The Comparison of Alternative Smoothing Methods for Fitting Non-Linear Exposure-Response Relationships with Cox Models in a Simulation Study

Govindarajulu Usha S, Malloy Elizabeth J, Ganguli Bhaswati, Spiegelman Donna and Eisen Ellen A
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Govindarajulu Usha S: Harvard Medical School
Malloy Elizabeth J: American University
Ganguli Bhaswati: University of Calcutta
Spiegelman Donna: Harvard School of Public Health
Eisen Ellen A: University of California, Berkeley

The International Journal of Biostatistics, 2009, vol. 5, issue 1, 21

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 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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DOI: 10.2202/1557-4679.1104

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