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Article
The Comparison of Alternative Smoothing Methods for Fitting Non-Linear Exposure-Response Relationships with Cox Models in a Simulation Study
The International Journal of Biostatistics (2011)
  • Usha S Govindarajulu, Harvard Medical School
  • Elizabeth J Malloy, American University
  • Bhaswati Ganguli
  • Donna Spiegelman, Harvard School of Public Health
  • Ellen A Eisen, University of California, Berkeley
Abstract

We examined the behavior of alternative smoothing methods for modeling environmental epidemiology data. Model fit can only be examined when the true exposure-response curve is known and so we used simulation studies to examine the performance of penalized splines (P-splines), restricted cubic splines (RCS), natural splines (NS), and fractional polynomials (FP). Survival data were generated under six plausible exposure-response scenarios with a right skewed exposure distribution, typical of environmental exposures. Cox models with each spline or FP were fit to simulated datasets. The best models, e.g. degrees of freedom, were selected using default criteria for each method. The root mean-square error (rMSE) and area difference were computed to assess model fit and bias (difference between the observed and true curves). The test for linearity was a measure of sensitivity and the test of the null was an assessment of statistical power. No one method performed best according to all four measures of performance, however, all methods performed reasonably well. The model fit was best for P-splines for almost all true positive scenarios, although fractional polynomials and RCS were least biased, on average.

Keywords
  • penalized spline,
  • simulation,
  • restricted cubic spline,
  • natural spline,
  • fractional polynomial,
  • Cox model
Publication Date
July 21, 2011
Citation Information
Usha S Govindarajulu, Elizabeth J Malloy, Bhaswati Ganguli, Donna Spiegelman, et al.. "The Comparison of Alternative Smoothing Methods for Fitting Non-Linear Exposure-Response Relationships with Cox Models in a Simulation Study" The International Journal of Biostatistics Vol. 5 Iss. 1 (2011)
Available at: http://works.bepress.com/elizabeth_j_malloy/2/