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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Govindarajulu Usha S & Malloy Elizabeth J & Ganguli Bhaswati & Spiegelman Donna & Eisen Ellen A, 2009. "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, De Gruyter, vol. 5(1), pages 1-21, January.
  • Handle: RePEc:bpj:ijbist:v:5:y:2009:i:1:n:2
    DOI: 10.2202/1557-4679.1104
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    References listed on IDEAS

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    1. David M. Zucker & Donna Spiegelman, 2004. "Inference for the Proportional Hazards Model with Misclassified Discrete-Valued Covariates," Biometrics, The International Biometric Society, vol. 60(2), pages 324-334, June.
    2. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
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    2. Felipe Diaz-Toro & Gabriela Nazar & Claudia Troncoso & Yeny Concha-Cisternas & Ana Maria Leiva-Ordoñez & Maria Adela Martinez-Sanguinetti & Solange Parra-Soto & Nicole Lasserre-Laso & Igor Cigarroa & , 2023. "Frailty Index as a Predictor of Mortality in Middle-Aged and Older People: A Prospective Analysis of Chilean Adults," IJERPH, MDPI, vol. 20(2), pages 1-11, January.
    3. Kyoji Furukawa & Munechika Misumi & John B. Cologne & Harry M. Cullings, 2016. "A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation," Risk Analysis, John Wiley & Sons, vol. 36(6), pages 1211-1223, June.

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