Using an onset-anchored Bayesian hierarchical model to improve predictions for amyotrophic lateral sclerosis disease progression

BACKGROUND: Amyotrophic Lateral Sclerosis (ALS), also known as Lou Gehrig’s disease, is a rare disease with extreme between-subject variability, especially with respect to rate of disease progression. This makes modelling a subject’s disease progression, which is measured by the ALS Functional Rating Scale (ALSFRS), very difficult. Consider the problem of predicting a subject’s ALSFRS score at 9 or 12 months after a given time-point. METHODS: We obtained ALS subject data from the Pooled Resource Open-Access ALS Clinical Trials Database, a collection of data from various ALS clinical trials. Due to the typical linearity of the ALSFRS, we consider several Bayesian hierarchical linear models. These include a mixture model (to account for the two potential classes of “fast” and “slow” ALS progressors) as well as an onset-anchored model, in which an additional artificial data-point, using time of disease onset, is utilized to improve predictive performance. RESULTS: The onset-anchored model had a drastically reduced posterior predictive mean-square-error distributions, when compared to the Bayesian hierarchical linear model or the mixture model under a cross-validation approach. No covariates, other than time of disease onset, consistently improved predictive performance in either the Bayesian hierarchical linear model or the onset-anchored model. CONCLUSIONS: Augmenting patient data with an additional artificial data-point, or onset anchor, can drastically improve predictive modelling in ALS by reducing the variability of estimated parameters at the cost of a slight increase in bias. This onset-anchored model is extremely useful if predictions are desired directly after a single baseline measure (such as at the first day of a clinical trial), a feat that would be very difficult without the onset-anchor. This approach could be useful in modelling other diseases that have bounded progression scales (e.g. Parkinson’s disease, Huntington’s disease, or inclusion-body myositis). It is our hope that this model can be used by clinicians and statisticians to improve the efficacy of clinical trials and aid in finding treatments for ALS. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1186/s12874-018-0479-9) contains supplementary material, which is available to authorized users.