Comparing Smoothing Techniques for Fitting the Nonlinear Effect of Covariate in Cox Models

BACKGROUND AND 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. MATERIAL AND 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. CONCLUSION 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.