S-EBM: Generalising event-based modelling of disease progression for simultaneous events

Estimating the temporal evolution of biomarker abnormalities in disease informs understanding of early disease processes and facilitates subject staging, which may augment the development of early therapeutic interventions and provide personalised treatment tools. Event-based modelling of disease progression (EBM) is a data-driven technique for inferring a sequence of biomarker abnormalities, or events, from cross-sectional or short-term longitudinal datasets and has been applied to a variety of different diseases, including Alzheimer’s disease. Conventional EBM (C-EBM) assumes the sequence of biomarker abnormalities occurs in series, with one biomarker event per disease progression stage. However, events may occur simultaneously, for example due to the presence of shared causal factors, a property which cannot be inferred from C-EBM. Here we introduce simultaneous EBM (S-EBM), a generalisation of C-EBM to enable estimation of simultaneous events. S-EBM can estimate a wider range of sequence types than C-EBM while being fully backward compatible with the original model. Using simulated data, we firstly demonstrate the inability of C-EBM to infer simultaneous events. We next assess the accuracy of S-EBM against ground truth data and subsequently demonstrate a real-world example application to sequence disease progression in Alzheimer’s disease. Simulations show that C-EBM can not discern serial events with high biomarker variance from simultaneous events, preventing its use for inferring simultaneous events. S-EBM has high estimation accuracy against ground truth for a range of sequence types (fully simultaneous, partially simultaneous, serial), number of biomarkers and biomarker variances. When applied to Alzheimer’s disease biomarker data from ADNI, S-EBM estimated a sequence where events within sets of biomarker domains occur simultaneously. Accumulation of total and phosphorylated tau in cerebrospinal fluid; performance on RAVLT, ADAS-Cog and MMSE cognitive test scores; and volumetric decline in temporal regional brain volumes, were better described as groups of simultaneous events rather than a single set of serial events (likelihood ratio ≫ 1,000). Furthermore, C-EBM may be confidently incorrect regarding the serial ordering. S-EBM may be applied to prospective and retrospective biomarker data to refine understanding of disease progression and generate new hypotheses regarding disease aetiology and spread.