1) (34 Marks in Total) Radial keratotomy is a type of refractive surgery in which radial incision are made in a myopic (nearsighted) patient's cornea to reduce the person's myopia. Theoretically, the incisions allow the curvature of the cornea to become less steep, thereby reducing the patient's refractive error. [Note: Myopic patients have negative refractive errors. Patients who are farsighted have positive refractive errors. Patients who are neither nearsighted nor farsighted have zero refractive error.] The incisions extend radially from the periphery toward the centre of the cornea. A circular central portion of the cornea, known as the clear zone, remains uncut. The diameter of the clear zone is determined by the baseline refraction of the patient. Patients with a greater degree of myopia may receive longer incision, leaving them with smaller clear zones. The thinking here is that \"more surgery\" 1s needed to correct the worse initial vision of these patients. Radial keratotomy and other vision-correction surgery techniques have been growing in popularity in the 1980s and 1990s, both among public and among ophthalmologists. The Prospective Evaluation of Radial Keratotomy (PERK) study was begun in 1983 to evaluate the effects of radial keratotomy. A researcher examined the variables associated with the five-year post-surgical change in refractive error. She selected 413 patients for the PERK study who met strict entry criteria. In fact, four clear zone sizes were used: 2.5 mm, 3.0 mm, 3.5 mm, and 4.0 mm. The following is the description of variables under study. Variable Description of Variables Gender Gender (Male, Female), Diameter Diameter of the clear zone (2.5 mm, 3.0 mm, 3.5 mm, and 4.0 mm), Age Age of patients (in years), Depth Depth of incision (in mm), CRE Change in refractive error. Consider the following regression model with change in refractive error (CRE) as the response: U{CRE | Age,Gender, Diameter) = S, + p,Age + f,Male + ,D1+ 3,D2 + . D3 + B, (Age x Male) + [, (Age x D1) + [, (Age x D2) + f,(Age x D3) + B,,(Age x Male x D1) + f3,,(Age x Male x D2) + 3,,(Age x Male x D3) This model will be referred to as the 'original\" model. e) (3 marks) Referring to the original model, write the null and alternative hypothesis, in terms of the coefficients, to test whether the effect of age is the same for all diameter of clear zone for females. What is the distribution of the test statistic under the null hypothesis? f) (3 marks) Referring to the original model, in terms of the regression coefficients, what is the effect of gender (male vs. female) on the mean CRE for each diameter of clear zone? Summarize your results in the following chart. Diameter of clear zone Effect of gender (male vs. female) on the mean CRE g) (2 marks) Re-write the original model indicating that gender has no effect on mean CRE