Development of Efficient Computational Methods to Solve Nonlinear Mixed Effects Models
College: Agricultural, Consumer and Environmental Sciences
Award year: 2000-2001
Longitudinal data such as patterns of HIV incidence in patients with AIDS a nd monthly measurements of milk production and body weights in livestock are commonly found in the biological sciences. These traits can be modeled using mathematical functions that depict the major characteristics of the observed patterns (e.g., immunology, yield) and estimates of these functions enhance the understanding of the genetic, biochemical and physiological pathways controlling these events. Parameters estimates allow the prediction of future values, of use in preventive medicine and livestock management for example, and the assessment of the individual's genetic potential to be used in gene therapy (humans) and in selection of parents for the next generation (livestock). From a statistical and computational point of view, these functions describe the trajectory of the trait over time with few parameters and make efficient use of the information contained in the data. Nonlinear mixed effects models account for the between and within individual variations observed in longitudinal data while describing an overall trend across time. The implementation of these models to analyze large longitudinal data sets has high computational demands, and the few algorithms available to simplify the computations were developed for linear models. Currently, the approximate Bayesian method used to estimate parameters relies on direct inversion of large matrices with variable degree of structure, and on iterative methods to solve the large system of equations. The matrices are dense and convergence to the final solutions is time demanding when the model is complex and the data set is large. The objective of this proposal is to develop efficient parallel computational methodologies to implement the iterative and computationally intensive statistical methods suitable for nonlinear mixed effects models.