We used the Veterans Lung Cancer data set to assess its suitability to fit a Cox regression model. To assess the linear relationship between covariates and logarithm of hazard, we can use the martingale residuals. To find influential observations, we use the score residuals. To investigate the appropriateness of the proportional hazards assumptions we use cox.zph(fit) or the residual-time correlations on R. We can also use the Schoenfeld residuals analysis and covariate-time interactions. We also introduced the concept of a time-dependent covariate Cox regression model and the time-dependent hazard model.
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