Abstract:
|
Symptomatic and disease modifying (DM) treatments work very differently but are often analyzed with similar models. Quantitative measurements (y-axis) of progression in degenerative diseases often follow a reverse S-curve over time (x-axis) starting high with slow progression, then nearly linear downward progression in the middle, with slow progression toward the later stages of disease. Non-linearity may be due to ceiling and floor effects, or changes in disease. Symptomatic effects are "vertical", meaning that they shift the curve upward while on treatment, but DM effects are “horizontal”, acting on the underlying disease process in a way that slows down time, or stretches out the curve over time. With linear progression, these effects are equivalent: 40% slowing = a 40% reduction in progression, but these effects differ with nonlinearity. We demonstrate that quantitative outcomes for DM treatments are better fit with our proposed “delayed progression model” than with a proportional disease progression model. Similarly, event-based outcomes for DM treatments are better fit with a delayed failure time model than with a proportional hazards model.
|