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Serial cognitive assessment in multiple sclerosis can help identify patients at higher risk of disability progression, but high dimensionality of reaction-time data makes analysis challenging. We developed a method to convert longitudinal reaction-time data into images and applied deep survival modelling to predict disability progression in relapsing-remitting MS (RRMS). In this cohort study, clinical data were obtained from the MSBase registry and cognitive data from the MSReactor computerised cognitive battery between February 2016 and September 2022, with a median follow-up of 3.2 years. The serial reaction-time data from three tasks (psychomotor function [R], attention [G], and working memory [B]) were converted into multicolour images using RGB encoding. We extracted the key features from the images using a convolutional neural network and combined them with clinical variables in a Transformer-based survival model (MS-TranSurv) to predict time to confirmed disability progression. Discrimination, calibration, and accuracy were assessed using the C-index, integrated Brier score (iBS), and time-dependent area under the receiver operating characteristic (tAUROC). Performance was compared with other machine learning models, including Dynamic DeepHit, Recurrent Deep Survival Machines, a Cox proportional hazards model in traditional statistics using clinical variables only, and a version of MS-TransSurv using mean test values. A total of 746 RRMS patients were included. MS-TranSurv showed slightly higher discrimination compared with benchmark models, with a C-index of 0.61 (95% CI 0.54-0.68) and tAUROC of 0.74 (95% CI 0.63-0.85), as well as comparable calibration, with an iBS of 0.24 (95% CI 0.16-0.32). Using individual test-level data provided slightly better performance than using summary measures. Longitudinal cognitive reaction-time data can be used for survival-based prediction of disability progression in RRMS. This framework supports remote cognitive monitoring and may improve risk stratification and clinical trial enrichment, with potential applicability to other high-dimensional digital biomarkers.