.g., getting easily distracted), forgetting (e.g., leaving the stove on after cooking), and problem-solving difficulties (e.g., getting confused when completing a multi-stage task like cooking). The burden of these deficits reduces quality of life and restricts daily activities and employment

• - and correspondingly, diminishes patient perceptions of personal competence and self-worth.

Cognitive rehabilitation is not routinely offered in the National Health Service (NHS)

• - and, when it is offered, largely focuses on teaching people to compensate for deficits (e.g., using external memory aids) rather than retraining cognitive skills.

A recent state-of-the-field review from international MS experts has called for research towards identifying effective, evidence-based, and clinically feasible interventions to address cognitive deficits in MS. There is evident uncertainty about how to intervene effectively, and this is recognised by the James Lind Alliance as a top-10 priority area for research-funding. Our trial tests the feasibility of a highly accessible and low-resource format of cognitive rehabilitation (online training). Given NHS resource constraints, the scale of the problem, and concerns about face-to-face consultation in the context of COVID-19, new and cost-effective ways of implementing promising cognitive rehabilitation interventions are needed. Low-resource online formats are more likely to be implemented if found to be clinically effective, enable wider access for patients, and provide active support for self-management

• - consistent with (1) models of care for managing longer-term conditions and (2) the digital healthcare agenda.

As a feasibility trial, outcomes are unlikely to immediately effect changes to NHS practice. However, this is a necessary step towards developing a definitive trial

• - and will give us a signal of efficacy, a prerequisite for progression to a definitive trial.

If found to be clinically- and cost-effective, the latter trial could create a step-change in MS cognitive rehabilitation

• - improving service-delivery and optimising support with limited additional resources.

Aim: To conduct a feasibility study to inform development of a definitive trial of SMART (an online 'brain training' treatment) for improving cognitive functioning in people with MS. The investigators will assess: 1. Acceptability to participants of the intervention, delivery format, inclusion/exclusion criteria, baseline and outcome measures, randomisation protocol, and study procedures. 2. The framework for a cost-effectiveness analysis alongside a definitive trial. 3. Participant recruitment and retention rates. 4. Sample-size needed for fully powered trial. 5. Signal of efficacy. Research plan: The investigators will conduct a three-arm feasibility Randomised Controlled Trial (RCT) comparing

• (1) SMART + treatment-as-usual (TAU) with (2) TAU and (3) active control ('sham') training + TAU.

Consenting eligible patients will complete a baseline cognitive assessment battery and questionnaires assessing impact of living with MS, health-related quality of life, subjective cognitive difficulties, and service/resource-use. After completing baseline assessments, participants will be randomly allocated to one of three arms (using minimisation to balance participant characteristics across arms): 1. SMART + TAU. 2. TAU. Content of TAU for cognitive concerns, based on our clinical experience and knowledge, is often informational support from an MS Nurse with signposting to the MS Society/MS Trust websites. 3. Sham training (active control: Sudoku) + TAU. The investigators selected Sudoku to control for expectancy effects based on popular conceptions that it broadly improves cognitive functions, coupled with little evidence supporting this notion, and its use as an active control in similar trials. Sham-training will be delivered online, over the same timeframe/regimen as SMART treatment, and with telephone support to facilitate access

• - controlling for modality, schedule of engagement, and relational support.

A Research Fellow will complete blinded outcomes at 3- and 6-months post-randomisation, by re-administering baseline measures. Quantitative data will enable sample-size calculation for a definitive study and determine signal of efficacy. After the first follow-up assessment (>3 months post-randomisation) a sub-sample of participants will engage in feasibility-feedback interviews.

Arms

Experimental: TAU + SMART

Participants in this arm will receive treatment-as-usual (TAU) plus the experimental SMART intervention (theory-based cognitive training)

Sham Comparator: TAU + Sham training

Participants in this arm will receive treatment-as-usual (TAU) plus a control (sham) cognitive training intervention

No Intervention: TAU (treatment-as-usual)

Participants in this arm will receive treatment-as-usual (TAU). Content of TAU for cognitive concerns, based on our clinical experience and knowledge, is often informational support from an MS Nurse with signposting to the MS Society/MS Trust websites.

Interventions

Behavioral: - SMART

SMART (Strengthening Mental Abilities Through Relational Training) is a web-based cognitive training program that directly trains 'relational skills' - skills necessary to understand how concepts relate to one another, which underpin complex cognition.

Behavioral: - Sham brain training (Sudoku)

Sudoku was selected to control for expectancy effects based on popular conceptions that it broadly improves cognitive functions, coupled with little evidence supporting this notion, and its use as an active control in similar trials.