Semi-parametric regression model for survival data: Graphical visualization with R

Abstract

Cox proportional hazards model is a semi-parametric model that leaves its baseline hazard function unspecified. The rationale to use Cox proportional hazards model is that (I) the underlying form of hazard function is stringent and unrealistic, and (II) researchers are only interested in estimation of how the hazard changes with covariate (relative hazard). Cox regression model can be easily fit with coxph() function in survival package. Stratified Cox model may be used for covariate that violates the proportional hazards assumption. The relative importance of covariates in population can be examined with the rankhazard package in R. Hazard ratio curves for continuous covariates can be visualized using smoothHR package. This curve helps to better understand the effects that each continuous covariate has on the outcome. Population attributable fraction is a classic quantity in epidemiology to evaluate the impact of risk factor on the occurrence of event in the population. In survival analysis, the adjusted/unadjusted attributable fraction can be plotted against survival time to obtain attributable fraction function.