A Quadratic Regression Approach to Maximize the Mean Simulated Likelihood in Microsimulation Models with Few Parameters

• Activity Number: 323
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: WNAR
• Author(s): Roman Gulati*+ and Lurdes Inoue and Ruth Etzioni
• Companies: Fred Hutchinson Cancer Research Center and University of Washington and Fred Hutchinson Cancer Research Center
• Keywords: quadratic regression ; simulated likelihood ; microsimulation model ; calibration

Abstract

Maximum likelihood methods can be very challenging for microsimulation models of complex nonlinear dynamics, such as cancer progression or infectious disease spread. We examine a grid-based method for estimating parameters and quantifying uncertainty when there are few parameters. The method approximates a noisy simulated likelihood surface using a quadratic regression model fit to likelihood evaluations over a discrete grid in the model parameter space and across multiple seeds for the random number generator. Using this approximation, we obtain analytic formulas for parameter estimates and corresponding standard errors. The standard errors reflect the curvature of the mean simulated likelihood and are independent of the Monte Carlo error due to the simulation framework. We apply this approach using a model of prostate cancer incidence and find it yields satisfactory estimates.