A Semiparametric Model Based on Partial Spline for Detecting Changes in Tumor Blood Flow

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sung Won Han*+ and Theresa Busch and Mary Putt
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: change point ; reproducing kernel Hilbert space ; spline ; nonparametric regression

Abstract

In an animal model, the extent and duration of the reduction in blood flow in solid tumors appears to be a key determinant of subsequent tumor response to therapy. Estimating the change-points corresponding to the initial reduction and the subsequent stabilization of flow is challenging because the baseline blood flow is not easily fit to a parametric model. We modeled the data using a smoothing spline for the baseline curvature and a parametric component to add a linear decrease in flow to the baseline between the change-points. While a generalized cross validation (GCV) is commonly used as a criteria for choosing the smoothing parameter in similar "partial spline" models, simulation indicates that the resulting estimates of the blood flow at the change-points have substantial bias and variance. We observed that GCV leads to under-smoothing of the data particularly with larger curvature in the baseline flow. We propose a modification to GCV that depends on the change-size to noise ratio and that corrects for this tendency to under-smooth. Results from both simulation and data collected in recent experiments suggest that this new method yields substantial improvement.