TY - JOUR
T1 - The comparison of alternative smoothing methods for fitting non-linear exposure-response relationships with Cox models in a simulation study
AU - Govindarajulu, Usha S.
AU - Malloy, Elizabeth J.
AU - Ganguli, Bhaswati
AU - Spiegelman, Donna
AU - Eisen, Ellen A.
N1 - Funding Information:
KEYWORDS: penalized spline, simulation, restricted cubic spline, natural spline, fractional polynomial, Cox model Author Notes: Funding for this research was provided through this grant: National Cancer Institute R01 CA081345-08.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Cox model
KW - Fractional polynomial
KW - Natural spline
KW - Penalized spline
KW - Restricted cubic spline
KW - Simulation
UR - http://www.scopus.com/inward/record.url?scp=62549164728&partnerID=8YFLogxK
U2 - 10.2202/1557-4679.1104
DO - 10.2202/1557-4679.1104
M3 - Article
C2 - 20231865
AN - SCOPUS:62549164728
SN - 1557-4679
VL - 5
JO - International Journal of Biostatistics
JF - International Journal of Biostatistics
IS - 1
M1 - 2
ER -