Use the dataset retinopathy available in the R survival package. See ?retinopathy in R for a description of the dataset. a) Fit a Cox model to estimate the crude hazard ratio comparing the treated eye to the untreated eye. Provide a point estimate and 95% confidence interval. Interpret your results. b) Adjust the variance in the model from part a) for clustering of the two eyes of each individual. Calculate a new 95% confidence interval. c) Now adjust for the risk score (risk) in each eye. Without adjusting for clustering, try models with polynomial or factor terms for risk. Which model fits best? Explain your reasoning. d) Adjust for clustering by individual in the model for part c). Give a new point estimate and 95% confidence interval for the hazard ratio of vision loss comparing treatment to control. e) Using the model from part d), plot the predicted survival for treated and untreated patients with risk = 9. Give meaningful axis labels, differentiate the treated and untreated survival curves, and provide a legend.