Existing methods to characterise the evolving condition of traumatic brain injury (TBI) patients in the intensive care unit (ICU) do not capture the context necessary for individualising treatment. We aimed to develop a modelling strategy which integrates all data stored in medical records to produce an interpretable disease course for each TBI patient's ICU stay. From a prospective, European cohort (n=1,550, 65 centres, 19 countries) of TBI patients, we extracted all 1,166 variables collected before or during ICU stay as well as 6-month functional outcome on the Glasgow Outcome Scale-Extended (GOSE). We trained recurrent neural network models to map a token-embedded time series representation of all variables (including missing data) to an ordinal GOSE prognosis every 2 hours. With repeated cross-validation, we evaluated calibration and the explanation of ordinal variance in GOSE with Somers' Dxy. Furthermore, we applied TimeSHAP to calculate the contribution of variables and prior timepoints towards transitions in patient trajectories. Our modelling strategy achieved calibration at 8 hours, and the full range of variables explained up to 52% (95% CI: 50-54%) of the variance in ordinal functional outcome. Up to 91% (90-91%) of this explanation was derived from pre-ICU and admission information. Information collected in the ICU increased explanation (by up to 5% [4-6%]), though not enough to counter poorer performance in longer-stay (>5.75 days) patients. Static variables with the highest contributions were physician prognoses and certain demographic and CT features. Among dynamic variables, markers of intracranial hypertension and neurological function contributed the most. Whilst static information currently accounts for the majority of functional outcome explanation, our data-driven analysis highlights investigative avenues to improve dynamic characterisation of longer-stay patients.