Comparing Smoothing Techniques for Modeling Exposure-response Curves in Cox Models

• Activity Number: 72
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Donna Spiegelman and Usha S. Govindarajulu*+ and Ellen Eisen
• Companies: Harvard School of Public Health and Harvard School of Public Health and Harvard School of Public Health
• Keywords: penalized spline ; fractional polynomial ; smoothing ; restricted cubic spline ; Cox model ; dose-response

Abstract

To allow for a nonlinear exposure-response relationship, we applied flexible nonparametric techniques (smoothing) to model time to lung cancer mortality in two occupational cohorts. We focused on three smoothing techniques in Cox models: penalized splines, restricted cubic splines, and fractional polynomials. We compared standard software implementations of these methods based on visual representation (curve fitting), criteria for model selection, and degrees of freedom. We propose a quantitative measure of the difference between a pair of curves based on the area between them. The between-curves-area was calculated up to selected quantiles of the exposure distribution and expressed as percentages of the total area difference. The relative performance of the three methods differed across the range of exposure. he three dose-response curves were similar where the exposure data were dense. The methods were less similar over the sparse regions of high exposure. The disparity was more obvious in one of the two examples, where the fractional polynomial differed from the other two splines by providing a more local fit to the extreme values.