Modeling outcome trajectories in patients with acquired brain injury using a non-linear dynamic evolution approach

Simona Panunzi, Lucia Francesca Lucca, Antonio De Tanti, Francesca Cava, Annamaria Romoli, Rita Formisano, Federico Scarponi, Anna Estraneo, Diana Frattini, Paolo Tonin, Ilaria Piergentilli, Giovanni Pioggia, Andrea De Gaetano, Antonio Cerasa, Simona Panunzi, Lucia Francesca Lucca, Antonio De Tanti, Francesca Cava, Annamaria Romoli, Rita Formisano, Federico Scarponi, Anna Estraneo, Diana Frattini, Paolo Tonin, Ilaria Piergentilli, Giovanni Pioggia, Andrea De Gaetano, Antonio Cerasa

Abstract

This study describes a dynamic non-linear mathematical approach for modeling the course of disease in acquired brain injury (ABI) patients. Data from a multicentric study were used to evaluate the reliability of the Michaelis-Menten (MM) model applied to well-known clinical variables that assess the outcome of ABI patients. The sample consisted of 156 ABI patients admitted to eight neurorehabilitation subacute units and evaluated at baseline (T0), 4 months after the event (T1) and at discharge (T2). The MM model was used to characterize the trend of the first Principal Component Analysis (PCA) dimension (represented by the variables: feeding modality, RLAS, ERBI-A, Tracheostomy, CRS-r and ERBI-B) in order to predict the most plausible outcome, in terms of positive or negative Glasgow outcome score (GOS) at discharge. Exploring the evolution of the PCA dimension 1 over time, after day 86 the MM model better differentiated between the time course for individuals with a positive and negative GOS (accuracy: 85%; sensitivity: 90.6%; specificity: 62.5%). The non-linear dynamic mathematical model can be used to provide more comprehensive trajectories of the clinical evolution of ABI patients during the rehabilitation period. Our model can be used to address patients for interventions designed for a specific outcome trajectory.

Conflict of interest statement

The authors declare no competing interests.

© 2023. The Author(s).

Figures

Figure 1
Figure 1
Panel (A) Contributions, in percentage terms, of each predictor to the first dimension from the principal component analysis. Panel (B) Plot of the loading vectors (coefficients of the variables on the principal components) for quantitative predictors. Panel (C) Plot of the coefficients of the variables on the principal components for qualitative predictors.
Figure 2
Figure 2
Patients’ scores on the two PCA dimensions at baseline (T0), panel (A); 4 months after the event (T1), panel (B); at discharge (T2), panel (C), for individuals with Positive (blue dots) and Negative (red dots) outcomes.
Figure 3
Figure 3
Time course of PCA Dimension 1 for individuals with Positive GOS (panel A) and for individuals with Negative GOS (panel B) in the Training sample. Dots represent the individual scores (blue dots for Positive GOS group and red dots for Negative GOS group) whereas thick continuous lines are the predictions from the Michaelis Menten model. Panel (C) shows the observed scores and the model fitting along with the corresponding 95% confidence intervals (dashed lines) based on a Monte Carlo approach along with the three thresholds: Threshold 1 (fine red continuous line), Threshold 2 (fine blue continuous line), Threshold 3 (blue two-dashed continuous line).
Figure 4
Figure 4
Time course of PCA Dimension 1 for individuals with Positive GOS and for individuals with Negative GOS in the Validation sample. Dots represent the individual scores (blue dots for Positive GOS group and red dots for Negative GOS group) whereas continuous lines are the predictions from the Michaelis Menten model fitted on the Training sample along with the three thresholds: Threshold 1 (fine red continuous line), Threshold 2 (fine blue continuous line), Threshold 3 (blue two-dashed continuous line).

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