Background & Dataset

The dataset liver .RData contains the survival times of patients who have  recently undergone treatment for liver cancer. Follow-up was for a maximum  of 50 months. In addition to standard care, some of the patients were ran-  domly assigned a new treatment - selective internal radiation therapy (SIRT)  for treating inoperable liver tumors and in which radioactive beads are in-  serted into the liver. The dataset contains the survival time of the patients in  months (time) along with a censoring indicator (dead;  0=alive,  1=dead),  age  (years), treat;  0=standard  care  (SC),  1=standard  care  +  SIRT  (SIRT) and stage;  0,  1  &  2  -  2  denotes  a  worse  stage  of  cancer  at treatment  initiation.

Questions

1. Produce a Kaplan-Meier plot showing the patients in the SC group and the SIRT group separately together with a suitable legend.      [5]

2. Perform a Log-Rank Test to assess whether there is a difference in survival between the SC and SIRT treatment groups                      [5]

3. Report the median survival and 95% CI and the Restricted Mean Survival Time (RMST) [restricted to 50 months] and 95% CI for the two groups separately, together with the difference in RMST and a 95% CI.                                                                                          [5]

4. Fit a log-Normal AFT model to the survival data for the two treatment groups, and report the parameter estimates and 95% CIs, including the Acceleration Factor (AF) and 95% CI and write a sentence interpreting the AF results for a clinician.                                                          [5]

5. Produce a plot of the fitted survival curves from Q4 superimposed on the Kaplan-Meier curves for the same patients and comment.         [5]

6. Fit a Cox Proportional Hazards regression model to the survival data for the two treatment groups, and report the Hazard Ratio (HR) and 95% CI for treat and write a sentence interpreting the HR results for a clinician.                                                                                      [5]

7. What other covariates need to be included in the Cox PH model in Q6? Report the HRs for all covariates in your ”final” model together with 95% CIs & P-values and write a sentence interpreting the HR results for a clinician.                                                                      [5]