Development and validation of a 1-year survival prognosis estimation model for Amyotrophic Lateral Sclerosis using manifold learning algorithm UMAP

Abstract

Amyotrophic Lateral Sclerosis (ALS) is an inexorably progressive neurodegenerative condition with no effective disease modifying therapies. The development and validation of reliable prognostic models is a recognised research priority. We present a prognostic model for survival in ALS where result uncertainty is taken into account. Patient data were reduced and projected onto a 2D space using Uniform Manifold Approximation and Projection (UMAP), a novel non-linear dimension reduction technique. Information from 5,220 patients was included as development data originating from past clinical trials, and real-world population data as validation data. Predictors included age, gender, region of onset, symptom duration, weight at baseline, functional impairment, and estimated rate of functional loss. UMAP projection of patients shows an informative 2D data distribution. As limited data availability precluded complex model designs, the projection was divided into three zones with relevant survival rates. These rates were defined using confidence bounds: high, intermediate, and low 1-year survival rates at respectively [Formula: see text] ([Formula: see text]), [Formula: see text] ([Formula: see text]) and [Formula: see text] ([Formula: see text]). Predicted 1-year survival was estimated using zone membership. This approach requires a limited set of features, is easily updated, improves with additional patient data, and accounts for results uncertainty.

Figure 1

Predictors: onset (b), sex (c); age (d); symptom duration in month (e); baseline weight in kg (f), baseline ALSFRS score (g); and estimated ALSFRS loss rate (h) distribution with regards to UMAP projection (a). Each point represents an individual patient. Age ranges between 18 and 81 years old (d), symptom duration ranges between 0.5 and 87 months (e), baseline weight ranges between 30 and 130 kg (f), ALSFRS score ranges between 0 and 40 (g) and estimated baseline ALSFRS slope ranges between 0.00 and − 1.50 ALSFRS points per month (h). Axes are dimensionless and come from UMAP dimension reduction.

Figure 2

Outcomes: overall survival (a); 1-year survival (b) and 1-year functional loss (c) distribution with regards to UMAP projection in Fig. 1a. Each point represents an individual patient. For overall survival (a), survival ranges between 0 and 12 months. 13+ refers to patients whose death date is 13 months or higher. ALSFRS score ranges between 0 and 40 (c). For overall survival (a) and 1-year functional loss, the data point colour is mapped to a specific time value (for a) or ALSFRS score (for c). Axes are dimensionless and come from UMAP dimension reduction.

Figure 3

One-year survival projection space segmentation: initial 1-year survival distribution (a), projection space division using square cells and survival probability estimation per cell (b), resulting projection space division using cell survival probability distribution (c), novel patient data projection (d). Each point represents an individual patient. The projection space is divided in a square grid (b) with each cell having a specific survival rate computed based on patients belonging to that cell (which have either survived or deceased within the year). The overall space is divided in three zones (c); the survival rate for each zone is calculated using patients belonging to each zone. Novel patient data is projected into the reduced space and prognosis is estimated based on projection coordinates (d). Axes are dimensionless and come from UMAP dimension reduction.

Figure 4

Outcomes with regards to UMAP projection for development and validation data: overall survival for development (a.1) and validation (a.2) data, 1-year survival for development (b.1) and validation data (b.2) and 1-year functional loss for development (c.1) and validation data (c.2) (for overall survival, 13+ refers to patients whose death date is 13 months or more). Each point represents an individual patient. For overall survival (a), survival ranges between 0 and 12 months. 13+ refers to patients whose death date is 13 months or higher. ALSFRS score ranges between 0 and 40 (c). For overall survival (a) and 1-year functional loss, the data point colour is mapped to a specific time value (for a) or ALSFRS score (for c). Axes are dimensionless and come from UMAP dimension reduction. (a.1), (b.1) and (c.1) represent development data plots; (a.2), (b.2) and (c.2) represent validation data plots.