title: Comparing Smoothing Techniques for Fitting the Nonlinear Effect of Covariate in Cox Models.
abstract: OBJECTIVE
  Cox model is a popular model in survival analysis, which assumes linearity of the covariate on the log hazard function, While continuous covariates can affect the hazard through more complicated nonlinear functional forms and therefore, Cox models with continuous covariates are prone to misspecification due to not fitting the correct functional form for continuous covariates. In this study, a smooth nonlinear covariate effect would be approximated by different spline functions.
  
  
  METHODS
  We applied three flexible nonparametric smoothing techniques for nonlinear covariate effect in the Cox models: penalized splines, restricted cubic splines and natural splines. Akaike information criterion (AIC) and degrees of freedom were used to smoothing parameter selection in penalized splines model. The ability of nonparametric methods was evaluated to recover the true functional form of linear, quadratic and nonlinear functions, using different simulated sample sizes. Data analysis was carried out using R 2.11.0 software and significant levels were considered 0.05.
  
  
  RESULTS
  Based on AIC, the penalized spline method had consistently lower mean square error compared to others to selection of smoothed parameter. The same result was obtained with real data.
  
  
  CONCLUSIONS
  Penalized spline smoothing method, with AIC to smoothing parameter selection, was more accurate in evaluate of relation between covariate and log hazard function than other methods.
authors.affiliation: Social Determinants of Health Research Center, Kurdistan University of Medical Sciences, Sanandaj, Iran; Department of Epidemiology and Biostatistics, Medical School, Kurdistan University of Medical Sciences, Sanandaj, Iran.
authors.forename: Daem
authors.initials: D
authors.lastname: Roshani
authors.affiliation: Social Determinants of Health Research Center, Kurdistan University of Medical Sciences, Sanandaj, Iran; Department of Epidemiology and Biostatistics, Medical School, Kurdistan University of Medical Sciences, Sanandaj, Iran.
authors.forename: Ebrahim
authors.initials: E
authors.lastname: Ghaderi
keywords: Cox Model; Natural Spline; Penalized Spline; Restricted Cubic Spline; Smoothing