2. The Sorbinil Retinopathy Trial was conducted among 497 type I (insulin-dependent) diabetic patients who had little or no evidence of retinopathy at baseline. Retinopa-thies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen at 1 year and then every 9 months up to 48 months after randomization. In addition, all subjects had a final visit at the end of the trial (max=56 months). Sixteen of the patients provided no follow-up. The primary endpoint of the trial was based on change in retinopathy severity level from baseline to maximum follow-up (i.e., severity level at maximum follow-up severity level at baseline). An ordinal grading scale was used to evaluate change: 2+ levels better, 1 level better, no change, 1 level worse, ,5+ levels worse. The outcome data by treatment group are given in Table 1. Table 1. Outcome Data for the Sorbinil Retinopathy Trial (n=481) change in retinopathy level Group Better 2+ Levels 1 No Worse 1 2 3 4 5+ Total Level change Level Levels Levels Levels Levels Placebo 5 17 84 59 37 18 9 14 243 Sorbinil 4 21 97 50 22 16 14 14 238 The primary outcome for the study was worsening by 2 or more levels. a) What test can be used to compare the two treatment groups on the primary endpoint? b) Implement the test in Problem a), and provide a p-value (two-tailed). A more efficient method of analysis would leave the change in retinopathy level in its raw form without grouping the data but would take into account the ordinal nature of the change scores. c) What test can be used to compare the two groups if this more efficient method is used? d) Implement the test in Problem c), and provide a p-value (two-tailed). e) Reanalyze the data in Table 1 using the Wilcoxon rank sum test. f) Compare your results in Problems c) and d). Which do you think is a better method of analysis?