W. C. Thompson, Y. Zhou, S. Talukdar, C. Musante; Pfizer, Cambridge, MA
BACKGROUND: Systems pharmacology models are often characterized by a high-dimensional parameter space and insufficient data to uniquely constrain the parameters. One solution to this problem, common in the engineering literature, is to use local sensitivity functions to determine a subset of parameters that are most sensitive to the available data. For instance, in the context of least squares regression, this can be accomplished by considering the singular value decomposition (SVD) of the covariance matrix of the least squares estimator.
METHODS: First, the relationship between sensitivity functions and nonlinear regression is reviewed. It is shown that, under certain conditions, the sensitivity functions can be used to compute an asymptotic estimate of the Fisher Information Matrix (and thus the estimator covariance matrix). Key assumptions and limitations of the theory are reviewed. The resulting theory is then demonstrated by application to a novel model of food intake and body weight regulation in non-human primates following treatment with CVX-PF05231023, an FGF21 mimetic.
RESULTS: In the context of least squares regression, subset selection based upon SVD of the asymptotic approximation of the estimator covariance can be accomplished with trivial additional computational cost. In a local region of the parameter space, the method provides a simple indication of which parameters can be most reliably estimated.
CONCLUSION: Parameter subset selection based upon SVD of the Fisher matrix has strong theoretical underpinnings, intuitive interpretation, and is easy to implement, as demonstrated by successful analysis of a model of obesity pharmacotherapy in non-human primates. The primary limitations of the method are its local nature and a risk of numerical instability.