SDE

SDE models population-count dynamics by deriving stochastic differential equations from the master equation (ME) and related continuous-time stochastic processes to capture both mean and variance for decision modeling and cost-effectiveness analyses.

Key Features:

• Stochastic modeling: Captures both the mean and the variance of population trajectories rather than only mean behavior.
• Continuous approximation via FPE: Derives a continuous approximation to the master equation (ME) by relaxing the integrality constraint using the Fokker Planck Equation (FPE) for real-valued random vectors.
• Direct SDE derivation: Derives stochastic differential equations from first principles to model the time-evolution of population counts as a stochastic process.
• Algorithmic implementation: Provides an algorithm to construct and solve the SDE via simulation using the same model parameters as cohort models.
• Empirical agreement: Matches population trajectories, means, and variances with other commonly used methods.
• Computational efficiency: Demonstrates superior computational speed compared with traditional microsimulation techniques.

Scientific Applications:

• Decision modeling: Quantifies expected outcomes and variability in decision-analytic models by modeling stochastic population dynamics.
• Cost-effectiveness analysis: Provides estimates of cohort means and variances to support cost-effectiveness studies.
• Population dynamics and cohort model validation: Enables comparison and validation of cohort model trajectories against alternative methods, including microsimulation.

Methodology:

The method derives a continuous approximation from the master equation (ME) via the Fokker Planck Equation (FPE) and/or directly derives stochastic differential equations from first principles, and it solves the resulting SDEs using simulation-based methods.