The lung dataset in the survival package contains data on survival in lung cancer patients. One of the variables recorded on each patient is the Karnofsky score. The Karnofsky score is a health status score that goes from 0 (dead) to 100 (perfect health) in increments of 10. In this study, there is a score rated by physicians (ph.karno) and a score rated by patients (ph.karno). a) Remove rows that contain missing valued for either ph.karno or pat.karno. Create contingency tables of the Karnofsky scores for both the physician and patient ratings. b) Fit two univariate Cox models with ph.karno and pat.karno. Determine if ph.karno or pat.karno is a better predictor or lung cancer survival. Explain your reasoning. For your chosen predictor, provide a point estimate and confidence interval for the hazard ratio associated with a 10 unit increase in Karnofsky score. c) Fit a multivariate Cox model, with pat.karno, age, and sex. Adjusting for the other covariates, calculate the hazard ratios associated with a 10 unit increase in pat.karno, a 10 year increase in age, and comparing females to males. d) Comparing this model to the univariate Cox model using pat.karno only in part b), does there appear to be confouding of pat.karno by age and sex? e) A fellow researcher questions the proportional hazards assumption for sex. Propose and fit a Cox model that addresses this concern. What is the hazard ratio for a 10-unit increase in pat.karno in this new model? Does this model provide any evidence of confounding of the prognostic value of pat.karno by age and sex?