The Comparison of Fitted Nonlinear Exposure-Response Relationships in Cox Models Using Smoothing Methods Through Simulations

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, July 29, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Usha Govindarajulu*+ and Betty Malloy and Bhaswati Ganguli and Donna Spiegelman and Ellen Eisen
• Companies: Yale University and American University and University of Calcutta and Harvard School of Public Health and Harvard School of Public Health
• Keywords: penalized spline ; restricted cubic spline ; fractional polynomial ; exposure-response ; simulations ; Cox model

Abstract

We fit non-linear exposure-response relationships using smoothing techniques in Cox models. Previously, we compared smoothing techniques on actual occupational cohort data, in which time to incidence or mortality is modeled as a function of exposure. We simulated data in order to further compare these smoothing techniques: penalized spline, restricted cubic spline, and fractional polynomial, to the true exposure-response curve, where we know particular characteristics such as the exposure distribution and dose-response curve. We used several measures to compare the fitted curves to the truth: mean-squared error calculations, test for linearity, test for null effect, and % relative bias calculations and concluded that of the various dose-response shapes, the linear dose-response function was the best fitting. Furthermore, the penalized splines were generally closer to the truth.