Interface Contraction in Biostatistics
Area: Nutritional Epidemiology
A specific automatic differentiation technique known as interface contraction is considered in the development of derivative codes for two log-likelihood functions used for biostatistical analysis. These functions were motivated by a problem in nutritional epidemiology investigating the relationships of age and dietary intakes of saturated fat, total energy, and alcohol with the four-year risk of developing breast cancer in a prospective cohort of 89,538 nurses. The likelihood functions take into account measurement error in total energy and binary misclassication in saturated fat and alcohol intake. Newton's method with a line search globalization is employed for the optimization of these nonlinear likelihood functions, and hence the Hessian and gradient are needed at every optimization step. The Hessian is also needed to evaluate the variance-covariance matrix of the resulting maximum likelihood estimates.