Simulation-based parameter estimation for complex models: a breast cancer natural history modelling illustration

Simulation-based parameter estimation offers a powerful means of estimating parameters in complex stochastic models. We illustrate the application of these ideas in the setting of a natural history model for breast cancer. Our model assumes that the tumor growth process follows a geometric Brownian motion; parameters are estimated from the SEER registry. Our discussion focuses on the use of simulation for computing the maximum likelihood estimator for this class of models. The analysis shows that simulation provides a straightforward means of computing such estimators for models of substantial complexity.

[1]  J. Steele.  Stochastic Calculus and Financial Applications , 2000 .

[2]  G. Giles,et al.  The histologic phenotypes of breast carcinoma occurring before age 40 years in women with and without BRCA1 or BRCA2 germline mutations , 1998, Cancer.

[3]  J. M. Charnes,et al.  Confidence Regions for Stochastic Approximation Algorithms , 1996 .

[4]  D. Duffie,et al.  Simulated Moments Estimation of Markov Models of Asset Prices , 1990 .

[5]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[6]  F. Arscott,et al.  Applied Bessel Functions , 1966 .

[7]  R. Rubinstein,et al.  Variance reduction by the use of common and antithetic random variables , 1985 .

[8]  Peter W. Glynn,et al.  Likelihood ratio gradient estimation for stochastic systems , 1990, CACM.

[9]  L Edler,et al.  Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis. , 2001, Mathematical biosciences.

[10]  J. Kiefer,et al.  Stochastic Estimation of the Maximum of a Regression Function , 1952 .

[11]  Peter W. Glynn,et al.  Grid-based simulation and the method of conditional least squares , 1996, Winter Simulation Conference.

[12]  P. Chappuis,et al.  Clinico-pathological characteristics of BRCA1- and BRCA2-related breast cancer. , 2000, Seminars in surgical oncology.

[13]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..