This exercise is a continuation of the exercise on Cox regression for the liver cirrhosis data. The liver cirrhosis data are described as before. There it is also explained how you may read the data into R. We first fit a Cox regression model with all four covariates by the commands: cox.fit-coxph (Surv (time/365.25, atatus) ~fa ctor (treat)+factor (sex) +age+prot,data-liv er) aummary (cox.fit) a) Perform the commands and inspect the results. b) Discuss the assumptions of the model fitted in question a). c) To investigate if there is a log-linear effect of age, we may give the commands cox.spage-coxph (Surv (time/365.25, status) - factor (treat) +factor (sex) +pspline (age) +pr et, data-liver) print (cox.spage) termplot (cox.apaga, se-T, terma-3) Discuss if it is reasonable to assume a log-linear effect of age. d) Investigate if there is a log-linear effect of prothrombin index. The result in d) give some indication (but not very clear!) that the effect of prothrombin index is not log-linear. In the remainder of this exercise, we will work with prothrombin grouped in the three groups: (i) prothrombin index 49 or below, (ii) prothrombin index 50-89, and (iii) prothrombin index 90 or above. We may create a new categorial covariate protgroup by the command: liver protgroup-cut (liver prot, breaks c (0,49,89, 150), labela-1:3) We may fit a Cox model with this variable (together with the other three covariates) by the commands cox.grfit-coxph (Surv (time/365.25, status) - factor (treat) +factor (sex) +age+factor (prot group),data-liver) aummary (cox.gefit) e) Perform the commands and interpret the estimates. f) Check if the assumption of proportional hazards seems to be fulfilled for the model in e). Use the cox. zph command as described in the lectures. g) Use the fitted model from question e) to provide estimated survival functions for the following combination of the covariates: A prednisone treated woman aged 60 years who has prothrombin index 90 or above A prednisone treated woman aged 60 years who has prothrombin index 49 or below A placebo treated man aged 60 years who has prothrombin index 90 or above A placebo treated man aged 60 years who has prothrombin index 49 or below