The data set retire has information on the life expectancy of individuals living in a senior care facility. We begin by modeling time column which is...

The data set retire has information on the life expectancy of individuals living in a senior care facility. We begin by modeling time column which is the survival time in months spent at the facility. The indicator column death will be used as our status variable. We would like to model the difference between men and women so there is a column gender which is 1 for men and 2 for women. (a) Use a Cox Proportional Hazards model to test whether there is a significant difference between men and women. Report the likelihood ratio statistic and the appropriate P value. (b) Fit another model that adjusts for the confounding variable ageentry which gives the age in months of the subject when they entered the facility. Use the anova function to calculate the appropriate likelihood ratio test. Do you come to the same conclusion as in part (a)? How do you explain any difference? (c) Fit a model with an interaction between age and gender. What do you conclude? (d) Plot complementary log-log plot comparing the effect of gender on the survival time. Do you think the proportional hazards assumption is reasonable for this model? (e) Explain clearly why we chose to use ageentry as our covariate and not age which is the age of the subject when the event occurred.