Modeling subject-specific phase-dependent effects and variations in longitudinal responses via a geometric Brownian motion process

The Dynamics of Disease Progression in Cystic Fibrosis

In cystic fibrosis, statistical models have been more successful in predicting mortality than the time course of clinical status. We develop a system of partial differential equations that simultaneously track mortality and patient status, with all model parameters estimated from the extensive and carefully maintained database from the Cystic Fibrosis Foundation. Cystic fibrosis is an autosomal recessive disease that leads to loss of lung function, most commonly assessed using the Forced Expiratory Volume in 1 second (FEV1%). This loss results from inflammation secondary to chronic bacterial infections, particularly Pseudomonas aeruginosa, methicillin-sensitive Staphylococcus aureus (MSSA) and members of the virulent Burkholderia complex. The model tracks FEV1% and carriage of these three bacteria over the course of a patient’s life. Analysis of patient state changes from year to year reveals four feedback loops: a damaging positive feedback loop between P. aeruginosa carriage and lower FEV1%, negative feedback loops between P. aeruginosa and MSSA and between P. aeruginosa and Burkholderia, and a protective positive feedback loop between MSSA carriage and higher FEV1%. The partial differential equations built from this data analysis accurately capture the life-long progression of the disease, quantify the key role of high annual FEV1% variability in reducing survivorship, the relative unimportance of short-term bacterial interactions for long-term survival, and the potential benefits of eradicating the most harmful bacteria.