2021 : Assessing the Proportional Hazard of Specific Predictor of Cox Model Using Smoothing Martingale Residual
Jerry Dwi Trijoyo Purnomo S.Si, M.Si., Ph.D
Recently years, Cox regression models have received much attention as a suitable method in survival analysis. This method is widely applied in many fields of research including health sciences. A notable assumption of the Cox model is the existence of a linear combination of covariates, including higher-order terms, interaction. Martingale residual is a common method to verify this assumption. The assumption of covariates linearity is said to be fulfilled if there is no curvature on the residual line, and this line falls around zero. In many cases, this assumption is frequently violated. Hence, in this paper, we propose to perform smoothing martingale residuals by adopting locally weighted regression and smoothing scatterplot (LOWESS), another variety of martingale residuals that has a higher flexibility. A data example of patients with cervical cancer disease is discussed. The smoothing martingale residual used in these data here gives a much better display compared to the classic martingale residual.